Question

Consider two balls on a horizontal, frictionless surface. Ball A (with mass ma) is moving toward ball B (with mass mb = 1 kg). Ball B is initially at rest.a. (5 pts) If their collision is perfectly elastic, what should be the mass of ball A such that it stops upon collision if ball A's initial velocity is +3.1416 m/s?b. (5 pts) Using conditions in question (a), what is the speed of ball B after collision? Is it moving in the initial direction of ball A or opposite it?c. (5 pts) Consider this 2nd scenario: If the collision is perfectly inelastic, what is the speed of the balls after collision? [Use the mass that you calculated from question (a) for ball A.]d. (5 pts) Now, consider a 3rd scenario: Ball A (with arbitrary speed va) collides with a stationary ball B (mass is mb = 1 kg). After collision, you observed that ball A and ball B are now moving at the same speed va but toward opposite directions: Ball A is heading opposite its original direction, while B is moving along the initial direction of A. What is the mass of ball A?

Answer 1

Answer:

Explanation:

When two ball of identical mass collides perfectly elastically , there is exchange of velocity between the two balls .

Here ball be was at rest initially . After collision ball A comes to rest , so there is complete exchange of velocity . Hence ball A must have same mass as that of B . mass of ball A = 1 kg .

b ) Due to complete exchange of velocity , velocity of ball A will be picked up by ball B . Hence velocity of ball B = 3.1416 m /s . Yes it will be moving in the direction of ball A .

c )

In case of perfectly inelastic collision they will become  single mass

total mass = 2 kg

applying conservation of momentum law

their common velocity after collision = 1 x 3.1416 / 2 = 1.57 m /s

d )

Applying conservation of momentum law

initial momentum = Ma x va

they move in opposite direction after collision

their total momentum after collision

1 x va - Ma va

applying law of conservation of momentum

1 x va - Ma va  = Ma va

va = 2Ma va

Ma = .5 kg .