Question

Superball in Weakening Gravitational Field

Answer 1

A superball is bouncing vertically up and down. It has a velocity v_0 when
it strikes the ground. The acceleration due to gravity is slowly reduced by
10% during a very long period of time.
Assuming that the collisions of the ball with the ground are elastic, find the corresponding change in v_0

Answer 2

isnt g always constant

Answer 3

not if the gravitational field is weakening

Answer 4

hint is given
The slow change of the acceleration of gravity implies that we will have an
adiabatic invariant I
\[I=\frac{1}{2\pi}\int\limits p dq\]
let x be the height of fall

Answer 5

@UnkleRhaukus

Answer 6

When it says the field is weakening over a long time, we can assume that it doesn't do much to affect the bouncing ball. Elastic collision indicates that the ball doesn't lose energy on the bounce.

Recall that by conservation of mechanical energy mgh=0.5mv^2.
after weakening, it's 0.9*g*mh = 0.5mv^2. Since it's essentially not losing any energy while bouncing, we can say that v_0 will remain the same since the kinetic energy was determined by the initial drop height, but it would be worth noting now the ball bounces higher.