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

  53 N/m  (nearest integer)

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