Question

A moving 4.20 kg block collides with a horizontal spring whose spring constant is 458 N/m.

The block compresses the spring a maximum distance of 6.00 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.160. What is the work done by the spring in bringing the block to rest?

Answer 1

The work done by the spring in bringing the block to rest is 0.8232 joules. This energy is used to overcome the kinetic friction between the block and the surface.

Step-by-step explanation:

The work done by the spring in bringing the block to rest can be calculated using the work-energy principle. The work done on the block by the spring is equal to the change in the mechanical energy of the block. Since the block comes to rest, all the work done by the spring goes into overcoming the kinetic friction between the block and the surface until the block stops.

The potential energy stored in the spring when compressed is given by ½ kx², where k is the spring constant and x is the compression distance. The spring constant is given as 458 N/m and the maximum compression is 6.00 cm (0.06 m).

Using the formula for potential energy: ½ (458 N/m) × (0.06 m)² = 0.8232 J

This is the work done by the spring, as this energy is used to overcome the kinetic friction and bring the block to a stop.