You are asked to design spring bumpers for the walls of a parking garage. a freely rolling 1200 kg car moving at 0.70 m/s is to compress the spring no more than 7.2×10−2 m before stopping. what should be the force constant of the spring? assume that the spring has negligible mass.

We can solve the problem by using law of conservation of energy.

The kinetic energy of the car when it is in motion is

where m is the car mass and v its velocity.

Then the car hits the spring and it compresses it by a certain , so all the kinetic energy of the car is converted into elastic potential energy of the spring:

where k is the spring constant.

For the conservation of energy, K=U. Also, the problem says that the maximum allowed value for the compression is : if we use this value, we can write

that we can solve to find the spring constant k: