For a lecture demo in front of class, a little cart (mass 0.5 kg) travels on a l

Question

For a lecture demo in front of class, a little cart (mass 0.5 kg) travels on a long, straight, level air track. Shown here is a graph of velocity vs. time of the cart. Let?s define right to be the positive direction. 1. (5 pts.) Calculate the net force on the cart at t=3s. Pay attention to the direction and show all your work. 2. (5 pts.) What is the velocity at t=2.5 seconds? Be sure to explain your answer (i.e. in which direction is the car moving and what is the magnitude of the velocity). 3. ( 5pts) For the entire period of time from t=0 to t=5 sec, what is the net work done on the cart? Be sure to show your work. 4. (5pts) At t=5 seconds, the air for the air track is suddenly turned off, so kinetic friction (alone) causes the cart to grind to a halt in another 0.5 sec. Let the mass of the track itself be 5.0 kg, i.e. ten times the mass of the little cart. Calculate the coefficient of kinetic friction between the cart and the track. Be sure to show your work.

Explanation / Answer

1) first find acceleration

a = dv/dt = slope of v = (-2-4)/(3.5-2)= -4 m/s^2

F = ma = 0.5*-4 = -2 N

so 2 N to the left

2) we can just read the velocity off the graph it is 2 m/s to the right (since poitive)

3) W = dKE = 1/2 m (vf^2 - vi^2) = 0.5*0.5*(2^2 -4^2)= -3 J

4) so v= v0 + at
a = -u g

0 = 2 - u*9.81*0.5

u=0.408

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