Initially sliding with a speed of 1.9 m/s, a 1.8 kg block collides with a spring and compresses it 0.35 m before coming to rest. what is the force constant of the spring?

Let k = the force constant of the spring (N/m).

The strain energy (SE) stored in the spring when it is compressed by a distance x=0.35 m is

SE = (1/2) * k*x²

= 0.5 * (k N/m) * (0.35 m) ²

= 0.06125k J

The KE (kinetic energy) of the sliding block is

KE = (1/2) * mass*velocity²

= 0.5 * (1.8 kg) * (1.9 m/s) ²

= 3.249 J

Assume that negligible energy is lost when KE is converted into SE.

Therefore

0.06125k = 3.249

k = 53.04 N/m

Answer: 53 N/m (nearest integer)