a) i. Derive an expression for the acceleration of the cart on the inclined portion of the ramp. Express your answer in terms of ?, M, and physical constants, as appropriate.

ii. Use your expression from part (a)(i) and data from the graph to determine a numerical value for angle of the incline ?

b) The cart reaches the bumper with speed v1 and rebounds with speed v2. The cart is in contact with the bumper with a time ?t

i. Derive an expression for the magnitude of the average net forceF exerted on the cart by the bumper. Express your answer in terms of M , v1 , v2 , ?t , and physical constants, as appropriate.

ii. Is the force the bumper exerts on the cart directed to the left or to the right?

iii. Assuming the mass of the cart is 0.25kg , use your expression from (b)(i) and data from the graph to calculate the value for the magnitude of the average net force on the cart during the collision with the bumper.

1.25 1.00- .. .. . . . . . . . . 0.75 0.50 Velocity (m/s) 0.25 0.00 -0.25- -0.50 -0.75+ 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 Time (s) A group of students conducts an experiment in which they use motion sensors to measure the velocity of a cart of mass M as it rolls down a track inclined at an angle O relative to horizontal. The cart then makes a smooth transition onto a horizontal section of the track and moves to the right along the track. At the end of the horizontal section is an elastic bumper with which the cart collides and rebounds. The graph of velocity as a function of time for the entire motion of the cart is shown. There is negligible friction between the cart and the track