ACCELERATING CARTS, F = ma

NAME ____________________________ PARTNER ________________________ DATE _______

PURPOSE

(1) To study the change in acceleration of a moving mass when the applied force changes.

(2) To study the change in acceleration produced by a given force when the mass changes.

MATERIALS

Ticker timer, tape; set of masses; pulley with table clamp; string; triple beam balance; dynamics cart, air track and accessories.

INTRODUCTION

Newton's law of acceleration, a = F/m, states that an unbalanced force applied to a mass produces acceleration. Because of friction, this law seems to contradict common experience. When driving a car, for example, a constant force is required to keep the car moving with constant velocity. If the force is removed, the force of friction brings the car to a stop. In the absence of friction, however, the car continues to move with constant velocity after the force is removed. The continued application of force then results in acceleration. In this experiment you will study, the change in acceleration when a constant mass is subject to a varying force, and then the change in acceleration when the force remains constant and the mass varies. Friction will be found by graphing the results and examining the intercepts of the graph.

PROCEDURE

Constant mass with varying force, using dynamics cart and dot timer.

1. Measure the mass of the cart on the triple beam balance. Use a book to hold the cart while placing the tape in the timer and attaching the tape to the cart. Fasten the timing tape to one end of the cart and tie the string that passes over the pulley to the other end of the cart. Pass the string over the pulley (Note: there must be at least three masses such as 100 g, 200 g, 500 g on the cart before you begin) Fasten a 100 g mass (Remember the weight of 100 g is 0.100 kg * 9.80 ms-2) to the end.

2. Start the timer while holding the tape tight, then release the cart. When the 100 g mass hits the floor, stop the cart and then the timer. Remove the tape and label it "Trial 1." Mark on the tape where the mass hit the floor and do not use dots after this point.

3. Repeat this procedure for Trials 2, 3 and 4 moving masses so there is a net force equal to the weight of 200 g, 300 g and 500 g, respectively on the end of the string. Label these tapes.

Calculations

Place the tape for Trial 1 flat on a table. Measure the distance (to the nearest 0.001 m) from the first dot to a dot before the mass hit the floor. Count the number of dots (start counting at zero). Calculate the total time. Repeat for the other trials. Since each mass started at s =0 and t=0, you can use the equation s = at2/2 to calculate the acceleration for all four trials.

! DATA / RESULTS

TRIAL	TOTAL MASS	DISTANCE± ___	# OF DOTS TIME ± ___	ACCEL.	Weight on String = FORCE	ma
1
2
3
4

Constant force with varying mass, using the air track and gliders.

4. Set up and level the air track by adjusting the screw until a glider on the track remains stationary; connect a string from the glider with the least inertia over the pulley to a 50 g mass. For all four trials in this part of the experiment, keep 50-g on the string; the weight of the 50 g mass is the accelerating force. Put the stop photogate about 35 cm from the end of the track and the start photogate about 80 cm from the other end. Adjust the length of the string so that as the glider starts the timer the falling weight is a few centimeters below the pulley and stops the timer before it hits the floor. Carefully measure the distance between the photo gates.

5. Hold the glider at rest as close as you can to the start photogate using a pencil eraser. You should be able to hold it so close that if it moves even one millimeter the timer will start. It is important that the timing begin at the instant the glider begins to move. Be sure the timers are reset, then release the glider. Have your partner catch it at the end. Repeat the procedure a few times and record the average time.

6. For Trial 6 use the red glider.

7. For Trial 7 use the blue glider.

8. For Trial 8 use two red gliders connected train style with a paper clip. Other trials with masses that you choose are optional.

Calculations

From the distance and time calculate the acceleration. Also calculate the net force on the mass and compare this with mass x acceleration.

! DATA / RESULTS

TRIAL	TOTAL MASS	DISTANCE± ___	# OF DOTS TIME ± ___	ACCEL.	Weight on String = FORCE	ma
5
6
7
8

ANALYSIS / CONCLUSION

1. Determine whether your data verify the equation F = ma (a) from the graphs (b) by calculating ma and comparing with F. If your error is very large, it means you were not careful or did not follow instructions and you may need to repeat the experiment during a free period.

2. Using the data for Trials 1-4, plot a graph with the accelerating forces (X-axis) vs. accelerations (Y-axis). Use Excel for graphing if possible. Determine the linear best fit equation for the trendline. Determine the frictional force on the cart from the graph and/or the equation.

3. Using the data for Trials 5-8,

a) Plot a graph of acceleration as a function of total mass.. Determine the linear best fit power curve for the trendline.

b) Plot a graph of acceleration as a function of the reciprocal of total mass.. Determine the linear best fit linear curve for the trendline

3. Examine the equations carefully. Re-write them is the form and interpret each term in each equation; what does the each term/coefficient on the right of the equation represent in terms of the force and mass data.

4. For the dot timer find the average frictional force by using the intercept of the graph.

5. If the board or air track were tilted, how would it affect the intercept of each linear graph.

Honors Physics Lab

Acceleration  can be covered in a few ways using standard lab equipment.  

1.  Rolling carts down an inclined board works well.  Attach timer tape to a 60 Hz timer (available through supply companies) and let the cart roll from rest.  Students can then plot two graphs;  (1)  a distance vs time graph and (2) velocity vs time graph.  The slope of the latter yields the rate of acceleration.  Also, using the d-t graph, students can find instantaneous velocity by drawing a tangent line at any point on the curve, then finding the slope of the line at that time. Have students find the area under the curve of the v-t graph and compare it to the total distance traveled.  Try solving for distance using d = 1/2 at2 and for velocity using v2 = 2as to verify your results.  

2.  An alternative that's more personal is to attach a long piece of tape to the back of a student. Then have the student begin running immediately after the timer is turned on.  Plotting the two graphs above will yield the acceleration of the student and the top speed (where the d-t graph straightens out).