## Extra Credit 7

### Impulse and momentum

In this exercise you will analyze two video clips,  impulse_1.mp4 and the impulse_2.mp4.  The clips show a cart being pulled by a constant force F for some time interval ∆t.  The velocity of the cart at t = 0 is zero.   After the time interval the force is zero and the cart moves with approximately constant velocity.   You will determine the magnitude of the impulse I = F∆t received by the cart, and its velocity and momentum after the force has dropped to zero.

Procedure:

In the video clip impulse_1.mp4 the cart is pulled by a constant force for some time ∆t.  If you bring up the clip and use the step up button, you will see that the force sensor reading varies between 0.76 and 0.72 N until you get to approximately 1.4 seconds.  (The time box displays the time for each frame.)   At ∆t  ~1.4 s the force sensor reading drops to ~0.

During the first 1.4 s, when the force is not zero, the cart is accelerating.  Its velocity and therefore its momentum are changing.  The impulse F*∆t  is equal to the change in momentum ∆p = pfinal - pinitial = pfinal, since pinitial = 0.
After 1.4 s the force is zero, there is no acceleration, the cart is moving with constant speed.  Use the step up button to step to t ~1.4s.  Then calibrate and start taking data.   Find the position of the cart as a function of time.   Import your data into Excel.

Start with the impulse_1.mp4 clip.  To play a video clip or to step through it frame-by-frame click the "Begin" button.  The "Video Analysis" web page will open.

## Begin

• To find the magnitude of the impulse received by the cart, step through the video clip frame-by-frame and note the time interval ∆t through which the force acts.  Multiply the force sensor reading by ∆t to find the magnitude of the impulse I.
• To find the final velocity of the cart step through the video clip and start taking data after the force has dropped to zero.  Determine the  position of the cart as a function of time by stepping through the video clip frame-by-frame and by reading the time and the position coordinates of the cart off each frame.  Construct a spreadsheet with columns for time and position.  The slope of a position versus time graph yields the velocity of the cart.
• To find the magnitude of the final momentum p of the cart multiply its speed by its mass.
• Estimate the uncertainty in F, ∆t, and I.
To estimate your uncertainties you must think about the uncertainties in the experiment.  How well did you estimate the average force?  (The reading in the impulse_1. mp4 clip varies between 0.77 N and 0.70 N.  If you estimate the average force to be 0.73 N, the uncertainty is probably on the order of 0.02 N to 0.03 N.)  How well did you estimate ∆t?  (At what time exactly did the force drop to near zero?  There is probably a one frame or 0.07 s uncertainty.)  What is the uncertainty in the slope and therefore in v?  Which quantities have the largest percentage errors?  Some estimates are quite subjective, but others, such as the uncertainty in the slope, are computed by Excel using a well-defined algorithm.
In every measurement there are uncertainties.  It important to make reasonable assumptions about the magnitudes of these uncertainties.  Then one can check how the uncertainties affect the results.  For example, if you estimated an error of 5% in the force, you would have an error of 5% in pfinal.
• Compare I and p.

Repeat for the impulse_2.mp4 clip.