Center of MassHard
Question
A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity u. An elastic impact lasts for a time ᐃt.
Options
A.The average elastic force acting on the ball is 
B. The average elastic force acting on the ball is 
C.The kinetic energy of the ball increases by 2mu (u + v)
D.The kinetic energy of the ball remains the same after the collision.
Solution
u1 = v v2 = − (v + 2u) e = 1.
|vdt| = m (v1 − u1)
vdt = m (+ v + 2u + v)
vdt = 2m (u + v).
v =
u1 = v v1 = 2u + v
ᐃk =
mv12 − 
mu12 = [m (2u + v)2 − v2]
[4u2 + v2 + 4uv − v2]
= 2mu (u + v)
By energy compression
mv2 + 0 = (2m) + kx2
kx2 = ⇒ x =.
at maximum compression k = (m + m)v2 ⇒ k = mv2 = mv2/4.
|vdt| = m (v1 − u1)
vdt = m (+ v + 2u + v)
vdt = 2m (u + v).
v =
u1 = v v1 = 2u + v
ᐃk =
mv12 − mu12 = [m (2u + v)2 − v2] [4u2 + v2 + 4uv − v2]= 2mu (u + v)
By energy compression
mv2 + 0 = (2m) + kx2
kx2 = ⇒ x =.
at maximum compression k = (m + m)v2 ⇒ k = mv2 = mv2/4.
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