Acceleration of a Laboratory Cart1

Equipment Needed:

1 Cart Track (short) 1-A-11 Set legs and endstops Demo Cart1 Carts OYS1 Level OYS1 Universal Clamp OYS1 10 Spoke Pulley OYS2 Mass hanger, masses and string Demo Cart1 Computer with Small Photogate attached

Part A.

INTRODUCTION

In the diagram to the right. gravity acts on the hanging mass (mw) to pull it downwards. This force, opposedby the friction of the system, acts to pull the mass down and also move the lab cart and the mass on top ofthe cart (mc) ((mc) is the combination of the mass of the cart plus any mass added to it) across the table. Inthis experiment, you will:

1. Determine mathematically the theoretical acceleration.

2. Determine the experimental acceleration using the computer for data acquisition.

Figure 1: Setup Assembly

Procedure1Adapted from PASCOc©1994, PASCO Scientific Roseville, CA

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1. Set up the apparatus as shown in Figure 1. Assemble the Smart Pulley photogate and start-up thecomputer.

2. On the computer, select Smart Pulley [Enter]:

(a) From the Main Menu, selectSensor Checkand test your sensor.

(b) When you have completed the check of your photogate, return to theMain Menu .

3. Place a total of 200 grams of mass on top of the cart and record the total mass of the cart plus addedmass as(mc) in yourTable 1.

4. Place 100 grams on the 50 gram mass hanger. Including the mass of the mass hanger, record the total(150 g) as (mw) in Table 1.

5. Move the cart backwards until the mass hanger almost touches the pulley.

(a) With the mass motionless, select [M ] - Motion Timer , on the main menu.

(b) Insuring the LEDIS NOT lighted.

6. Now press [Enter] on the computer.

(a) Release the mass hanger which will fall downward, pulling the cart along the track.

(b) Stop the timing just before the mass hanger reaches the floor by pressing [Return].

7. When the computer finishes converting the times, choose [G] which will move you to the graphingfunction. When you get to the graphing, select [A] which will interpret the timing as a linear motion.Choose [V] which will give you a velocity vs. time graph.

8. The next choices give you the style of graph wanted. Choose [S] Statistics, to indicate the statisticaldata, [L ] Line Connect, will be displayed along with the graph and [R] Regression, to plot the regres-sion or best fit line, also include [P] Point Protector and [G]Grid. To choose these, move the cursorto the choices and push the [Space Bar] changing the ”Off” to an ”On” next to the choices. Whencompleted, press [Enter] to have the computer plot the graph.DO NOT PRINT GRAPH .

9. At the top of the graph you should see three labels. They are:

(a) M – The slope of the graph

(b) B – The y-intercept

(c) R – The correlation coefficient (how close to a straight line, it is)

10. If the value forR is 1.00, the graph is statistically a straight line (ifR is not 1.00, redo the trial). Thisindicates that the acceleration is constant. Record the slope of the graph as the acceleration Table 1. inmeter/sec2. Study the graph as long as you wish, and when finished, press [ENTER]. Press [ESC]until you move to the main menu to make another run.DO NOT PRINT GRAPH .

ANALYSIS :

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Table 1:Trial and Data

mc mw Exper. Tension Applied Total Theor. % Diff.Accel Force Mass Accel.

g g ms2

N N g ms2

Cart + ’M’ the slope F Applied ColumnMass of the graph mwg mc + Mw F & C

by computer

1. Calculate the tension ”T” in the string. Put the value in Table 1. The tension in the string (if frictionis neglected) can be calculated as:

T = (mwg)(mc

(mc + mw)),

NOTE:BE ABLE TO DERIVE THIS EQUATION .

2. Calculate theApplied Force.

3. Fill in Total Mass.

4. Calculate the theoretical acceleration using the equation:

atheory =mwg

(mc + mw)

NOTE:BE ABLE TO DERIVE THIS EQUATION !

Questions

• Knowing the average Experimental Acceleration and the average Theoretical Acceleration, calculatethe frictional force for your run. Show your work below.

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• Calculate the coefficient of friction(µ) below for your run and compare it to the coefficients of frictionfound in the reference table posted in the classroom.

• What substances, does yourµ value, come closest to?

• Are these low friction carts?

• Explain your conclusion.

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