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Newton’s Second Law of Motion

Saddleback College Physics Department 1. Purpose To observe and measure the acceleration of an object in motion under a constant net external force and verify Newton’s Second Law of Motion 2. Theory

According to Newton’s Second Law, maFNET

= , NETF is the net force acting on the object

of mass m, which has an acceleration a . For a cart of mass 1m on a horizontal track with a string

attached over a pulley to a mass 2m , the net force

NETF on the entire system is the weight of the

hanging mass, gmFNET 2= , assuming a massless pulley, negligible friction and negligible air

resistance. According to Newton’s Second Law, this net force should be equal to ma , where m is the

total mass that is being accelerated, which is mM + in this experiment. The experiment will verify Newton’s Second Law, by checking that

ammgm )( 212 += eqn. (1) assuming the ideal circumstances described in italics above. Be sure to draw and label the complete Free Body Diagrams of the masses used in the experiment, and then apply Newton’s First and Second Laws to each F.B.D. and solve for the acceleration of the system. Do you get the same relationship for acceleration as equation (1) yields? 3. Equipment PASCO 2 meter Air Track PASCO Air Supply PASCO Air Cart Air cart sail Air cart hook Air track mountable super pulley A-Stand with threaded rod PASCO 750 Interface box PASCO Interface box power cord and SCSI Interface Cord PASCO Motion Sensor II Laptop Computer w/ Data Studio Approx. 1 meter string Hanging mass holder with masses 4. Procedure Equipment Setup

CAUTION: Be careful not to scratch or knick the air tracks as they are expensive and easily damaged. Never slide the cart across the air track unless the blower is running. This lab contains a lot of hoses and wires, be careful to keep them out of the way of the experiment and the experimenters.

Set up the pieces as in the picture below, making sure that the air cart is free to move through the length of the track.

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Clean the airtrack and underside of the carts very well with the provided ethanol and Chemwipes. Level the air track. To do this, turn on the air supply and place an unladen cart on the track and watch it move. If it moves and accelerates, then the track is not level. Use the leveling feet to achieve level longitudinal and latitudinal attitudes of the track. Once leveled, do not move the air track from its location. Note: Even if the track is level, the cart may still move due to the air currents.

To improve the motion sensor readings you should turn the air track down as low as possible, without experiencing frictional effects. You can test to see if friction is significant by letting your cart bounce back and forth off the rubber bands at either end of the track.

Position the motion sensor in line with the sail; make sure that the motion sensor itself is level according to the air track. If the motion sensor is not positioned correctly, the data will be dirty.

Attach a string to the base of the sail on the cart (the picture below has the string attached to the wrong part of the cart) and hang the string over the pulley placing a known hanging mass on the end opposite the cart. Make sure that the string is perfectly horizontal between the cart and pulley. The hanging mass will provide the force on the cart.

Computer Setup

Provide power to the PASCO 750 Interface box, connect the box to the computer with the SCSI cord and turn on the box, making sure the word “Honda” on the cord is facing upward when it gets plugged into the computer. Only after you have turned on the PASCO 750 Interface box 750 and plugged it into the computer, can you turn on the computer. (If you do not perform these tasks in the above listed order, your computer will not recognize the PASCO 750 Interface box.) When the computer is first turned on, it may have a Found New Hardware window open. If so, just ignore the window and proceed with the steps below. Start up Data Studio and select Create Experiment. Remember, if the program cannot find the Interface box right away, click Scan. If it doesn’t find it after you have clicked Scan, make sure that it is connected properly. If it is connected properly and everything seems to be in order, restart the computer and the Interface box should load properly.

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Under Experiment Set-Up, click Add Sensor or Instrument and a window will open. Then click on the small black arrow near the top of the window to open a drop-down menu and select Scientific Workshop Digital Sensors. Finally select Motion Sensor and click Ok. Plug the Motion Sensor into the channels indicated (usually 1 and 2). Since this is the first time using the motion sensor, a few words are required.

The Motion Sensor uses sound wave reflection to ascertain position. The gold disk emits a sound pulse and receives the reflected pulse allowing it to determine where the object is located. On the sensor itself, there is a switch that allows wide angle sound emission or narrow angle sound emission. For most applications, choose the narrow angle sound emission, it is good for up to 2 meters.

Now you can set the properties and pulse, or trigger, rate of the sensor. The sensor can be set to emit up to 120 pulses per second, but the pulses cannot travel very far. Conversely, it can send out 5 pulses per second and detect objects as far away as 8 meters. For this experiment, the Sample Rate should be set around 50 Hz.

Click on the “Motion Sensor” tab near the bottom left of the Experiment Setup window to calibrate the Motion Sensor. You should hear the Motion Sensor ticking and see the window shown below (possibly with different numbers in the Present Sensor Distance box). Place the Motion Sensor EXACTLY 1 meter away from a highly reflective target (like a book), making sure the surface of the book is perpendicular to the emitted sound waves, and click Set Sensor Distance = Standard Distance. The Motion Sensor will automatically recalibrate.

Under the Measurement tab on the Experiment Setup window, you have the opportunity

to choose what the sensor is going to measure. Turn off the Acceleration measurement, as seen in the picture below, making sure the Position and Velocity measurements are selected and click OK.

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The physical quantity, which the motion sensor measures, is position. Velocity and

acceleration are derived from the position function. Because of this, the velocity curve may come out looking dirty and unusable. If that happens, you can do either of two things: (1) readjust the motion sensor so that it is hitting the sail of the air cart (2) record only the position data and determine velocity based on the derivative of the curve-fit of the position curve. There is a fine art to the use of the motion sensor; the best thing is to experiment with its position and orientation until the velocity curve comes out cleanly. Data Collection Setup For this experiment, you will be using the

graphs function of Data Studio. In the Displays window on the left side of your screen, double click on Graph. Choose Position from the screen that comes up and click OK. A graph screen will come up and will be labeled with the appropriate measurement.

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From the data window on the left below, drag the velocity title (data) into the graph window. The graph window should split into two separate windows and be labeled appropriately, as seen below.

Graph Labels

Now, when you collect your data, the position and velocity curves will be plotted

simultaneously.

Note: To change the x and y scales on the graph, mouse over the Time (s) or (m/s) label (the cursor will change when you do it correctly) and click and drag in the direction you want the scale to change. If you drag it to the left, the scale decreases (less ticks per second), if it is dragged to the right, the scale increases (more ticks per second). Now, you should be ready to collect your data. Data Collection You will be performing this experiment with two different cart masses (the hanging mass will remain unchanged) and doing three trials for each cart mass. The challenging part of this lab is getting clean data on the velocity graph which is directly related to your alignment of motion sensors with cart sails and air currents. Be perseverant!

1) Attach the first hanging mass to the string and get ready to release the cart.

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2) Start the motion sensor and release the cart. As soon as the weight hits the floor, click Stop.

3) You should have two graphs, one for position and one for velocity. 4) If your data looks relatively clean (ask your Professor to be sure your data is adequate),

then proceed to the Data Studio Analysis section of the lab.

Clean data section

NOTE: As you can see, the position graph is parabolic and the velocity graph is linear. Do not worry about the junk on the velocity curve. If you have a section that is clean, like the one above, you can generally use it for your velocity calculations (constant acceleration produces a linear velocity curve). It is also a good idea to change the labels on your runs to reflect the weight used for the experiment.

5) Perform steps 1 through 4 at least two more times for the same masses. 6) Place additional mass on the cart and perform the experiment as before. You should have 3 trials for each cart mass, thus 6 graphs in total.

5. Analysis & Results

Your professor will tell you whether to use Excel or Data Studio for the analysis of this lab (Katherine’s students will use Data Studio!). The purpose of the analysis is to find the experimental acceleration of the cart and to compare that with the theoretical or expected acceleration based on Newton’s Second Law. By examining the slope of the best-fit-velocity curve (the graph of the derivative of the position curve), you will find the constant acceleration applied to the cart. You may also wish to look at the second derivative graph of the position curve to validate the velocity curve.

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Data Studio Analysis: Data studio has a built in curve fit tool that can be used to find the slope of any part of the graph.

Curve fit tool and dropdown box

Before you choose a curve fit, be sure that the velocity curve is selected (ie. The label is

highlighted). Choose linear fit from the dropdown and a slope line will appear. Caution, the curve fit will produce a line based on all the given data. To fix this, with your mouse, click and drag a box around the data that seems to be most applicable to the experiment (the clean section). The linear curve fit will readjust itself to reflect the selected data and give you the slope, which will be your acceleration.

Selected portion of graph

Slope of the graph

Record the slope of each graph in your laboratory notebook and print each graph from Data Studio. In order to print Data Studio graphs, save the file to disk and then print it out on the classroom computer. Do a rough comparison to see that the slope of the graph is close to the acceleration calculated using eqn (1). Now go back to the Data Collection section of this lab and complete steps 5) and 6).

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Data Analysis

Due to the presence of experimental error in both the slope of the graph (acceleration) and the calculation of acceleration using eqn (1), we will define the slope of the best-fit trendline to be your theoretical acceleration, and compare it with the experimental acceleration calculated from eqn (1). Thus enabling us to practice error propagation.

In the end you should have 6 graphs, all of which have a linear trendline drawn, and display the slope of the trendline. Calculate the average theoretical acceleration for each combination of masses (this should yield two different theoretical values). Compare each theoretical acceleration to the corresponding experimental acceleration, yielding two percent differences.

Cart Mass, 1m

Hanging Mass, 2m

Experimental Acceleration

Theoretical Acceleration

(slope) % Diff.

Cart Mass, 1m

Hanging Mass, 2m

Experimental Acceleration

Theoretical Acceleration

(slope) % Diff.

Questions: (Discuss in Conclusion) 1) Would you expect amm )( 21 + to be approximately the same value for PART I & II?

Explain why or why not? (Hint: Did NETF change from PART I to PART II?)

2) When calculating the net force on the system using mass 2 times gravity, why isn’t the mass of the cart included? (Hint: Drawing a Free Body Diagram of the cart may help.)

3) Why is the mass in maFNET

= not just equal to the mass of the cart? 4) Why is the acceleration of the cart not equal to g, the gravitational acceleration constant?

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Average: