A superball is dropped from a height of 1 m and bounces a number of times before

Question

A superball is dropped from a height of 1 m and bounces a number of times before it is caught. Below are shown graphs of some of the physical variables of the problem. Match the graphs that best show the time dependence of the variables in the list below the graphs. (Assume for these first few bounces the superball can be treated as a perfect bouncer.) You may use a graph more than once or not at all. If none of the graphs work well for a variable, put N. Note: the time axes are to the same scale, but the ordinates {"y axes"} are not. The time t = 0 is taken to be the instant when the ball leaves the hand. Use a coordinate system in which the positive direction is taken as up and the origin is at the floor.

(a) The velocity of the ball
---Select--- 1 2 3 4 5 6 N

(b) The kinetic energy of the ball
---Select--- 1 2 3 4 5 6 N  

(c) The potential energy of the ball
---Select--- 1 2 3 4 5 6 N

(d) The momentum of the ball
---Select--- 1 2 3 4 5 6  N

(e) The total mechanical energy of the ball
---Select--- 1 2 3 4 5 6 N

(f) The position (y coordinate) of the ball
---Select--- 1 2 3 4 5 6 N

Explanation / Answer

a)

As the velocity increases at a constant rate as the ball reaches the ground ,so the velocity vs time graph will be as shown in graph 6.

b)

As KE is proportional to the velocity squared, so the graph will look like 3

c)

As the potential energy is maximum at t = 0 and it decreases at a non-uniform rate with time, so the PE graph will look like 5

d)

As momentum is proportional to velocity, the momentum curve is same as part (a)

So, answer is 6)

e)

Total mechanical energy remains constant, so answer is 4)

f)

Position is proportional to Potential energy,

So, answer is 5

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