Question

A block with mass 0.400 kg is on a horizontal frictionless surface and is attached to a horizontal compressed spring that has force constant k=200 N/m. The other end of the spring is attached to a wall. The block is released, and it moves back and forth on the end of the spring. During this motion the block has speed 3.00 m/s when the spring is stretched 0.160 m. (a) During the motion of the block, what is its maximum speed? (b) During the block's motion, what is the maximum distance the spring is compressed from its equilibrium position? (c) When the spring has its maximum compression, what is the speed of the block and what is the magnitude of the acceleration of the block?

Answer 1

As block moves back and forth, total energy ( sum of kinetic energy of block and spring potential energy ) of spring-block system remains constant.

Kinetic energy of block, K= mv2 /2

m is mass of block and v is it's speed.

Potential energy of spring, U = kx2 /2

k is spring constant and x is compression or extension in spring.

For x = 0, total energy is in the form of kinetic energy of block and v is maximum.

For v = 0, total energy is in form of potential energy of spring and x is maximum.