Problem 2.

(University Physics, 12th Edition, Young & Freedman 6.33) A 10-kg box moving at 5 m/s on a horizontal, frictionless surface runs into a light spring of force constant 100 N/cm. Use the work-energy theorem to find the maximum compression of the spring.

Solution:

We need to write down the energy conservation in the present problem:

The initial energy is just the kinetic energy of the box:

The final energy is the elastic energy of the spring:

Then

and