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University Physics 1Lab Manual

version 1

The labs in this manual accompany Calculus-based University Physics 1, a first-semester Physics course offered at the Physical Sciences department of Madison Area Technical College.

All labs in this manual are freely available as pdf documents to students – see the course Blackboard page. Others may inquire at the Madison College Physical Sciences department.

Contents:

General Lab Instructions

Lab 1: MeasurementsLab 2: VectorsLab 3: One Dimensional MotionLab 4: Two Dimensional MotionLab 5: DynamicsLab 6: Circular MotionLab 7: Work and EnergyLab 8: Momentum and CollisionsLab 9: Rotational DynamicsLab 10: Statics

(no lab week 11)Lab 12: Fluid MechanicsLab 13: OscillationsLab 14: WavesLab 15: Sound

Equation Sheet

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University Physics 1General Lab Instructions

Most weeks we will have a three-hour lab period that will include a brief discussion by the instructor, time to work through the lab, and a short chapter quiz. Any remaining time may be used to work on homework or other study.

Each lab in this manual has two sections: instructions and report. As you work, you should• Read and follow the steps in the instructions

• Perform calculations in a lab notebook (or other scratch paper)

• Record only the results requested in the report (and answer the questions there)

Please carefully read and follow every step in the instructions. Students will work together in pairs or groups of three, but each student must submit an individual completed report.

Recorded measurements always include uncertainty (see Lab 1). Expected results should not be too far off from your measured results – if you observe and error greater than about 20%, check with the instructor to identify the source of the error.

If time is running out before you have completed the lab, don't attempt to rush toward the end.Check with the instructor for how to finish satisfactorily.

Lab reports are due within one week of the lab period in which it is performed, though you will often be able to submit your report on lab day.

Feel free to (safely) explore the properties of the lab equipment beyond the required instructions. Learn some science and have fun...!

University Physics 1Lab 1: Measurements

Objectives:

• Record measurement uncertainty and determine the uncertainty in calculations.• Develop an understanding of the connection between data and results through the use

of simple error analysis techniques.• Practice unit conversions within the metric system.• Get an introduction to using the IPython Notebook.

Theory:

Measurements are at the heart of all science. In your daily life, measurements are often taken quickly and casually. In scientific experiments we must measure and record the values carefully.

We will distinguish between the following:

raw data: the number you observed on the measuring instrument in the units that instrument provides.

derived data: values computed using the raw data such as changes of units or calculations required to compute the final results

results: derived data that are prepared for presentation

When a measurement is taken properly we do the following:• note the units used by the instrument• carefully take the measurement, interpolating to estimate of the last digit of

precision• estimate the absolute uncertainty in the measurement• record the raw data: the measured value, the uncertainty, and the units • double-check the measurement, uncertainty and units

Lab 1: Measurement page 1 of 6

To express the uncertainties we will use both of the following:

Absolute uncertainty: x ± y units

Relative uncertainty: x units ± z %

where z is given by

also known as “percent uncertainty”

Example: Suppose you used aruler to measure the objectshown. This length might berecorded as 7.45 ± 0.02 cm. Thelast digit (5) has been estimatedfrom the ruler, and the uncertaintyexpresses the minimum range of values that I'm sure the measurement falls in. The percent uncertainty would be 7.45 cm ± 0.27% (note the units are now written on the first value since the percent uncertainty is dimensionless).

Every measurement should be made as accurately as possible, and should be recorded along with the measurement uncertainty. When two values (with known uncertainties) areadded or subtracted, the result will have an absolute uncertainty equal to the sum of the absolute uncertainties of all the parts. When two values (with known uncertainties) are multiplied or divided, the result will have a relative uncertainty equal to the sum of the relative uncertainties of all the parts. When a value with known uncertainty is multiplied by a precise scalar (such as finding the radius from the diameter: r=½d), the scalar also multiplies the absolute uncertainty (the relative uncertainty remains unchanged).

The digits that are actually measured (including the one digit that is estimated) are called the significant figures. The concepts of significant figures and how they behave when multiplied or added are covered in your text (section 1.6), which you should review for a detailed discussion. When written in scientific notation, all digits are considered significant.


The following symbols and equations are used in this lab:

A = aread = diameterh = heightℓ = lengthm = massr = radiusV = volumew = width

A = ℓ w for a rectangleV = ℓ wh for a rectangular boxA = πr2 for a circleV = πr2 h for a cylinderV = 4πr3 / 3 for a spherer = d / 21 cm3 = 1 mL

The percent difference between two values a and b is given by ∣a−b∣½ (a+b)

⋅100% .

Equipment:

Welch measurement set, micrometer, graduated cylinder, top loading mass balance (on back counters)

Procedure:

Part 1: Raw Data

Measure the following dimensions and record the raw data in the lab report.

1. dimensions (length, width and height) of the aluminum block2. diameter of the metal sphere3a. diameter and height of the exterior of the metal cylinder (the one with the cavity)3b. diameter and height of the interior cavity of the same metal cylinder4. thickness of a sheet of paper using the micrometer5. mass of aluminum block6. volume of large metal cylinder measured by fluid displacement

These numbers are raw data. If the instrument is graduated in cm, the raw data must be recorded in cm. Include an estimate of the absolute uncertainty in every measurement. Also compute the relative uncertainty when it is requested in the report.


Part 2: Derived Data

Compute the following data and record your answers in the lab report. All results should be expressed with its relative uncertainty. Only final results should be written in the lab report – use a lab notebook for your intermediate calculations.

1. Volume of the aluminum block in m3.2. Volume of the metal sphere in m3.3. Volume of the metal cylinder computed from the diameter and height measurements

(i.e., outside volume – inside volume), recorded in m3. You may neglect the volume of the beveled edge.

4. Compute the thickness of a stack of 100 sheets this paper, in cm.5. Density (mass/volume) of the aluminum block in kg/m3.6. Percent difference between the two volume measurements of the metal cylinder (from

Part 1 step 6 and from Part 2 step 3). You do not need to calculate the uncertainty in the percent difference.

For any values above 103 or smaller than 10–3, report the result using scientific notation.

Part 3: Using the IPython Notebook

Using computers to solve physical problems is a necessity for all but the most simple systems. This semester we will use a powerful computational environment called the Jupyter Notebook (also known as the IPython Notebook).

In this part you are asked to get Jupyter up and running, the system that will run our Python code. You will download the notebook for Lab 1, and edit it to answer the questionsthat appear there. You will print the completed notebook and attach it to your lab report when you turn it in.

1. Start Jupyter. Obtain a computer and visit our course web site. Find the “Computation” links. At the bottom of the page find a link to “getting IPy started” and follow these instructions.

2. Download the lab_01.ipynb (on the Computation web page) file and save it where you will do your computational work.

3. Complete the work in the lab_01.ipynb file. You may submit this work by either printing out the complete notebook or submitting it electronically on Blackboard.


Appendix: Using the Instruments

Vernier Scale: Extra precision is often obtainedwith a Vernier scale.

The figure shows the vernier calipersmeasuring the diameter of a sphere. To readthe measurement, note where the left-mostmark of the Vernier scale (called the “index”)aligns with the main scale. The figure showsthis be at something between 2.1cm and2.2cm (closer to 2.2). The next decimal ofprecision is found by identifying which tickmark of the vernier scale lines up exactly witha mark on the main scale. This can be seen better in the figure at the right. The index markshows the measurement to be 2.1_ cm, where the extra “_” digitis found on the Vernier scale as follows: find which tick mark of theVernier scale lines up with the main scale. In this case it is the 8th tick mark of the Vernier scale. Thus the measurement is 2.18 cm.

Uncertainty is estimated by inspection. We can be sure that the measurement above is between 2.17 and 2.19 cm, so it could be recorded as 2.18 ± 0.01 cm.

Graduated Cylinder: This device is calibrated such that the volume is read from the center of the fluid meniscus.


Micrometer: The figures show a micrometer measuring in mm. The micrometer is opened and then closed firmly onto the piece to be measured. The get the correct firmness of the tool, use the friction knob at the end.

As the thimble is opened,the scale on the referenceline is exposed and themeasurement can be readfrom it. The graduations onthe thimble give the extraprecision in the value, asshown in the figures.

The measurement in this figure should be recorded as 8.115 ± 0.005 mm.


University Physics 1Lab 1: Measurements

ReportName:______________________

partner name:______________________

Part 1: Raw Data

1. aluminum block

raw data (include units and estimated absolute uncertainty):

l = ______________________________________

w = ______________________________________

h = ______________________________________

measurements with relative uncertainty:

l = ______________________________________

w = ______________________________________

h = ______________________________________

2. metal sphere

raw data with either caliper or micrometer (include units and estimated absolute uncertainty):

d = ______________________________________

measurement with relative uncertainty:

d = ______________________________________


3a. metal cylinder (exterior)

raw data with calipers (include units and estimated absolute uncertainty):

d = __________________ h = __________________


d = __________________ h = __________________

3b. metal cylinder (cavity)

raw data with calipers (include units and estimated absolute uncertainty):

d = __________________ h = __________________


d = __________________ h = __________________

4. thickness of this sheet of paper measured with the micrometer (include units and estimated absolute uncertainty):

t = ______________________________________

5. mass of block from digital mass balance (include units and estimated absolute uncertainty):

m = ______________________________________

measurement with relative uncertainty:

m = ______________________________________

6. metal cylinder volume by fluid displacement (include units and estimated absolute uncertainty):

V1 (water only) = ______________________________________

V2 (water and metal) = ______________________________________


Part 2: Derived Data

1. aluminum block

volume (with relative uncertainty): V = _____________________________________

volume (with absolute uncertainty): V = _____________________________________

2. metal sphere



3. cylinder



4. thickness of 100 sheets of paper

thickness (with relative uncertainty): t = _____________________________________

thickness (with absolute uncertainty): t = _____________________________________

5. density (ρ)

density (with relative uncertainty): ρ = _____________________________________

density (with absolute uncertainty): ρ = _____________________________________

6. percent difference

_____________________________________


Part 3: Using the IPython Notebook

You may either print your completed IPython Notebook and attach it here, or submit the notebook (the ipynb file) electronically on Blackboard.


University Physics 1Lab 2: Vectors

Objectives:

• balance force vectors• analytically and graphically add vectors• manipulate vectors computationally

Theory:

If multiple force vectors balance, it means the vectors add to zero. We will observe this effect as forces are applied to a metal ring by hanging masses from attached strings.Since the strings are very light compared to the weights, we will not consider the weight ofthe string itself. In this lab we will use the convention to measure all angles counter-clockwise from the positive x-axis, labeled 0°. The magnitude of the vector is the amount of weight, and the direction of the vector is its angle. To avoid unnecessary computation, we will use grams (a unit of mass) as a proxy for units of force (kg m/s2).

Equipment:

Kennon force table and accessories, slotted masses, weight hangers, protractors and rulers, computers

Procedure:

Part 1: Force Vectors

You will assemble the following three cases and adjustthe free parameters so that all forces balance. Whenthis happens, the force vectors will add to zero. On thetable, you should see the center ring is not leaningagainst the center pin (you may remove the pin to seethis). For each case below, balance the forces and thenanswer the questions that follow in the lab report.

Lab 2: Vectors page 1 of 4

CASE 1:

Two perpendicular forces, F1 and F2 ,balanced by force F3, which is equal inmagnitude but opposite in direction to the sum of F1 and F2 .

CASE 2: CASE 3:

For each case, set up the apparatus accordingly. Observe the additional requirements specified in the following paragraphs. Units of grams (g) will be used for the force magnitudes. Set up each case and fill in the empty data cells in the table in the lab report.


Two forces, F1 and F2 , balanced by force F3, which is equal in magnitude but opposite in direction to the sum of F1 and F2 .

Four forces with different magnitudes and directions, all balance out. The vectors you choose must not make a symmetric pattern.

For Case 1, use the magnitudes of |F1|=400g and |F2|=300g. F1 should be at 0°, and F2 should be at 90°, as shown in the figure. Adjust the magnitude and angle of F3 to balance all three forces.

For Case 2, use the magnitudes of |F1|=250g and |F2|=300g. F1 should be at 0°, and F2 should be at 107°, as shown in the figure. Adjust the magnitude and angle of F3 to balance all three forces.

For Case 3, set the forces however you like, but choose different magnitudes and directions for each. They do not have to look like the figure. Also, choose masses over 100g (small forces don't balance as well).

Complete the data tables and questions on the lab report.

Part 2: Vectors in IPython

Download and complete the notebook titled lab_02.ipynb.You may submit the completed notebook by printing it and attaching it to the lab report, orby submitting it electronically on Blackboard.



University Physics 1Lab 2: Vectors

Report

Name:______________________

partner name:______________________

Part 1: Force Vectors

Data:

F1 F2 F3 F4

Case 1magnitude (g) 400 300

direction (°) 0° 90°

Case 2magnitude (g) 250 300

direction (°) 0° 107°

Case 3magnitude (g)

direction (°)

Questions:

1. For Case 1, Find the components of force .

F3 x = ________________________

F3 y = ________________________

Compare these components to the other two vectors, and . How do they compare?


2. For Case 2:

a. Add force vectors F1 and F2; call this sum F12. To do this, compute the components of F1 and F2 and then add their components and determine the resultant. Then compute the magnitude and direction of the resultant (using the Pythagorean Theorem and an inverse trig function). You may use the last page for extra room to work.

magnitude of F12 : ____________ g

direction of F12 : _____________ º

b. The three vectors must add to zero total force: F1 + F2 + F3 = 0, or F12 + F3 = 0. Considering your answers to part a (the direction and magnitude of F12), what must be themagnitude and direction of force F3 ?

magnitude: ____________

direction: _____________

c. How do your results from question 2b compare to the data you recorded in the table on the previous page?


3. For Case 3, use the graphical (“head-to-tail”) method to add all four vectors. First choose a scaling factor to scale your grams of force to centimeters of arrow length on paper.

Record your scale factor here: ___________________________________________

In the space below, add the four vectors. You will need a protractor to get the angles correct, and a ruler to get their magnitudes correct.


Part 2: Vectors in IPython

You may submit the completed notebook (lab_02.ipynb) by printing it and attaching it to the lab report, or by submitting it electronically on Blackboard.


University Physics 1Lab 3: One Dimensional Motion

Objectives:

• to explore how various motions are represented in graphs• integrate a time-dependent velocity to find position• fitting a function to position data to find free-fall acceleration

Theory:

In this lab, you will observe the motion of objects in one dimension. The two cases you will investigate are that of a cart moving along a track and a mass in free-fall. You may start with either Part 1 or Part 2.

Notes on using the Motion Detector:▪ The motion detector will measure the cart's position. "Position" means the distance

from the motion detector. The face of the motion detector is a position of . 1 m in front of the motion detector is a position of , 2 m in front of the motion detector is a position of , and so on.

▪ The motion detector detects the closest object directly in front of it. This means it will record your hands, clothes or other objects that get between the sensor and the cart.

▪ Always keep the cart at least 10 cm away from detector. The detector gets confused when the distance is too small.

Notes on using Logger Pro:▪ To nicely scale a graph, select the graph you want to affect (click it), and click the the

auto-scale button (labeled “A”).▪ To scale a graph manually, double-click the graph. In the window that appears, click

the “axes options”. Enter the y-axis “top” and “bottom” values there.▪ To remove data from the graphs, select the data and in the “Edit” menu select “Strike

Through Data Cells”. You may select the data to remove with a click-and-drag on a graph or in the data table.

Equipment:

Free-fall apparatus with spark timer, computer running Logger Pro, Vernier interface and motion detector, track, Low friction cart, Fan

Lab 3: One Dimensional Motion page 1 of 4

Procedure:

Part 1: Motion Graphs of Cart

Part 1a: Speeding up, moving away

1. After discussion with your lab partner, predict the position, velocity, and acceleration graphs that you would see if you release the cart from rest at a distance of 10 cm from the detector and allow it to speed up (with the fan) as it moves away from the detector. Sketch the predicted graphs in the lab report using dotted lines. Make an educated guess about the values you should expect for position (distance from detector in meters), velocity (m/s) and acceleration (m/s2). Write these values on the vertical axes of each of the prediction graphs.

2. Set up the track with the motion detector at the end of the track. Make sure the track is level (you may need to added folded paper under one end). Remove any extra weight on the fan (if there are aluminum plugs attached to top). Turn on the fan and hold the cart with your hand, getting ready to start data collection at the computer. Release the cart from rest and start data collection at nearly the same time, and be ready to stop the data collection before the cart runs off the end of the track. Take a few trial runs to get a good graph. You want a graph that only includes free cart motion – no hands or crashing (see the Logger Pro notes on the first page for how to remove data).

3. Sketch your position and velocity graphs neatly on the same axes in the lab report where you made your prediction, but use a solid (not dotted) line.

4. Answer the questions in the lab report.

Part 1b: Speeding up, moving toward the detector

1. After discussion with your lab partner, predict the position, velocity, and acceleration graphs that you would see if you release the cart from rest at the far end of the track and allow it to speed up moving toward the detector. Sketch the predicted graphs (with axis values) in the lab report with a dotted line. Consider the sign (+ or –) of the valuesyou expect.

2. Perform this experiment. Again, take a few trials until you obtain a graph that includes only free cart motion (under influence of the fan alone). Sketch your position and velocity graphs neatly on the same axes in the lab report where you made your predictions. Your graphs should only include free cart motion (see the Logger Pro notes on the first page for how to remove data).



Part 1c: Reversing direction

In this part, you will look at what happens when the cart slows down, reverses direction, and then speeds up in the opposite direction. The fan should push the cart inthe direction of the detector, while it is released moving away. The fan will slow the cart down, turn it around, and then move it back toward the detector while speeding up.

1. After discussion with your lab partner, predict the position, velocity, and acceleration graphs that you would see in this case. For each part of the motion – away from the detector, at the turning point, and toward the detector – indicate in the table (in the lab report) whether the values of position, velocity and acceleration are positive, zero or negative. Sketch the predicted graphs (with axis values) in the lab report using a dottedline. Consider the sign (+ or –) of the values you expect.

2. Perform this experiment. Again, take a few trials until you obtain a graph that includes only free cart motion (under influence of the fan alone). Sketch your position and velocity graphs neatly on the same axes in the lab report where you made your prediction, but use a solid line.


Part 2: Integrating the Velocity Graph

1. For this section you need a graph of the motion from the Part 1c, above. You might want to re-run it so that a clean graph of motion out and back is visible. Arrange the graphs so that you can see the position and velocity graphs only (and the data table). Make sure your graphs only include free cart motion (see the Logger Pro notes on the first page for how to remove data).

2. Select the velocity graph, then select the integral tool in the “Analyze” menu. You may adjust the left and right boundaries of the integral by dragging the brackets on the graph. Keep the left boundary at the initial time and put the right boundary at a time near the cart’s turn-around moment. The value of the integral is shown in the small boxon the graph. You will need to know the time at the right boundary of the integral.

3. In the “data” menu select “New Manual Column”. Give it a name such as “int v”; units will be meters. In the data table, find the time at which the integral is calculated (the right boundary of the integral) by scrolling up and down. At this time in the table enter the value of the integral in the “int v” column. Choose ten other times in the graph, some before and some after the turn-around time, and record the integral values in the new column. (Making the data table a bit wider will make this process easier.)


4. On the position graph, display both the position and the “int v” data. You may do this byclicking the vertical label on the graph and selecting “more” from the menu, then checking the boxes for the data you want displayed. Sketch the position graph and the “int v” graph in the lab report. How do the two graphs compare? (Hint: they should not be the same.)

5. Next we want to create a new data column that equals the integral of the velocity (“int v”) plus the initial position, . You will need find the value of from the data table – it’s the position at the first time entry. In the “data” menu select “New Calculated Column”. Give it a name such as “int v +x0”; units will be meters. In the large box you will write a formula to calculate data for this new column – it will be your value of plus the variable data from the “int v” column (choose this column from the “Variable” drop-down menu). Describe how the graph of position agrees with the “int v +x0” data. (If they are not very close to equal, check with the instructor.) Using the appropriate kinematic equation, explain why these graphs should agree.

Part 3: Free-fall Acceleration



University Physics 1Lab 3: One Dimensional Motion

ReportName:______________________

partner name(s):______________________

Part 1: Motion Graphs of Cart

Part 1a: Speeding up, moving away

Predictions for the position-time graph, thevelocity-time graph, and the acceleration-time graphs. (Use dotted lines.)

Observed graphs for the position, velocity,and the acceleration. (Use solid lines.)

How can you tell from the velocity graph that the cart is moving away from the motion detector?

How can you tell from the velocity graph that the cart is speeding up?

How does the acceleration change in time as the cart speeds up? Is this what you expect based on the velocity graph? Explain.


Part 1b: Speeding up, moving toward the detector

Predictions for the position-time graph, thevelocity-time graph, and the acceleration-time graphs. (Use dotted lines.)

Observed graphs for the position, velocity,and the acceleration. (Use solid lines.)

How can you tell from the velocity graph that the cart is speeding up?

Does speeding up always mean positive acceleration? Explain why or why not.


Part 1c: Reversing direction

Indicate your prediction for whether each quantity will be positive, negative or zero:

Moving Away Turning point Moving TowardPosition

Velocity

Acceleration

Predictions for the position-time graph, thevelocity-time graph, and the acceleration-time graphs.

Observed graphs for the position, velocity,and the acceleration.

Re-visit your positive/negative/zero predictions above and make any necessarycorrections.

Explain how the acceleration can be non-zero even while the cart's velocity is zero (at the moment of turn-around).


Part 2: Integrating the Velocity Graph

4. How do the two graphs compare?(see question in lab instructions)

5. How do the two graphs compare? Explain.(see question in lab instructions)

Part 3: Free-fall Acceleration

You may submit the completed notebook by printing it and attaching it to the lab report, orby submitting it electronically on Blackboard.


0time (s)

posi

tion

(m

)

University Physics 1Lab 4: Two Dimensional Motion

Objectives:

• observe and measure two-dimensional acceleration on an inclined table• fit a parabola to the data to find the acceleration vector• solve the projectile “monkey hunter” problem

Theory:

Vectors are required to solve kinematics problems in two and three dimensions, such as the motion of a projectile. In this lab, you will use the kinematic equations to describe an object's x-motion and y-motion, and obtain its acceleration vector.

For constant acceleration, these equations are:

Equipment:

Air table with steel pucks, air compressor, ruler, computer (with Logger Pro), “monkey hunter” demo

Procedure:

Part 1: Acceleration in a Plane

We will use a camera to observe the path of a friction-free puck sliding on a slight incline.

1. Set up a table so that one corner is slightly higher than the others (the feet screw in and out to change elevation). The puck should slowly accelerate toward the opposite corner when released from rest. Get a large sheet of paper an tape it to the sloping table. Draw a dark line of precise length (about 0.5 m) to calibrate distance on the video. Use the digital angle measuring tool to measure the angle of the slope (make sure to rotate the device to find the largest angle it reports). Record the incline angle (θ) on the paper.

2. Practice launching the puck so that it moves in a large arc across most of the paper. When you know how to do it consistently, record a video of the motion. Use the video analysis of Logger Pro to trace its path. Make sure to “set scale” using the calibration line you drew on the paper. Save the data in a csv file. We will call this path “C” (for curve).

Lab 4: Two Dimensional Motion page 1 of 4

3. Before you proceed, make a rough sketch of the table and the path C in the lab report.

4. Record another path, call it “R”, with the puck released from rest near the top of the slope.Use Logger Pro to trace its path and save the data in a csv file (use a different file name than the C path data).

5. Make a rough sketch of path R in the lab report in the same square as path C. Label both paths.

Part 2: Data Analysis



Part 3: Monkey Hunter

A classic projectile problem involves ahunter shooting a dart at a monkey in atree. When the gun is fired the dart willexecute projectile motion, so if thehunter aims right at the monkey the dartwill pass below it.

From experience, the hunter knows thata hanging monkey will let go of the treeand begin to fall the instant it hears thegun. From Physics, the hunter knowsthat if the dart is fired at the instant the monkey lets go, the parabolic arc of the dart will always hit the monkey in free-fall provided it was aimed at the monkey in the tree. This will happen regardless of the dart's initial speed or the distances involved (as long as the dart has enough range to cross the monkey's path).

The process will be demonstrated the lab room. You are asked to show mathematically that the dart must hit the monkey.

Here are a couple hints to get you started:

• Assume the dart is fired and the monkey lets go at time .• Use the variables , , (initial dart speed), (initial dart angle) in your equations. The

values of all these variables should not matter.• Write an equation for the vertical position of the monkey: .• Write equations for the horizontal and vertical position of the dart: and .• Find the time it takes the dart to go a horizontal distance (call this time ), and then

show that at this time . If this is true, the dart hits the monkey.

• You may want to use the fact that .



University Physics 1Lab 4: Two Dimensional Motion

Report

Name:______________________

partner name:______________________

Part 1: Acceleration in a Plane

Sketches of path C and path R. Label the paths and include the and axes on the figure.


Part 2: Data Analysis


Part 3: Monkey Hunter

Show (mathematically) that the dart musthit the monkey if the gun was aimed at themonkey's initial position, and the monkeylets go at the instant the gun is fired.


University Physics 1Lab 5: Dynamics

Objectives:

• measure the forces on a body on a ramp• describe these forces with free-body diagrams• find the acceleration of the building elevators using Newton's 2nd Law

Theory:

We will investigate Newton's Second Law for a cart on a ramp being pulled by a mass on a connected string. The equations are no more complicated than and

, but these can be difficult to employ without a free-body diagram.

A free-body diagram (FBD) shows the body we are interested in as a point and shows all the forces acting on it. Be careful not to double-count forces in the FBD.

Equipment:

computer running Logger Pro, Vernier interface and motion detector, low friction cart, track with ramp-mount hardware, wireless force sensor, string and hanging mass set

Procedure:

Part 1a: Forces on a ramp

1. Construct the ramp with motion sensor as shown in the diagram. Consult the model setup in the lab.

2. Use the digital level to measure the ramp angle, θ . Also measure the cart's mass,call this m0 .

3. Allow the cart to roll up and down the ramp. Draw the free-body diagram of forces on

Lab 5: Dynamics page 1 of 4

θ

motion sensor

the cart while it is rolling freely,. This will be called FBD-1. (Hint: there should only be two vectors on FBD-1.) Use this FBD to compute the predicted magnitude of the net force on the cart, Fnet .

4. Give the cart a push up the ramp, and use the motion sensor to measure its velocity as it is rolling freely. Use the slope of the velocity to find the acceleration, a0 . Usethis measurement and the mass m0 to calculate the net force on the cart, Fnet .

5. Compare your two results for net force (from steps 3 and 4). Record the percent difference between them.

6. Without doing the experiment, suppose you doubled the mass of the cart. How do you predict the acceleration, a0 you measured in part 4 to change? Should it double, decrease by half, or remain about the same?

7. Place extra mass on the cart to approximately double its mass, and repeat the acceleration measurement from step 4. Discuss what you find and how this matches your prediction.

Part 1b: Forces on a ramp with tension

1. Now remove any extra masses from the cart and attach the wireless force sensor. Quit Logger Pro if it is currently running. Note the name of your force sensor, and connect it by bluetooth to the computer as follows:• turn on the power to the wireless force sensor• open the computer's bluetooth preferences and find your device• pair your device (it's ok if it reports “not connected” at this point)• start Logger Pro and select Experiment > Remote > Retrieve Wireless > ScanConnect the string to the force sensor. The pulley should be adjusted so the string is parallel to the ramp. Make sure to zero the force sensor when there is no force on it (use the blue Ø button). Measure the cart's mass with the force sensor attached, call this m0 .

2. Compute the net force that this cart would experience if it were to roll freely on the ramp (see Part 1a, step 4)—this is force you will need to overcome to pull the cart up the hill. Note that the hanging mass set has masses of 10g, 20g, 50g, 100g, 200g, 500g and 1kg. Use the force result to predict which one of the masses in the set is the smallest mass that will pull the cart up the ramp when connected to the


motion sensor

θ

force sensor

cart

string over the pulley. Record your prediction for this mass, m1 . Note, m1 must be either 10g, or 20g, 50g, 100g, because you must use only one hanging mass.

3. Check by experiment if your prediction was correct. This hanging mass will be called m1 . Record it.

4. Double check that the force sensor reads zero when the string is relaxed. Then allow the mass m1 to rest on the floor as the string holds the cart stationary on the ramp. Record the string tension reported by the force sensor, T 0 .

5. With the cart at rest, held by the string, draw a free-body diagram of it. This we will call FBD-2. What should be the magnitude of the vector sum of all the forces on it?

6. Without doing the experiment, consider the following situations and record your predictions (greater, less, or equal).A. Suppose the cart was held stationary near the bottom of the ramp with the

hanging mass suspended in air. While stationary, the string tension will beT1 . Do you predict that tension T1 will be greater, less than or equal to

what you measured above, T 0 ? B. Suppose the hanging mass were allowed to pull the cart up the ramp by the

string. While accelerating, the string tension will be T2 . Do you predict that tension T2 will be greater, less than or equal to T 0 ?

C. Finally do you predict that tension T1 will be greater, less than or equal to tension T2 ?

7. Double check that the force sensor reads zero when the string is relaxed. Set Logger Pro to graph the force versus time. Pull the cart down the ramp and hold it near the bottom of the ramp. Record the tension in the string while held stationary on the ramp, T1 . Was your prediction from step 6A correct? If not, explain why.

8. Again check the zero point of the force sensor. Pull the cart down the ramp, start data collection and then release the cart to accelerate up the ramp. Record the tension in the string while moving up the ramp, T2 . You may want to find the average of a portion of the force graph – use the Analyze > Statistics tools for this. Was your prediction from step 6B correct? If not, explain why. Was your prediction from step 6C correct? If not, explain why.

9. Draw two free-body diagrams of the hanging mass:A. while the mass is hanging but not moving (step 7), this will be FBD-3. Note, the

hand force should also be shown in this diagram.B. while the mass is accelerating downward (step 8), this will be FBD-4.Make sure the force vectors you draw have the correct size relative to each other.

10. Consider the three tensions you have measured, T 0 T1 and T2 . Which of these should be equal to the gravity force on the hanging mass, m1g ? Compare


the percent difference of these numbers (i.e., the difference between m1g and the measured tension it should equal).

11. Use your known forces (and mass m0 and ramp angle) to compute your predictionfor the acceleration of the cart as it is pulled up the ramp by mass m1 . Record this prediction for acceleration a2 .

12. Measure the acceleration a2 with the motion sensor. Compute the percent difference between your computed and measured values for a2 .

Part 2: Elevator acceleration

In this part your object is to measure an elevator'sacceleration. To do so you you will need to measurethe weight of a person while not accelerating (theirtrue weight W=mg ), and the apparent weight ofthe person (what the scale reads) while the elevatoris accelerating up and down.

First answer the preliminary questions in the labreport.

Bring a scale to the elevator and measure the weightsas shown in the lab report. When you take your data,record all the values in pounds (lbs). Convert toNewtons using 1 lb = 4.45 N.

Find the net force on the person in each case, and use this (along with the person's mass) to compute the acceleration of the elevator.


Normal force (scale reading)

Gravity ( FG= mg )

University Physics 1Lab 5: Dynamics

Report

Name:______________________

partner name:______________________

Part 1a: Forces on a ramp

2. θ = _______________________ m0 = _______________________

3.FBD-1:

predicted Fnet = _______________________

4. measured a0 = _______________________

measured Fnet = _______________________

5. % difference in Fnet : _______________________

6. predicted change in a0 : _______________________

7. Discuss prediction versus result:


Part 1b: Forces on a ramp with tension

2. predicted m1 : _______________________

3. measured m1 : _______________________

4. measured T 0 = _______________________

5. FBD-2: magnitude of the vector sum: _________

6. A. prediction (greater, less, or equal): _______________________

B. prediction (greater, less, or equal): _______________________

C. prediction (greater, less, or equal): _______________________

7. measured T1 = _______________________

8. measured T2 = _______________________


9. FBD-3: FBD-4:

10. Which tension: __________________

% difference: _____________________

11. predicted a2 : _______________________

12. measured a2 : _______________________ % difference: ____________________


Part 2: Elevator acceleration

Preliminary Questions:

1. Will the mass of the person change as the person accelerates?

2. What is the magnitude of the gravitational force on the person?

3. Will this gravitational force change as the person accelerates?

Data:

A. Stationary: scale reading (lbs) ____________________

B. Moving down, speeding up: scale reading (lbs) ____________________

C. Moving down, slowing: scale reading (lbs) ____________________

D. Moving up, speeding up: scale reading (lbs) ____________________

E. Moving up, slowing: scale reading (lbs) ____________________

Analysis:(letters indicate the type motion, as above)

scale reading (N) net force on person (N)

A. ____________________ ____________________

B. ____________________ ____________________

C. ____________________ ____________________

D. ____________________ ____________________

E. ____________________ ____________________

What is the mass of the person (in kg)? ____________________


Use Newton's 2nd Law to find the acceleration of the elevator in each case. Include the sign (+ or –) to indicate the direction of the acceleration.

B. Moving down, speeding up: acceleration (m/s2) ____________________

C. Moving down, slowing: acceleration (m/s2) ____________________

D. Moving up, speeding up: acceleration (m/s2) ____________________

E. Moving up, slowing: acceleration (m/s2) ____________________



University Physics 1Lab 6: Circular Motion & Computational Dynamics

Objectives:

• balance force vectors for a body moving in a circle• calculate centripetal force in two ways: by equation and by force decomposition• run and analyze some simple computational models

Theory:

An object moving in a circle requires a force to keep its direction changing; this force is directed toward the center of the circle, and so is called centripetal force.

We will study a mass hanging on a string while swinging in a horizontal circle, called a conical pendulum. The net force must be centripetal (since it's moving in a circle), which means it must be horizontal. If the net force is horizontal, the vertical component of the string tension must cancel the vertical gravity force.

We will use this analysis to find the centripetal force on the mass and compare it to the equation

.

Equipment:

computer running Logger Pro, Vernier interface, wireless force sensor, string, meter stick, slotted masses

Lab 6: Circular Motion & Computational Dynamics page 1 of 4

Procedure:

Part 1: Conical Pendulum

1. Connecting the force sensor by bluetooth can sometimes require troubleshooting. Before you start the Logger Pro software, make sure the sensor is powered on and that bluetooth is enabled on your laptop. Start Logger Pro and choose Experiment > Remote > Retrieve Wireless > Scan. Check the name on the label of the force sensor and find it on the list of devices found. Make sure the sensor is working; ask the instructor if you're having trouble.

2. Click the “Data Collection” button and choose a time of 120 seconds.

3. First zero the sensor while there is no tension in the string by clicking the blue Ø (do this occasionally throughout the lab for best results). Measure the weight of the forcesensor using the sensor itself: let the sensor then hang freely and record its weight, W. Use this weight to compute its mass m (using W=mg).

4. Wrap or tie the top of the string to a pen tomake it easy to hold the string while swinging.Practice swinging the string and sensor in alarge horizontal circle with about 1m of string(see the figure below). Measure the distancefrom the top pivot to the center of mass of theforce sensor (the center of mass will be at thebolt hole in the sensor). Call this distance ℓ(see figure).

5. Slowly swing the sensor around in a circle at asteady rate. Make sure the force readout isgreater than the weight recorded in step 3. You will get best results if you have a large circle radius. When the revolution rate is constant, start the data collection (green ► button) to measure the force of tension in the string, and begin counting revolutions. When you reach a predetermined number of revolutions (say, 50), stop the data collection. Divide the total time elapsed (see data record) by the number of revolutions to get the period, T.

6. Record the average force (string tension) during the circular motion, Fave. The average force can be found from the Analyze > Statistics option (the average is also known as the “mean”).

7. Draw the free-body diagram for the sensor. Include the angle θ in the diagram. Use this diagram to calculate the angle (θ) from the average tension force (step 6) and theweight (step 3).

8. Considering the free-body diagram, compute the component of the tension that is


providing the centripetal force, Fc .

9. Use the angle θ and string length ℓ to compute the circle radius, r .

10. Compute the tangential speed, v, of the sensor in its circular motion. This will be onecircumference per period ( v=2π r /T ).

11. Using this speed and the radius, find the required centripetal acceleration ( v2/ r ), and the required centripetal force ( m⋅ac ).

Part 2: Computational Dynamics




University Physics 1Lab 6: Circular Motion & Computational Dynamics

Report

Name:______________________

partner name:______________________

Part 1: Conical Pendulum

weight and mass of force sensor:

W = ______________ N m = ______________ kg

length, period, average force:

ℓ = ______________ m T = ______________ s Fave = ______________ N

free body diagram, angle θ, and centripetal force:

θ = ______________

Fc = ______________ N

radius of circle and velocity:

r = ______________ m v = ______________ m/s


centripetal acceleration, second calculation of centripetal force:

ac = ______________ m/s2 Fc2 = ______________ N

Do your two computations of centripetal force agree (Fc and Fc2 )? Give the percent difference between them.

Part 2: Computational Dynamics

You may submit the completed notebook by printing it and attaching it to the lab report, orby submitting it electronically on Blackboard.


University Physics 1Lab 7: Work and Energy

Objectives:

To study conservation of mechanical energy by measurements of kinetic energy and gravitational potential energy.

Theory:

In this lab we consider the conservation of mechanical energy. When energy isconserved, the change in potential energy will equal the opposite change in kineticenergy.

The potential energy in this lab will be the energy stored in an object's height, y:

where m is the object's mass (in kg), g is the gravity constant (9.8 m/s2), and y is theheight of the object (in meters).

Kinetic energy is the energy in the motion of an object – the faster it goes, the morekinetic energy it has. For an object of mass m (in kg) and moving at a speed v (in m/s),its kinetic energy is:

So, for example, if you lose 5J of potential energy by falling to a lower height, then (ifmechanical energy is conserved) you must gain 5J of kinetic energy by moving faster.

If there is friction, then mechanical energy will not be conserved. In this case the energyloss will be equal to the work done by friction. Note that friction opposes the motion, andso it will be doing negative work on the way up the ramp and on the way down.

Equipment:

Computer, Vernier interface, motion sensor, cart, ramp

Lab 7: Work and Energy page 1 of 4

Procedure:

Part 1: Cart on ramp (no friction)

1. Assemble the ramp so that when the cart rolls downward it is traveling toward the motion sensor. The slope of the ramp should be less than 5º.

2. Attach a small post to the cart. Measure the mass of the cart. Record it in kilograms.

3. Practice releasing the cart so it has some initial speed up the ramp. Try to release it right when data collection begins, and try to stop data collection right when you catch the cart at the bottom (using the 'start' and 'stop' buttons in Logger Pro).

4. When you have a good data set, add a “new calculated column” (use the 'data'

menu). The formula for the new column should be 12

mv 2, where m is the mass of

the cart from step 2.

5. Record the ramp angle, θ and calculate sin θ .

6. Add a “new calculated column” to convert values of x (called “position” in Logger Pro) into values of y (height). The formula should be y=x⋅sin θ (use the value of

sin θ above).

7. Now add another “new calculated column” for potential energy. The formula for the new column should be m⋅g⋅y ( where g is 9.8 N/kg and m is the mass of the cart.). Also make a new column for total energy, TE (TE = ).

8. Use Logger Pro to make a graph of the potential, kinetic and total energy versus time.Have the software show all three energies on the same graph (click the axis name and select “More...”, then check which data to show). Have the instructor check your graph to make sure the calculations look right. When it checks out, sketch that graph in the lab report and answer the questions there.


motionsensor

θ

cart

Part 2: Cart on ramp (some friction)

1. We will now repeat part one, but with friction. Keep the calculated columns from theprevious part. Tape a small wad of paper to the bottom of the cart so it drags slightlyagainst the ramp as it moves. When you have it so that it will roll, but with some drag,then give it a push up the ramp, as before.

2. Sketch the graph of the potential energy, kinetic energy, and total energy versus time in the lab report, and answer the questions there.

3. Choose an initial and final time from the graph that encloses most of the period of free motion of the cart, call them and . Record these times. Find the position of the cart at initial time ( ), the final time ( ), and when it was farthest from the motion detector ( ).

4. Find the work done by friction during this time. Hint: the total energy is reduced by anamount equal to the work done by friction: . You will need the total distancetraveled in the time Record your answer.

5. Use the position graph to find the total distance (not displacement) traveled during this time interval. This is the distance over which the friction acted. Use this information along with its work done (step 3) to find the average friction force acting on the cart during this time period. Record your answer.

Part 3: Cart on ramp connected to dropping mass

1. Remove the friction pad and connect the cart to a hanging mass over a pulley, asshown. The hanging mass must be sufficient to pull the cart up the ramp, this will bemass m1 . The length of the string should be long enough so the mass will rest onthe floor when the cart is near the top of the ramp. The angled portion of the stringshould be parallel to the ramp.

2. When assembled, start the cart near the top of the ramp and give it a gentle pushdown the slope, allowing it to go down, turn around, and accelerate up the ramp.Catch it again near the top of the ramp. When you can make it travel down and up,start the motion sensor to record its position and calculate its kinetic and potentialenergies, as before.


motionsensor

θ

cart

3. Sketch the graph of the cart’s potential energy, kinetic energy, and total energy versustime in the lab report, and answer the questions there.

4. Now we want to compute the kinetic and potential energies of the hanging massm1 . You will need a new calculated column for the height of the mass m1 , call

this . This height will be related to the position of the cart on the ramp. If you set to be the position of the cart when the mass is on the floor (you can measure this withthe motion sensor), then you can write “position”. Use the value of to calculate the potential energy of the hanging mass, . The kinetic energy of the mass, , can be calculated from its mass and the velocity of cart.

5. Now add two more calculated columns for the kinetic and potential energy of massm1 . Change the calculation of total energy to be the sum of all four energies (

and of the cart and and of hanging mass).


University Physics 1Lab 7: Work and Energy

Report

Name:______________________

partner name:______________________

Part 1: Cart on ramp (no friction)

cart mass: _______________________

ramp angle: θ = ____________________ sin θ = ____________________

Graph of the potential energy, kinetic energy, and total energy versus time. Label axes and indicate which line corresponds to which type of energy.

Explain how the total energy (kinetic energy plus potential energy) changes at the variouspositions shown on the graph.


Part 2: Cart on ramp (some friction)

ramp angle: θ = ____________________ sin θ = ____________________

Graph of the potential energy, kinetic energy, and total energy versus time. Label axes and indicate which line corresponds to which type of energy.

Explain how the total energy (kinetic energy plus potential energy) changes as the cart slides down the ramp. Why is this different from the answer to Part 1?

initial and final times: = _________________ = _________________

work done by friction during this time interval: _____________________

cart positions: = ___________________________________

= ___________________________________

= ___________________________________

distance traveled in this time interval: _____________________

average friction force acting on the cart: _____________________


Part 3: Cart on ramp connected to dropping mass

Graph of the potential energy, kinetic energy, and total energy of cart versus time. Label axes and indicate which line corresponds to which type of energy.

Explain how the total energy (kinetic energy plus potential energy) changes as the cart moves down and up the ramp. Why is this different from the answers to Parts 1 and 2?

Graph of the potential and kinetic energies of the cart and hanging mass, and total energy of the system. Label axes and indicate which line corresponds to which type of energy.

Explain how the total energy changes throughout the motion, and why.



University Physics 1Lab 8: Conservation of Momentum

Objective:

To investigate several collisions, measuring the initial and final momenta and kinetic energies in each case, and observe the conservation of momentum in one and two dimensions.

Equipment:

Part 1: computer running Logger Pro, Vernier interface and two motion detectors, track, two low friction carts

Part 2: Air tables, steel pucks, compressors, foot pedals, spark timers, recording paper, carbon paper, levels.

Procedure:

Part 1: Momentum Conservation in 1D

1. You will need two carts with repelling magnets. Make sure the track is level. Measure velocities with Logger Pro and two motion detectors, one at each end of the track. Set up the motion detectors so they are a few cm away from the end of the track. Start data collection and move each cart individually to be sure both detectors are seeing the carts. The motion detectors should be set to “cart” mode (using the switch on the detector).

2. You will need to be careful about which velocities are positive and negative. We willspecify rightward motion as positive and leftward as negative. To keep these straightin the experiments, label the carts A and B, keeping A on the left and B on the right.In Logger Pro, add a "new calculated column" (from the data menu), and make acolumn that multiplies cart B's velocity by –1 (this will fix the direction reversal due toone of the detectors facing toward the left). Now set your graph to simultaneouslydisplay both cart velocities (you can do this by clicking on the vertical graph label,choosing "more" and checking the quantities to show in the graph). Make sure yourtrack is level, and that the motion sensors are pointing horizontally. Start the datacollection and move one of the carts so you know which graph color is for which cart;record the colors in the lab report.

3. There are many calculations to make in this lab, and they are repeated for each case.

Lab 8: Conservation of Momentum page 1 of 4

To reduce errors and effort, it is recommended that you use a spreadsheet program toperform the calculations. For each case below, there are two tables to fill in: one withmeasurements and another with calculations. Data in each of the calculated tables isbest found by using the spreadsheet.

4. Practice with a couple of collisions before taking data. Be clear on which color line iscart A and which is cart B. Record the graph colors for each cart in the lab report.When you record the velocities in the experiments below, do so for the velocityimmediately before the collision and the velocity immediately after the collision. Youcan use the "examine" tool in the toolbar to easily read the data values off a graph.Since large mass will tend to introduce more friction, do not exceed 1kg of mass forany cart.

5. Start with cart A initially moving and cart B stationary. The collision should be aselastic as possible. You can use either the spring or the repelling magnets (better) foran elastic collision. Do not exceed 1kg of total mass for a cart. Perform twoexperiments:

Case 1: carts of equal mass, viB = 0 m/s. Case 2: increase mass mB, viB = 0 m/s.

6. The next two collisions should be inelastic. Use the velcro to get the carts to stick andmove together after the collision. Perform two experiments:

Case 3: carts of equal mass, viB = 0 m/s. Case 4: carts of equal mass, both final velocities ≈ 0 m/s

7. The next two cases will not be a collision, but a sort of explosion (with energyreleased in the interaction). Initially, both carts are in contact. There is a spring-loaded plunger on one of them which can be triggered to push them apart. Performtwo experiments:

Case 5: carts of equal mass, viA = viB = 0 m/s. Case 6: carts of equal mass, viA = viB > 0 m/s.


In this part, two steel pucks will be suspended on an air cushion, and will be made to collide with very little friction. In this way, the total momentum of the two pucks should beconserved.

We will study two cases:Case 1: One puck at rest, one puck in motion, pucks collide at a glance and move off

in different directions.Case 2: Both pucks initially in motion, colliding and moving off in different directions.

1. Set up and level the table. Label the pucks A and B. Find the mass (m) of each puckand record them.


2. Prepare for the case under consideration. Take a few trial runs, trying to get no interference from the air tubes. When ready, begin taking video and execute the collision.

3. Use the Logger Pro video analysis to find the x and y velocities. Create a “New Calculated Column” for the x and y components of the momentum for each puck.

4. Find the magnitude and direction of each puck’s momentum. For each case, make a sketch of the collision showing the initial and final speeds, with the positive x-axis pointing horizontally to the right. Label the angles of the velocities (with respect to the positive x-axis). Follow the example shown.

example:initial final

5. We will analyze the momentum for each case. This is best done on a spreadsheet where the calculations can be checked and easily duplicated. Start a spreadsheet application and construct a table like the one shown below (using the example data from the figure). Enter the data you have measured for each case. Using a negative angle when the vector points below the x-axis will ensure that the y-component is negative. The momentum values should be calculated by entering the correct equation using the data you have entered.

initial final

v p θ px py v p θ px py

m/s kg m/s deg kg m/s kg m/s m/s kg m/s deg kg m/s kg m/s

A 0.64 -40 0.47 -57.5

B 0.30 20 0.53 9.5

total


For the example shown in the figure above, the result should be as follows (using a mass of 0.500 kg for each puck, and converting angles to radians for the spreadsheetcalculation). Check your sequations with these numbers to verify they are working.

initial final


m/s kg m/s deg kg m/s kg m/s m/s kg m/s deg kg m/s kg m/s

A 0.64 0.32 -40 0.245 -0.206 0.47 0.235 -57.5 0.126 -0.198

B 0.30 0.15 20 0.141 0.051 0.53 0.265 9.5 0.261 0.044

total 0.386 -0.154 0.387 -0.154

Enter your results in the tables in the lab report (or make a printout of your spreadsheets).

6. For each case, calculate the magnitude and direction of the total momentum vector before and after collision. These calculations can (and probably should) also be donein the spreadsheet. Answer the related questions in the lab report.

7. Compute the total kinetic energy of the pucks (both initial and final). Answer the related questions in the lab report.


University Physics 1Lab 8: Conservation of Momentum

Report

Name:______________________

partner name:______________________


Graph colors: cart A color: _________________ cart B color: _________________

Elastic Collisions:

measurements:case mA (g) mB (g) viA (m/s) viB (m/s) vfA (m/s) vfB (m/s)

1

2

Complete the table below with the total momentum initially (pi ) and finally (pf ). Repeatfor the kinetic energies. Make sure that all quantities have the correct sign (+/-).

calculations:case pi (g m/s) pf (g m/s) Δp (g m/s) KEi (mJ) KEf (mJ) ΔKE (mJ)

1

2

Calculate the percent change of momentum for each case, where

% change in p =Δ ppi

· 100%.

Calculate the percent change in KE similarly. Note that loss of momentum should beshown as a negative value for percent change.


case % change in p % change in KE

1

2

Was momentum (mostly) conserved in these two cases? If not, check with instructor.

Was kinetic energy (mostly) conserved in these two cases? If not, discuss why not.

Inelastic Collisions:


3

4



3

4

Was momentum (mostly) conserved in these cases? If not, check with instructor.

Was kinetic energy (mostly) conserved in these cases? If not, discuss why not.


Explosions:


5

6



5

6

Was momentum (mostly) conserved in these cases? If not, check with instructor.

What happened with the energy in these interactions? Discuss how and why this isdifferent than the results from the collisions of the previous parts.



puck masses and spark time interval:

mA: _____________ kg mB: _____________ kg Δt = _____________ s

collision figures:

Case 1:initial final

Case 2:initial final


Enter your collision data in the tables below (or make a printout of your spreadsheets andattach it).

Case 1:

initial final


(units)

A

B

total

Case 2:

initial final


(units)

A

B

total

Give the magnitude and direction of the total momentum vector before and after collision:

Case 1: ∣⃗pi∣ = _____________ direction of p⃗i : _____________

∣⃗p f∣ = _____________ direction of p⃗ f : _____________

Case 2: ∣⃗pi∣ = _____________ direction of p⃗i : _____________

∣⃗p f∣ = _____________ direction of p⃗ f : _____________

Was momentum conserved (or nearly conserved) in the collisions? Explain any differences you saw.


Give the total kinetic energy of the pucks (both initial and final).

Case 1:

initial KE : _________________ final KE : _________________

Was kinetic energy gained, lost or conserved in the collision?

Case 2:

initial KE : _________________ final KE : _________________

Was kinetic energy gained, lost or conserved in the collision?


University Physics 1Lab 9: Rotational Dynamics

Objectives:

To study the principles of rotational dynamics: torque, kinetic energy and angular momentum.

Theory:

In this lab, two metal disks are suspended on air to provide very little friction. We will attach a weight to provide a torque that will spin up the disks with some angular acceleration.

As the disks spin up, they will gain rotational kinetic energy:

Also, a falling mass will have translational kinetic energy:

The total energy gained in kinetic will have to be equal to the amount of potential energy lost by the falling mass ( ).

The disks are not solid, so we cannot use a formula to calculate their rotational inertia. Instead we will measure this value as explained in part 1 below.

As the disks spin, the digital readout shows the number of black stripes (along the disk edge) that are passing every second (note that there is a slight time delay in the readout.)The switch on the side of the readout controls whether it shows the upper or lower disk's speed. Since there are 198 black stripes along the edge, a readout of 198 would mean exactly one revolution (or 2π radians) per second of angular velocity of the disk. So to convert between the readout which shows f (in Hz) and ω (in radians/sec), use

Equipment:

rotational dynamics apparatus and accessories, air compressor, ruler, stopwatch

Lab 9: Rotational Dynamics page 1 of 4

Procedure:

Part 1: Conservation of Energy

1. Assemble the apparatus as instructed, and attach the air compressor to the tube. Use the screw with a hole in it to hold down the two steel disks and thread spool (we won't be using the aluminum disk). A pin can be inserted in the hole to direct air between the disks – in this way the top disk can move alone. Make sure the “B” is on the bottom of the lower disk.

Record the mass of the falling weight (not including spool).

2. As the mass on the string drops, it will lose potential energy. Pick a convenient height (above the floor) that you will have it drop. Record the height and calculate the amount of potential energy it has lost when it hits the floor.

3. Set up and start the apparatus, allowing the mass to fall the distance you have chosen. Observe the greatest value shown by the readout and convert that to radians per second (note that the peak value might appear slightly after the mass hitsthe floor, due to the readout delay). Perform the experiment twice: once with one disk, and again with both disks. Record the maximum angular velocity observed in each case.

4. Next calculate the linear velocity of the falling mass for each case (v1 and v2). To do so you will need to measure the radius of the thread spool (rspool), since this is the radius that will convert the angular velocity into the tangential velocity of the thread (and mass).

5. Calculate and record how much kinetic energy the falling mass has when it hits the ground.

6. Finally, use your measurements above and energy conservation to calculate the rotational inertia for the single disk and for the double disk (I1 and I2 , respectively). Use scientific notation and express your values with at least three significant digits.

Note: If I2 is not close to double I1, check your results before proceeding..


Part 2: Newton's Second Law

1. We will now analyze the same experiment with Newton's Second Law for rotation: .

2. Repeat the experiment with both disks spinning together, recording the same data as in Part 1, but also the time taken for the mass to fall from rest to the floor (from the same height used in part 1). One partner will use a stopwatch to measure the time taken to fall (be careful to achieve maximum accuracy possible in this measurement).Record the new data.

3. Use this data to compute the average angular acceleration of the disk and the average translational acceleration (a) of the falling mass.

4. Next use the weight of the mass (mg) and its acceleration (a) to compute the tension in the string during the fall. Recall that the force of gravity (down) minus the tension (upward) must equal the total force, which equals ma.

5. Given the string tension and the radius of the thread spool, calculate the torque that the tension exerts on the disk ( ).

6. Finally, compare this value to . Are they similar?

Part 3: Conservation of Angular Momentum

1. Set up the apparatus to spin without a falling weight, and with only one disk spinning. As it spins, friction will gradually slow it down. At some instant, remove the pin so that both disks begin spinning. Record the angular velocities just before (ωi) and after (ωf) this "rotational collision".

2. Use the known rotational inertias to calculate the angular momentum before (Li) and after (Lf) the collision. Also calculate the initial and final rotational kinetic energy of the system. For these calculations, use the rotational inertia you obtained in Part 1.

3. Answer the remaining questions in the lab report.



University Physics 1Lab 9: Rotational Dynamics

Report

Name:______________________

partner name:______________________

Part 1: Conservation of Energy

Mass of the falling weight: m = _______________________ kg

Distance weight falls: h = _______________________ m

Potential energy lost: U lost: _______________________ J

Maximum angular velocity observed in each fall:

ω1 = _______________________ rad/s (one disk)

ω2 = _______________________ rad/s (two disks)

radius of the thread spool: rspool = _______________________ m

linear velocity of the falling mass for each case :

v1 = _______________________ m/s (one disk)

v2 = _______________________ m/s (two disks)


Kinetic energy of the falling mass when it hits the ground:

for 1 disk, (of falling mass): = _______________________ J

for 2 disks, (of falling mass): = _______________________ J

total kinetic energy (equal to potential energy lost)

= _______________________ J

Does have a significant contribution to the total energy calculation?

Calculation of the rotational inertia for the single disk and for the double disk. Use scientific notation and express your values with at least three significant digits.

I1 = _______________________ kg m2

I2 = _______________________ kg m2

Part 2: Newton's Second Law

final (max) angular velocity: ωf = _______________________ rad/s

final (max) velocity of mass: vf = _______________________ m/s

time taken: t = _______________________ s


angular acceleration: = _______________________ rad/s2

translational acceleration: a = _______________________ m/s2

string tension: T = _______________________ N

torque on disk: = _______________________ N m

Compare the torque to the value . Are they similar?

Part 3: Conservation of Angular Momentum

angular velocities just before (ωi) and after (ωf) this "rotational collision":

ωi = _______________________ rad/s

ωf = _______________________ rad/s

angular momentum before (Li) and after (Lf) the collision.

Li = _______________________ kg m2 /s

Lf = _______________________ kg m2 /s

initial and final rotational kinetic energy of the system.

Ki = _______________________ J

Kf = _______________________ J


Was angular momentum conserved in the collision (or nearly conserved)?

Was energy conserved in the collision (or nearly conserved)?

Was this an elastic collision?


University Physics 1Lab 10: Static Equilibrium

Objectives:

To verify that the sum of torques equal zero for objects in equilibrium using any point as areference point. Apply the first and second conditions of equilibrium to find unknown forces; and verify theoretical results with experimental results.

Theory:

An object at rest or moving with constant velocity (or constant angular velocity) is in equilibrium. If the object is in equilibrium, then the following two conditions are true:

First Condition of Equilibrium: The sum of forces equal zero: Σ F⃗ = 0

This is just another way of stating part of Newton’s First Law. If components of the forces are used, then the first condition of equilibrium (for two dimensions) can be stated as follows: A. The sum of all forces in the x direction equal zero. Σ Fx = 0.B. The sum of all forces in the y direction equal zero. Σ Fy = 0.

Second Condition of Equilibrium: The sum of torques (using any reference point) equal zero: Σ τ = 0

A torque causes rotation, clockwise (cw) or counterclockwise (ccw). A clockwise torque can be designated a negative value, positive for counterclockwise torques, so the SecondCondition of Equilibrium can be restated as follows: The sum of the clockwise torques plus the sum of the counterclockwise torques equal zero. (Remember - ccw torques are positive values.)

Although a proper treatment of torques requires forces (in units of N) to be used, to do so would involve a common factor of g (9.8 N/kg). So in this case it is acceptable to use grams as a proxy for force units. It is still important to make sure that units agree when you're adding several torques.

Equipment:

Meter stick, knife-edged clamps, support stand, hanging weights, mass balance

Lab 10: Static Equilibrium page 1 of 4

Procedure:

Part 1: Summing Torques

1. Balance just the meter stick on the knife-edged clamp. Note the screw must be below the meter stick forit to balance. Thisbalance point is thecenter of mass (CM) ofthe meter stick. Recordthe location of CM.

2. Attach 150 g to a hanger on the 25 cm mark and 100 g to a hanger on the opposite side. Move the 100 g until balance is achieved. Don’t forget to include the mass of the clamp as part of the 150 g and 100 g masses. Record the masses and their locations with respect to the zero-end of the meter stick.

3. Draw an extended free-body diagram of the meter stick showing all forces and their location.

4. Compute the clockwise (cw) and counterclockwise (ccw) torques. Record and compare them.

Part 2: Weigh the meter stick by balancing torques

1. Move the support stand to the 30 cm mark on the meter stick. Hang a weight only on the short side of the meter stick and move the weight to achieve balance. Record themass (including hanger) and location of this counterweight (with respect to the zero-end of the meter stick).

2. One torque is caused by the mass that you have attached. The other torque is caused by the mass of the meter stick, which acts at the stick's center of mass (foundin Part 1). Draw an extended free body diagram of the meter stick showing all forces and their location.

3. Use the torque sum to compute the unknown mass of the meter stick. (Do not measure the mass of the meter stick yet.)

4. Now take everything off the meter stick and weigh it. Find the % difference betweenthese masses.


Part 3: Summing torques about a different reference point

1. Place the support-stand at any position (at least 10 cm away from the stick CM) of thestick. Add four additional masses, two on each side of the support stand, to achieve balance. Draw an extended free-body diagram of the meter stick showing the locationof all forces. Don't forget the meter stick weight and the support stand force.

2. Use the Σ Fy = 0 to find the force of the support stand on the meter stick.

3. Use the location of the far left edge of the meter stick as the reference point to find thesum of torques.

4. Use the center of mass of the stick as a reference point to find the sum of torques. Draw an extended free-body diagram of this situation. On it, show distances with respect to the center of mass.

Part 4: Use both conditions of equilibrium to find support forces

1. Observe the setup with a 2-meter stick and two mass balances. Measure mass of thestick and find find the location of its center of mass.

2. Measure the mass of a 500g weight combined with its mass hanger. Call this mass m1. Measure the mass of a 200g weight combined with its mass hanger. Call this mass m2. Record the masses.

3. Place the support stands, with knife-edge clamps, in the middle of the mass balances and zero the balances. Hang m1 between the two support stands and hang m2 to the right of both supports. Record the balance readings (FA and FB ). Also record thedistances to each support, as shown in the figure.


4. Draw an extended free body diagram of the system.

5. Use both conditions of equilibrium to find the theoretical values for both balances (excluding the masses of the support stands and knife-edged clamps).a. You will need two equations: torque balancing and vertical-force balancingb. Solve these equations for the two unknowns: FA and FB .

6. Find the percent difference between the balance and theoretical values of FA and FB .


University Physics 1Lab 10: Static Equilibrium

Report

Name:______________________

partner name:______________________

Part 1: Summing Torques

Location of the CM of the meter stick: _______________________

With 150 g at 25 cm mark and 100 g to a hanger on the opposite side. Record the masses and locations of the 100g mass and hanger:

mass (g) location (cm)

Extended free-body diagram of the meter stick showing all forces and their location:

Clockwise (cw) and counterclockwise (ccw) torques:

Sum of cw τ :

Sum of ccw τ :

% difference between

cw τ and ccw τ


Part 2: Weigh the meter stick by balancing torques

mass of counterweight: ______________________

location of counterweight: ______________________

calculated mass of meter stick: ______________________

measured mass of meter stick: ______________________

% difference: ______________________

Part 3: Summing torques about a different reference point

Extended free-body diagram of the meter stick showing the location of all forces:

Support stand force on the meter stick: _____________________

Sum of torques (using the far left edge as the reference point):

Σ τ = ________________________


Sum of torques (using the CM as the reference point):

Σ τ = ________________________

Part 4: Use both conditions of equilibrium to find support forces

Mass and the location of center of mass for the 2-meter stick:

ms ______________________ CM location: ________________

Hanging masses (including bracket) and their locations:

m1 ______________________ m2 ______________________

r1 ______________________ r2 ______________________

Locations of support stands:

rA ______________________ rB ______________________

Mass balance readings (not including support and bracket mass):

FA ______________________ FB ______________________


Extended free body diagram:

Calculation of support-stand forces:

FA ______________________ FB ______________________

Percent difference between the balance and theoretical values.

Left Side Percent Difference __________

Right Side Percent Difference __________


University Physics 1Lab 12: Fluid Mechanics

Objectives:

• test Archimedes' Principle• observe certain buoyant forces and their effects• Gain experience with changes in pressure during fluid flow• Observe and explain several example of the Bernoulli effect

Theory:

According to Archimedes' Principle, the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object. In part 1 of this lab, the fluid is water and the object will be one of four different materials.

If an object floats in water, it will float even higher in a fluid of greater density. We can use this fact to measure the density of a fluid. This is the way a hydrometer works: the height of the fluid level on a floating object is measured to give the density of the fluid.

Equipment:

mass balance, beaker, graduated cylinder, metal masses, hydrometers, Cartesian diver

Procedure:

Part 1: Archimedes' Principle

1. Get three objects made of different materials. Record the material that each object ismade of.

2. Measure their mass and volume. The volume can be found by observing how much fluid the object displaces (use the graduated cylinder for this measurement).

3. Use this data to compute the density of each object in units of g/cm3.

4. Now measure the buoyant force on each object. This can be found from the difference between the measured mass of the object when it's in air, and the measured mass of the object when it is submerged in the fluid.

Use the balance (shown below) to measure the submerged mass of the object. Note

Lab 12: Fluid Mechanics page 1 of 4

that the mass of the object does not change when submerged, but its measured value does because the buoyant force is included in the measurement.

5. Record the difference in thesubmerged mass measurementand the dry mass measurement.Using the water density (1.0 g/cm3 )and the volume of water displacedby each object (from step 2), recordthe mass of the water displaced.Find the percent difference betweenthese quantities.

Part 2: Buoyancy Simulation

1. Obtain a computer and start the simulation called “Buoyancy”, which may be found on the course web page, or at phet.colorado.edu.

2. Using the Buoyancy sim, consider the wood, ice, and Styrofoam blocks in a pool full of gasoline. While floating in gasoline, find the percentage of the block that is under water. You can do this by comparing the volume of fluid displaced when afloat and the volume of fluid displaced when fully submerged. Record your values along with the object density.

How is the % submerged related to the density of the object?

3. Create a formula to show how much of a floating object would be submerged in any fluid. (Hint: it will involve the densities of the object and fluid.)

4. In the “Buoyancy Playground” tab, choose to see two blocks. Make one Styrofoam and the the other brick, and stack the brick on the Styrofoam to make a sort of boat, floating in water. You may still adjust the mass and volume of the objects, but their density will remain fixed by the type of material.

Adjust the two object masses so that they float (with the brick on the Styrofoam) and with some the Styrofoam above water. Record the mass of each object, and the amount of water displaced. Discuss the relation between these three quantities.

6. Is it possible to adjust the object masses so that they float (with the brick on the Styrofoam) but with part of the brick submerged? Set this up, and record the mass of each object, and the amount of water displaced. Discuss the relation between these three quantities.


http://phet.colorado.edu/en/simulations/category/physics

Part 3: “Cartesian Diver”

A “Cartesian diver” is a small tube that floats because of a small air pocket inside it. Makesure your bottle is full of water and has its top on firmly. If you squeeze the bottle, the “diver” will sink. How does this work? (Hint: observe the air/water level in the diver.)

Part 4: Fluid Flow Simulation

Find and start the simulation called “Fluid Pressure and Flow”, which can be found on our Blackboard page, or at phet.colorado.edu/en/simulation/fluid-pressure-and-flow.

There are three tabs along the top: Pressure, Flow, and Water Tower. Explore the simulation and answer the questions below.

Pressure :

1. As the sensor is moved deeper into the liquid, how does the pressure change?

2. As more liquid is added, how does the pressure near the bottom of the tank change?

3. How does the pressure in the water change when the atmosphere is removed? Why is this?

4. Does the shape of the tank play a role in the pressure under the surface? Why is this?

5. How does the density of the fluid relate to the pressure it exerts? How does increasing gravity change the pressure in the fluid? Why do you think this is?


http://phet.colorado.edu/en/simulation/fluid-pressure-and-flow

Flow :

Now change to the “Flow” tab. Take some time and play with the simulation.

Consider the various pipes carrying water shown in the lab report. How would the speed and pressure of the water in the center of the pipe change as it moves from the initial location at the left end to the final at the right end? For each pipe, indicate increase, decrease or constant. You may verify your answers with the simulation.

Water Tower :

Now change to the “Water Tower” tab. Take some time and play with the simulation. Answer the questions below as you play. When allowing fluid out, assume tank is filled.

1. Does the speed of the flow of the water (out of the tank) depend upon the height of the tank (drag the yellow handle to change this)? Why do you suppose this is? Doesthe speed of the flow depend upon the fluid density? What does flow speed depend upon?

2. Describe the shape of the fluid steam after it leaves the tank.

3. Check the ”Match Leakage” button on the input pipe. Use the Speed tool to measure how fast the water hits the ground. Attach the hose and rotate the nozzle so that the water shoots out horizontally. At what speed does the water hit the ground after leaving the hose? Direct the nozzle straight upward. At what speed does the water leave the hose when it is placed at ground level? How do these speeds compare?

4. Turn on the hose and leave it aimed directly upward. What do you notice about the height this little fountain achieves? (Adjust the other pieces of the simulation to see what affects the height of the water spout.)

Part 5: Fluid Dynamics Demos

Experiment with the following demonstration equipment (in any order). Answer the questions that appear in the lab report.

1. Cart with rotating barrel and fan: Place the cart (with barrel) on the track and make sure the track is level. When the barrel is spinning it will affect air flow around it. Predict what will happen in each case:


Now get the barrel spinning as fast as possible and turn on the fan and blow air across the cart perpendicular to the track (the fan must be held close to the barrel). What is direction of the net force on the cart? Draw a sketch of the air flow, showing the direction of the net force.

2. Hanging Cans: Observe the two hanging aluminum cans. Predict what their (initial) motion should be if you blow between them. Try it, and sketch the air flow and force on the cans.

3. Venturi tube with air compressor: With the air compressor on, compare the heights ofthe water columns in the first two tubes. Why is the water level in the middle tube higher than the first?

Note that the last water column is affected by the pressure in the final (wide) tube. Due to turbulence in the air flow, the Bernoulli effect cannot be seen here. That is, the pressure is lower than you would expect from Bernoulli, since it does not apply to turbulent flow.

Measure the height difference between the water columns in the first two tubes. What is the pressure difference between them?

4. Ping pong ball and air jet: With the compressed air source connected to atube, try to balance a ping pong ball vertically on the air stream. Once youhave the ball balanced, you can even lean it over slightly and the ball willstill not fall. Why does it not fall off to the side?

Sketch the air flow around the ball when it is slightly off center, as shown. Show the direction of the net force on the ball in your sketch.

Place a funnel on the tube and put the ball in the funnel. Will the ball fallout of the funnel when the air is flowing? What if it is upside down?Sketch the situation and explain what is happening.



University Physics 1Lab 12: Fluid Mechanics

ReportName:______________________

partner name:______________________

Part 1: Archimedes' Principle

Materials:

object 1: _________________________________

object 2: _________________________________

object 3: _________________________________

Masses:

mass of object 1: _________________________ g

mass of object 2: _________________________ g

mass of object 3: _________________________ g

Volumes:

volume of object 1: _________________________ cm3




Densities:

density of object 1: _________________________ g/cm3



Submerged “apparent” mass, and difference from dry mass:

Differences:

submerged object 1: __________________ g __________________ g



Mass of displaced water, and percent difference from above:

mass of fluid displaced (g) % difference*

object 1

object 2

object 3

* between mass of fluid displaced and the difference between the dry and submerged “apparent” masses

Describe what Archimedes' Principle says about how these values should compare.


Part 2: Buoyancy Simulation

Floating in gasoline:% Wood submerged % Ice submerged % Styrofoam submerged

Density of Wood Density of Ice Density of Styrofoam

Create a formula to show how much of a floating object would be submerged in any fluid.

Floating with Styrofoam and brick above water:mass of brick mass of Styrofoam volume displaced

Discuss the relation between these three quantities.

Floating with Styrofoam below water:mass of brick mass of Styrofoam volume displaced

Discuss the relation between these three quantities.


Part 3: “Cartesian Diver”

How does it work?

Part 4: Fluid Flow Simulation

Pressure:

1. pressure change:

2. pressure change:

3. pressure change:

why?

4. does the shape of the tank play a role ?

why?

5. How does the density of the fluid relate to the pressure it exerts?


Flow:

Now change to the “Flow” tab. Take some time and play with the simulation. Answer the questions below as you play.

For each pipe, indicate increase, decrease or constant.

Speed Pressure


Water Tower:

1. dependence on height of the tank:

why?

dependence on fluid density:

why?

2. path of the fluid steam:

3. compare speeds in the three circumstances:

4. what about the height the fountain achieves?


Part 5: Fluid Dynamics Demos

1. Cart with rotating barrel and fan: What is direction of the net force on the cart?

Draw a sketch of the air flow, showing the direction of the net force.

2. Hanging Cans: Sketch the air flow and force on the cans.

3. Venturi tube with air compressor: Why is the water level in the middle tube higher than the first?

What is the pressure difference between the first two tubes?


4. Ping pong ball and air jet: Why does the ball not fall off to the side?

Sketch the air flow around the ball when it is slightly off center, as shown in the figure.Show the direction of the net force on the ball in your sketch.

Will the ball fall out of the funnel when the air is flowing? What if it is upside down? Sketch the situation and explain what is happening.


University Physics 1Lab 13: Oscillations

Objectives:

• measure the elastic constant of a spring• measure damped and forced oscillations of a spring• determine what factors contribute to the period of a pendulum

Theory:

The application of to a system with a linear restoring force (such as a spring ) leads to a 2nd order differential equation: , where

gives the frequency of oscillation.

The resulting motion is called simple harmonic motion (SHM), described by

where .

Equipment:

set of springs, stopwatch, slotted mass set, string, wave driver, function generator,computer (with Logger Pro)

Procedure:

Part 1: Measuring the spring constant

1. Set up a square arrangement of support bars, following the model in the lab. Obtain two springs: spring 1 should be of low spring constant and spring of relatively high spring constant.

2. Place a weight on the hanger, hang the mass from spring 1 and measure the distanceto the bottom of the hanger from the bar. Repeat this several times for each spring with a variety of masses. Compile your data in a spreadsheet. Measure the slope of the F versus x graph to find the each spring constant.

3. If you get a spring constant less than one, double-check your calculations or check with the instructor.

Lab 13: Oscillations page 1 of 4

Part 2: Spring Oscillations

1. With spring 1, choose a mass that allows it to oscillate fairly slowly (~1 Hz). Place the position detector under the mass and make sure that the mass will not get closer than20 cm to the detector during oscillation.

2. Start the oscillation then start the data recording, taking 5 seconds of position data.Record the mass (m) of the oscillator (including the hanger), and the spring constant(k). Record the amplitude of oscillation, , which may be derived from the min-maxof the graph (in the toolbar, use “Analyze > Statistics”). Also find the oscillationperiod, , from the graph. Record uncertainties with all data.

3. From these data compute the angular frequency and . Find the percent

difference between these quantities.

3. Repeat steps 1-3 for spring 2.

4. Return to spring 1 and record the oscillation for 5 seconds. Select this graph and clickthe “curve fit” button in the toolbar. Fit the cosine function to your data (if it does not appear in the menu you may have to define it as “A*cos(B*t+D)+E)”). Compare the curve fitting data with this function: . Record the values of theconstants in the equation: , , , and .

5. Use these data (and your mass) to compute the spring constant for this spring. Does your result agree with your answer from Part 1?

6. Now repeat step 4 two more times, but varying the amplitude of oscillation. Fit thesine function to your results in each case. How does the frequency (or period) dependon the amplitude of the oscillation?

Part 3: Damped Spring Oscillations

1. For spring 1, set up the data recording to run for 120 seconds (click the “data collection” button in the toolbar).

2. When complete, select this graph and click the “curve fit” button in the toolbar. Fit the sine function with decaying exponential to your data: A*exp(-Bt)*cos(C*t+D)+E). Compare the data with this function: . Record the values of the constants in the equation: , , , , and .

3. From these data, determine the damping constant .

4. From the Data menu select “New Calculated Column”. Use your data above to graph the “envelope” exponential function on the same axes as your oscillation. Print this graph and attach it to your lab report.


Part 4: Forced Spring Oscillations

1. Take spring 2 and a mass that will allow it to oscillate at about 2 Hz. Hang it and the mass on a string passing over a pulley on the bar assembly. The other end of the string should be tied to an oscillating object (called a wave driver) which is powered by a function generator. Arrange the motion detector under the mass as before so youcan record mass oscillations.

2. Set the function generator to zero amplitude before you turn on the power. Turn on the power, and set it to deliver a sine wave at 1.0 Hz (you will need to use the “range”buttons and the frequency “adjust” knob). Increase the amplitude slightly until a small oscillation is visible at the wave driver.

3. Record a few seconds with the motion sensor (click start and stop). Record the amplitude of the oscillation and the driving frequency. You may want to create a new calculated column in Logger Pro to compute the amplitude in real time:(max(“Position”)-min(“Position”))/2. Increase the frequency slightly, bring the oscillating mass to rest, and repeat the amplitude measurement at the new frequency.

4. Make several frequency-amplitude measurements at frequencies below, at, and above resonance, most of them near the resonant frequency. Create a scatter plot of the response curve: amplitude versus frequency.

5. At what frequency ( ) is the peak amplitude? Convert this to angular frequency ( ). Use this value (and the mass) to compute again the spring constant.


Part 5: Pendulum Oscillations

1. Make a simple pendulum with a string and hanging mass. Use a compact mass, notthe mass hanger, to approximate a simple pendulum. Record the mass and thependulum length (from the pivot to the center of the hanging mass). Measure thetime for 10 oscillations, then divide to find its period.

2. Predict how you think changing the mass, length, and amplitude of the pendulum willaffect its period. Record your predictions.

3. Change the pendulum length three times and find the new period each time. How dolength changes affect the period? Make sure the length changes are substantial.

4. Change the pendulum mass three times and find the new period each time. Makesure the mass changes are substantial. Do mass changes substantially affect thependulum period?

5. Change the pendulum amplitude three times and find the new period each time.Make sure the changes are substantial, but keep the amplitude under 15º max(otherwise it will no longer be in simple harmonic motion). Do amplitude changessubstantially affect the pendulum period?

6. Try to explain why you got the result you did in question 4. (Hint: does free-fallacceleration depend on the mass of the falling object?)


University Physics 1Lab 13: Oscillations

Report

Name:______________________

partner name:______________________

Part 1: Measuring the spring constant

Spring constants:

k1 = ________________ k2 = ________________

Attach data and graphs to this lab report. You may submit one graph per group. If your graph is attached to your partner's report, please note that here.

Part 2: Spring Oscillations

m k A T % diff

Spring 1

Spring 2

4. For spring 1, .

= =

= =

5. spring 1:

6. How does the frequency of oscillation vary with amplitude of the oscillation?


Part 3: Damped Spring Oscillations

function: .

=

=

=

=

=

3. spring 1:

Part 4: Forced Spring Oscillations

Attach a graph of the response curve (amplitude versus frequency).


Part 5: Pendulum Oscillations

first pendulum

mass: _______________ length: _______________

average period: _______________

period change predictions (circle one)

Increasing the pendulum length will (increase) (decrease) (not change) the period.

Increasing the pendulum mass will (increase) (decrease) (not change) the period.

Increasing the oscillation amplitude will (increase) (decrease) (not change) the period.

period change observations from experiment:

explain these observed results:



University Physics 1Lab 14: Waves

Report

Name:______________________

partner name(s):______________________

Part 1: Predicting Pulse Velocity on a Spring

Cubic function fit (A+BY+CY^2+DY^3):

Where is the predicted speed greatest?

Explain:

Part 2: Measuring Pulse Velocity on a Spring

attach your data and graphs of velocity versus height y (predicted and measured)

Part 3: Standing Wave on a String

initial mass density (μ0) of elastic string: μ0=mL0

= ______________________

length of string available to wave: L = ______________________

stretched total length: L01 = ______________________

Lab 14: Waves page 1 of 4

actual mass density (μ1): μ1=L01

L⋅μ0 = ______________________

string tension: T = ______________________

Sketch the shape of the oscillating string:

frequency of standing wave: f = ______________________

wavelength of standing wave: λ = ______________________

velocity of standing wave: v = ______________________

sketch frequencyHz

number ofwavelengths

wavelengthm

velocitym/s


average wave velocity: v = ______________________

wave velocity (from tension): v = ______________________

percent difference: % diff = ______________________

Predictions: With higher tension in the string, the fundamental standing wave will (increase, decrease, or not change)

wave velocity: ____________________

frequency: ____________________

wavelength: ____________________

Observations: With higher tension in the string, the fundamental standing wave will (increase, decrease, or not change)

wave velocity: ____________________

frequency: ____________________

wavelength: ____________________



University Physics 1Lab 14: Waves

Objectives:

• to predict and measure wave speed in a long spring• to measure the velocity of different kinds of waves by setting up a standing wave with

a known frequency.

Theory:Although the velocity of a wave can be found from its frequency and wavelength ( v = fλ ), the velocity will not change if either f or λ are changed. In order to change thewave velocity, you must change the nature of the medium in which the wave travels.For waves on a string, the velocity is given by

where is the string tension (in N) and is the string's linear mass density (that is,its mass per unit length in kg/m).

When a wave is confined to a length , a standing wave will result whenever thefrequency (and velocity given by ) yield a wavelength such that

where is an integer.

Equipment:

slinky spring, computer with camera and Logger Pro, elastic string, wave driver, lab jack,table-mounted pulley, hanging masses


Procedure:

Part 1: Predicting Pulse Velocity on a Spring

For a vertically hanging spring, the wave velocity varies along the length. At a given point its tension equals the weight of the spring hanging below that point. The mass density is also changing along the length of the spring. We will measure the tension and mass density at all points to predict wave speed.

1. Obtain a long spring and set up a T-shape support (see lab model). Allow the spring to hang from the support so that the end is just above the floor. Get some masking tape and put a small piece on the spring marking every 10 loops, counting from the bottom to the top.

2. With a 2-meter stick, measure the height from the floor ( ) to each 10-loop marker. Record your data in the spreadsheet provided. For , should be the distance in cm from the floor to the bottom of the hanging spring.

3. Find the mass per loop of spring as follows. Measure and record the total mass of thespring in the spreadsheet (in kg). Enter the number of loops counted (the multiple of 10 that you marked last with tape in step 2). With the spring completely compressed, determine what fraction of the spring that this number of loops occupies. The spreadsheet will then divide the two to find the mass per loop.

4. The spreadsheet now has enough data to find the mass of spring hanging below each point on the spring. It will report the tension at every height. It will also compute the mass density from . From these it will compute the predicted wave speed at each height ( ).

5. Finally, we need a way to predict what the wave speed will be at any height . We will do this by fitting a polynomial to the data of versus . Open Logger Pro, then copy and paste in the versus data from the spreadsheet. Make a graph of speed vs y data and click the “curve fit” button in thetoolbar. Choose the equation for a cubic(A+BY+CY^2+DY^3) and “try fit”. If the dataare not well fit check with the instructor,otherwise click OK. Your graph should looksimilar to the one shown here (the coefficientsyou need are in the box). Record thecoefficients of the fit in the lab report.

6. Observe the predicted graph of speed vs height. At what point in the spring is the speed greatest? Explain why this is.


Part 2: Measuring Pulse Velocity on a Spring

1. Restart Logger Pro to remove your old data and open the “video capture” window from the Insert menu. Position the camera so it can see the entire spring against a dark background. With the spring initially at rest, give it a vigorous and very rapid transverse pulse.

2. When ready, take a video (start capture, then stop capture). At some point in the video a meter stick should be held near the spring. If you want to take another video, first remove the previously recorded video. Remove the video capture window when you have a good recording.

4. Find the playback window and make it larger for ease of use. Click the “Set Origin” button and then click the bottom of the spring. Use the meter stick to set the length scale in the video (use the “set scale” button in the video window).

5. Find the point in the video where the pulse is created, then advance frame-by-frame to see it move down the spring. When the pulse is clearly visible, back up frame-by-frame until it becomes difficult to see. Then begin placing points on the pulse as it travels away, ending before it reflects back up.

6. Create a “new calculated column” (from the Data menu) for the wave speed: the absolute value of the y-velocity. Make a graph of wave speed versus y. You may haveto neglect points near the top of the spring where the pulse is not well-formed.

7. Create a “new calculated column” called “predicted v” and enter the cubic formula from Part 1 step 5. The Y variable should be the Y values from the video analysis. Plot the predicted velocities in the same plot as the measured velocities from the video analysis. If there is not reasonable agreement, check with the instructor. Attach a printout of the graph.

Part 3: Standing Wave on a String

1. Measure the mass (m) and length (L0) of an elastic string. Note that L0 should be the length of whole string if it were untied and laid out flat. Calculate the string's initialmass density (μ0) in standard metric units.

2. Tie the string to a fixed point and allow the other end to pass over a pulley. On the end over the pulley, hang a known mass. Use whatever mass will hold the string under tension without touching the floor. Connect the wave driver to a point of the string near where it is tied; the string should be firmly in the notch of the wave driver. Keep the wave driver as near the tied end as possible.

Measure the length of the string that will hold the wave (L). This is the distance from the wave driver to the top of the pulley.


3. Due to stretch of the elastic, the mass density is now reduced from its initial value μ0 .With the hanging mass providing tension, grasp the string at the top of the pulley and move it toward the tied end until the tension is zero. While the string is relaxed, measure the (now shorter) length from the tied end to the point you are holding it, call this L01 .

The mass density of the stretched string (μ1) is reduced by the ratio of L01 to L .

Record the corrected mass density: μ1=L01

L⋅μ0

4. Use the force of gravity on the hanging mass to calculate the string tension (T). For greater accuracy, approximate the mass of string which is also hanging over the pulley (hanging length × μ1) and add this to the hanging mass.

5. Start the function generator, driving the string with a sine wave at a frequency near 0 Hz. Slowly increase the frequency until the first standing wave appears. (Use the smallest amplitude that gives a nice wave; if it starts to rattle, your amplitude is too large.) This is called the fundamental standing wave. Record the frequency (f ) at which this standing wave appears. Sketch the shape of the oscillating string.

6. The wavelength of this wave (λ) with be some multiple of your value L (from question 2). Record the wavelength.

7. Use v= f λ to calculate the wave velocity on this string.

8. Copy the sketch, frequency, wavelength, and velocity from the steps above into the first row of the table in the lab report. Increase the frequency to find the next three standing waves. Complete the data table.

9. Use the equation for string velocity to find another check on wave velocity. Give the percent difference between these two velocities.

10. Suppose more mass was added to increase the string tension, and then the fundamental standing wave is again produced. Predict what should happen to the wave velocity, and the frequency and wavelength of it.

11. Now increase the hanging mass slightly for a higher string tension. Find the fundamental standing wave on the string and check your predictions.


University Physics 1Lab 15: Sound

Report

Name:______________________

partner name(s):______________________

Part 1: Standing Sound Waves (open-closed cavity)

tuning fork frequency: f = ______________________

sound velocity (based on temperature formula): v = ______________________

sound wave wavelength: λ = ______________________

expected standing waves:

sketch length of aircolumn (L)

observed standing wave lengths: comments:

L1 = ______________________

L2 = ______________________

L3 = ______________________

Lab 15: Sound page 1 of 2

Part 2: Standing Sound Waves (open-open cavity)

predicted frequency: f = ______________________

standing wave sketch:

prediction correct?

Part 3: Doppler Effect

2.angular frequency = _______________________

source frequency = _______________________4.

radius: r = ______________________

period of rotation: = ______________________

speaker speed: = ______________________5.

predicted frequency: = ______________________6.

measured frequency: = ______________________7.

period of rotation: = ______________________

speaker speed: = ______________________

predicted frequency: = ______________________

measured frequency: = ______________________8.

Compare:


University Physics 1Lab 15: Sound

Objective:

The purpose of this lab is to measure the velocity of different kinds of waves by setting upa standing wave with a known frequency.

Theory:

The speed of sound can be modeled by the equation

where T is the air temperature in Kelvins ( ).

A standing sound wave can be made in a tube that supports a certain fraction of thewavelength.

The Doppler Effect shifts the frequency of a source ( ) to an observed frequency ( )according to

assuming the observer is not moving.

Equipment:

water resonance tube, tuning forks, and DI water, copper tube, Doppler effect apparatus,computer (Logger Pro), Vernier interface and microphone


Procedure:

Part 1: Standing Sound Waves (open-closed cavity)

1. Get a water resonance tube, and fill the container with water until the tube is nearly full. Find a tuning fork with a frequency greater than 300 Hz and record its frequency.

2. Check the room temperature and calculate the expected velocity of sound in the room. Use this velocity and the tuning fork frequency to calculate the wavelength of the sound wave it will produce.

3. Sketch the standing waves that should resonate with the wavelength you calculated. Include the fundamental and all harmonics up to a tube length of 1.0 m. For each sketch indicate the length of the air column (L) at which the standing wave can exist.

4. Hold the tuning fork above the mouth of the tube, as close to the tube as possible with touching it, with the two fork tines in a vertical plane. Strike the tuning fork and adjust the water level. Record the air column lengths at which the sound volume is maximum. At resonance, you should notice a substantial difference in volume when the fork is held above the tube or to the side of the tube.

5. Comment on whether your results agree with the predicted lengths.

Part 2: Standing Sound Waves (open-open cavity)

1. Obtain the copper tube (both ends open) and measure its length. Also obtain tuning forks of the following frequencies: 256 Hz, 384 Hz, 426 ⅔ Hz, and 480 Hz.

2. Consider the various standing waves that the open-open tube will support. Predict which of the tuning forks will resonate in the tube and draw the corresponding standing wave.

3. Test the four tuning forks. Was your prediction correct?


Part 3: Doppler Effect

1. Setup: Connect a microphone via the Vernier interface to a computer running Logger Pro and obtain a Doppler Effect demo device. Click the “Data Collection” button (looks like a clock) and set the duration to 1.0 second and the sampling rate to 50 000samples per second (or use the maximum possible sample rate).

2. Measure : Turn on the speaker and record a small portion of the sound wave whenthe source is stationary. To get the frequency, click and drag a selection box around the data in very short time interval, then click the “Zoom In” button. Select several periods of this data and click the “curve fit” button. Fit a sine function to the selected data to find its angular frequency, (the coefficient of the time ). Record (use all digits) and give its relative uncertainty. Use to find the source frequency and record it with an absolute uncertainty (it has the same relative uncertainty as ).

3. Collect data: Set the demo device to make a brief sound only once per revolution. Position the microphone (1) in the plane of the circular motion, (2) in a direction pointing toward the approaching speaker when it is on and (3) as near the speaker asis safely possible. Correct positioning of the microphone is important. Turn on the sound, begin rotating the demo device at a constant angular velocity, and then click “Collect”. You should have one second of waveform.

4. Measure : Use a ruler to measure the radius of the circle that the speaker will move in, . Use your data to find the time the source takes to make one revolution, the period of rotation, , in seconds. Recall that the speed of circular motion is onecircumference per period . Use this relation to find the speed of the speaker, .

5. Predict frequencies: Use the Doppler Effect to predict the frequency observed whenthe source is approaching the observer at the speed . The approaching frequency can be called (the Doppler equation when using the –). Also calculate the observed frequency when the source is receding, .

6. Measure : As in step 2, measure the frequency of the sound during one of the highvolume portions of data. Record the measured approaching frequency with its absolute uncertainty.

7. Measure : Repeat steps 3-6 to measure the receding frequency . Record it withits absolute uncertainty.

8. Compare: Discuss how your measured values compare to predicted.



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University Physics 1 - madisoncollegephysics.netmadisoncollegephysics.net/223/extras/lab_manual_223-v1.pdf · General Lab Instructions Lab 1: Measurements Lab 2: Vectors ... To express