Question 2.6.13: Two masses of 2.0 kg and 4.0 kg are held with a compressed s...
Two masses of 2.0 kg and 4.0 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a speed of 6.0 m s^{-1}, what is the speed of the other mass? (See Figure 6.11.)
Here our system consists of the two masses and the spring. There are no external forces here, since gravity is cancelled by the upward reaction forces from the table where the masses rest. The only force is the elastic force of the spring with which it pushes the masses away.
But this is not an external force so total momentum will stay the same. The spring exerts equal and opposite forces on each mass. Before the masses start moving apart, the total momentum is zero, since nothing moves. After the masses move away, the total momentum is (2 × 6 – 4 × u) N s, where u is the unknown speed of the heavy mass. Note the minus sign. The masses are moving in opposite directions, so one of the velocities (and also one of the momenta) is negative. Thus, 12 – 4u = 0 and so u = 3.0 m s^{-1}.