Question

1. two clay balls of masses m and 2m are heading directly towards one another on a frictionless surface. if the ball of mass m is traveling at a velocity of v, how fast must the ball of mass 2m be traveling for there to be no motion after the collision? assume that this is a perfectly inelastic collision.

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that \(p_{initial}=p_{final}\). Since there is no motion after the collision, \(p_{final} = 0\). Let the velocity of the ball of mass \(2m\) be \(v_{2}\). The initial momentum is \(p_{initial}=mv+(2m)v_{2}\). So, \(mv+(2m)v_{2}=0\).

Step2: Solve for \(v_{2}\)

From \(mv+(2m)v_{2}=0\), we can factor out \(m\) (since \(m
eq0\)) to get \(v + 2v_{2}=0\). Then, \(2v_{2}=-v\), and \(v_{2}=-\frac{v}{2}\). The negative sign indicates the direction is opposite to the direction of the ball of mass \(m\).

Answer:

The ball of mass \(2m\) must be traveling at a speed of \(\frac{v}{2}\) in the direction opposite to the ball of mass \(m\).