Question

A 1.07 kg block slides across a horizontal surface directly toward a massless spring with spring constant 4,794 N/m. The surface is frictionless except for a rough patch of length 0.461 m that has coefficient of kinetic friction 0.358. The initial velocity of the block is 4.12 m/s directed straight toward the spring. What is the maximum compression of the spring?

Answer 1

KE – W(fr) =PE(spring)
m•v²/2 - μ•m•g•s = k•x²/2
x= sqrt[(2/k) •(m•v²/2 - μ•m•g•s)] =
=5.5•10^-2 m =5.5 cm