Question

A 0.1 -kg piece of modeling clay is tossed at a motionless 0.1 kg block of wood and sticks. The block slides across a frictionless table at 15 m/s

a. At what speed was the clay tossed ?

b. The clay is replaced with a bouncy ball tossed with the same speed. the bouncy ball rebounds from the wooden block at a speed of 10 m/s. In this case, what would be the velocity of the wooden block?

Answer 1

Consider v be the initial velocity of the clay.
Initial momentum of the clay, P1 = mv, where m = 0.1 kg

After the collision, clay + wood moves with velocity, V = 15 m/s
Final momentum, P2 = (m + m) V

Equating both momentum,
mv = (m + m) V = 2mV
v = 2V
= 2 x 15 = 30 m/s

b)
Velocity of the ball before collision, v = 30 m/s
Velocity of the ball after collision, v1 = - 10 m/s
Consider v2 be the velocity of the wooden block after collision
Momentum before collision, P1 = mv
Momentum after collision, P2 = mv2 - mv1

Equating P1 and P2,
mv = mv2 - mv1
v = v2 - v1
Substituting the values,
30 = v2 - 10
v2 = 40 m/s