For Number 8. please draw a diagram and do the math to explain the momentumFor Number 9. please also do the math to show the relations between impulse and momentumFinally for 10, please show how momentum and impulse relate to the Force-time graph shown. 8-10) A rubber ball and a clay ball have equal mass and are dropped onto a digital scale. The rubber ball bouncesback to nearly the same height. The clay ball sticks to the scale when it hits.8. Which one of these objects undergoes the bigger momentum change?A) Both of them undergo zero momentum change.B) Both of them undergo the same non-zero momentum change.C) The ballD) The clay9. Which of the following is true?A) The rubber ball has half as much impulse imparted to it as the clay ball.B) The rubber ball has twice as much impulse imparted to it as the clay ball.C) The rubber ball has 3/2 as much impulse imparted to it as the clay ball.D) The rubber ball has 2/3 as much impulse imparted to it as the clay ball.E) The rubber ball has the same impulse imparted to it as the clay ball.10. Which of the following graphs could represent, to the same scale, the force exerted by the scale on each ballas a function of time? Select an answer for the rubber ball and an answer for the clay ball.F (N)F (N)A)F (N)t(s)D)F (N)t (s)B)F (N)t (s)I (s)E)rubber ball:1 (s)clay ball:

8) Analyze the following figure. Let both balls have the velocity vi before the collision as they have the same mass and fall from the same height. Thus, their initial momentum is also the same. Here, pR, pC, and p0 represent the rubber ball’s momentum, the clay ball’s momentum, and the initial momentum of both the balls, respectively. The rubber ball bounces off to almost the same height after the collision, thus, its final velocity is the same as its initial velocity. Thus, the rubber ball’s initial and final momentum is equal in magnitude and opposite in direction. Thus, the change in rubber ball’s momentum is, Substitute the relevant values. Now, after the collision, the clay ball sticks to the scale, thus, its final velocity becomes zero and so its momentum. Substitute the relevant values. Thus, it can be concluded that the change in the rubber ball’s momentum is greater than the clay ball’s momentum.9) The impulse exerted on the scale can be represented as, Here, F and t represent the force that the ball exerts on the scale and the time for which the force is applied, respectively. The force exerted by the scale on the ball is the same as the force exerted by the ball on the scale. Thus, the impulse imparted on the ball is the same as the impulse exerted by the ball. Now, the impulse can be represented as the change in momentum as, Now, for the rubber ball, For the clay ball, Thus, the impulse imparted on the rubber ball is twice of the impulse imparted on the clay ball.10) From equation (1) and (2), Thus, the area of a force-time graph gives the change in the momentum of an object. From the given graphs, graph D and E represent the clay ball’s collision and the rubber ball’s collision, respectively. This is because, the change in the rubber ball’s momentum is greater than the change in the clay’s ball momentum, thus, the area of the force-time graph of the rubber ball’s collision should be greater than the clay ball’s collision graph. Also, after the collision, the clay ball keeps on applying the force on the scale as it gets stick to it. Whereas, the rubber ball exerts no force as it gets bounced off.