Question

elastic ball (m=0.1kg) fall from 2m touch the rigid floor and bounce to 1.6m. how to calculate the momentum of the ball before and after the choc?

Answer 1

Momentum is given by the product of a body's mass and velocity. Mass is given to be 0.1 kg, so we calculate velocity just before and just after impact using the formula
\[v^{2}=u ^{2}+2as\]
where v is final velocity
u is initial velocity
a is acceleration acting on body (here, a=g=9.8 m/s^2 since acceleration is only due to gravity)
s is the distance travelled

Velocity of ball just before it hits the floor:
Ball started from rest, u=0 m/s, and travelled s=2m
Plugging all of these in the formula, we get final velocity
\[v=2\sqrt{10} m/s\]\[v=6.33m/s\]
Momentum \[p=mv=(0.1)(6.33)=0.63kg.m/s\]
Velocity of ball just after impact:
Ball bounces to a height s=1.6 m before momentarily coming to rest (final velocity v=0)
Here we calculate initial velocity u
\[u ^{2}=v ^{2}-2as=0-(-10)(1.6)=16\]\[u=4m/s\]
Momentum just after the ball hits the floor:
\[p=m u=(0.1)(4)=0.4kg.m/s\]

Answer 2

(**Considered g=10m/s^2, sorry about that.)