Question

In Figure 9-61, block 1 (mass 2.0 kg) is moving rightward at 8 m/s and block 2 (mass 4.8 kg) is moving rightward at 2.8 m/s. The surface is frictionless, and a spring with spring constant of 1180 N/m is fixed to block 2. When the blocks collide, the compression of the spring is maximum at the instant the blocks have the same velocity. Find the maximum compression.

Answer 1

Using conservation of momentum:

2*8 + 4.8*2.8 = (2+4.8)*vf = 6.8*vf

Solve for vf, the final speed of the blocks when they have the same velocity.

1/2*k*x^2 = 1/2*m*vf^2

Solve for x; k is the spring constant = 1180 N/m; x is the maximum compression of the spring