A moving 1.60 kg block collides with a horizontal spring whose spring constant is 295 N/m. The block compresses the spring a maximum distance of 3.50 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.500. What is the work done by the spring in bringing the block to rest?
How much mechanical energy is being dissipated by the force of friction while the block is being brought to rest by the spring?
What is the speed of the block when it hits the spring?
1 answer
The work done by the spring is the elastic potential energy, which is (kx^2)/2. The energy dissipated by the friction is the work done by the friction force (the friction force x the distance). These two things added together (the work of the spring and the energy of the friction) must equal the kinetic energy of the block when it hits the spring. That's how you would calculate the velocity of the block.