Question

A 3.00 kg mud ball has a perfectly inelastic collision with a second mud ball that is initially at rest. the composite system moves with a speed equal to one- third the original speed of the 3.00 kg mud ball. what is the mass of the second mud ball?

Answer 1

Perfectly inelastic collision is type of collision during which two objects collide, stay connected and momentum is conserved. Formula used for conservation of momentum is:

$m_{1} * v_{1} + m_{2} * v_{2} = m_{1} * v'_{1} + m_{2} * v'_{2}$

In case of perfectly inelastic collision v'1 and v'2 are same.

We have following information:
m₁=3 kg
m₂=? kg
v₁=x m/s
v₂=0 m/s
v'1 = v'2 = 1/3 * v₁

Now we insert given information and solve for m₂:
3*v₁ + 0*? = 3*1/3*v₁ + m₂*1/3*v₁
3v₁ = v₁ + m₂*1/3*v₁
2v₁ = m₂*1/3*v₁
2 = m₂*1/3
m₂= 6kg

Mass of second mud ball is 6kg.