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 Suggested Teaching Activities

Impulse and Momentum

1. Introduction

The impulse-momentum theorem relates impulse, the average force applied to an object times the length of time the force is applied, and the change in momentum of the object:

Here we will only consider motion and forces along a single line. The average force, is the net force on the object, but in the case where one force dominates all others it is sufficient to use only the large force in calculations and analysis.

For this experiment, a dynamics cart will roll along a level track. Its momentum will change as it reaches the end of an initially slack elastic tether cord, much like a horizontal bungee jump. The tether will stretch and apply an increasing force until the cart stops. The cart then changes direction and the tether will soon go slack. The force applied by the cord is measured by a force sensor. The cart velocity throughout the motion is measured with a motion sensor. Using "datalogger software" to find the average force during a time interval, you can test the impulse-momentum theorem.

2. Objective

 Measure a cart momentum change and compare it to the impulse it receives. Compare average and peak forces in impulses.

3. Equipment List

 Datalogger interface Motion sensor Force sensor Dynamics cart and track Elastic cord String

Procedure

 1. Measure the mass of your dynamics cart and record the value in the data table. 2. Connect the motion sensor and force sensor to the datalogger interface. Reset the force sensor. 3. Open the datalogger software and the experiment worksheet. 4. Place the track on a level surface. Confirm that the track is level by placing the low-friction cart on the track and releasing it from rest. It should not roll. If necessary, adjust the track. 5. Attach the elastic cord to the cart and then the cord to the string. Tie the string to the force sensor a short distance away. Choose a string length so that the cart can roll freely with the cord slack for most of the track length, but can be stopped by the cord before it reaches the end of the track. Clamp the force sensor so that the string and cord, when taut, are horizontal and in line with the cart motion. 6. Place the motion sensor beyond the other end of the track so that the detector has a clear view of the cart motion along the entire track length. When the cord is stretched to maximum extension, the cart should not be closer than 0.4cm to the detector. 7. Reset the force sensor to zero. 8. Practice releasing the cart so it rolls toward the motion sensor, bounces gently, and returns to your hand. The force sensor must not shift and the cart must stay on the track. Arrange the cord and string so that when they are slack they do not interfere with the cart motion. You may need to guide the string by hand, but be sure that you do not apply any force to the cart or force sensor. Keep your hands away from between the cart and the motion sensor. 9. Start the datalogger software to collect data; roll the cart and confirm that the motion sensor detects the cart throughout its travel. Inspect the force data. If the peak is flattened, then the applied force is too large. Roll the cart with a lower initial speed. If the velocity graph has a flat area when it crosses the x-axis, the motion sensor was too close and the run should be repeated. 10. Once you have made a run with good distance, velocity, and force graphs, analyse your data. To test the impulse-momentum theorem, use the datalogger software to calculate the velocity before and after the impluse and record the value in your data table. 11. Now record the time interval of the impulse. 12. Perform a second trial by repeating Steps 9 - 11, and record the information in your data table. 13. Change the elastic material attached to the cart. Use a new material, or attach two elastic bands side by side. 14. Repeat Steps 9 - 12, and record the information in your data table.

DATA TABLE
 Mass of cart kg

 Trial Final Velocity Initial Velocity Change of Velocity Average Force F Duration of Impulse Impulse Elastic 1 (m/s) (m/s) (m/s) (N) (s) (N*s) 1 2 Elastic 2 1 2

 Trial Impulse Change in Momentum % Difference between Impulse and Change in Momentum Elastic 1 (N*s) (kg*m /s) or (N*s) (N*s) 1 2 Elastic 2 1 2

Analysis

 1 Calculate the changes in velocities and record the results in the data table. From the mass of the cart and change in velocity, determine the change in momentum as a result of the impulse. Make this calculation for each trial and enter the values in the second data table. 2 Determine the impulse for each trial from the average force and time interval values. Record these values in your data table. 3 If the impulse-momentum theorem is correct, the change in momentum will equal the impulse for each trial. Experimental measurement errors, along with friction and shifting of the track or force sensor, will keep the two from being exactly the same. One way to compare the two is to find their percentage difference. Divide the difference between the two values by the average of the two, then multiply by 100%. How close are your values, percentage-wise? Does your data support the impulse-momentum theorem? 4 Look at the shape of the last force versus time graph. Is the peak value of the force significantly different from the average force? Is there a way you could deliver the same impulse with a much smaller force? 5 When you use different elastic materials, what changes occur in the shapes of the graphs? Is there a correlation between the type of material and the shape? 6 When you used a stiffer or tighter elastic material, what effect did this have on the duration of the impulse? What effect did this have on the maximum size of the force? Can you develop a general rule from these observations?

Extensions

 Use other elastic materials and repeat the same experiment.

 Mechanics Distance and Time How steady is a pendulum? Impulse and Momentum

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