Determine the coefficient of kinetic friction between the block and the rough surface

Question

8.5-kg block is released from point A with speed of initial speed 2.2m/s. (Block is given a push) (Point A is 3.3m high). The track is frictionless except for the portion between points B and C (6.0m). The block travels down the track, hits a spring of force constant 1,950N/m, and compresses the spring 0.21m from its equilibrium position before coming to rest momentarily.

Determine the coefficient of kinetic friction between the block and the rough surface between B and C.

Input your answer to three decimal places.

Answer 1

Assuming the change in height = 3.3 m (otherwise the question is missing information):

Initial energy is entirely kinetic energy + gravitational potential energy: E₀ = ½mv² + mgh

Final energy is entirely spring potential energy: E_f = ½kx²

Assuming the portion between points B and C is flat (otherwise the question is missing information):

Energy lost to friction = f_k × d = μ_kmg × d = E₀ – E_f = mgh + ½(mv² – kx²)

Plugging in m = 8.5 kg, g = 9.8 m/s², h = 3.3 m, v = 2.2 m/s, k = 1950 N/m, x = 0.21 m, d = 6 m gives

μ_k = 0.505