Question

a 1 kg block is sliding along a level plane with a speed of 5.2 m/s when it is 1.4 meters from a spring with stiffness constant 675 N/m. The block comes to rest when it compresses the spring by 0.16 meters. What is the coefficient of kinetic friction between the block and plane?

Answer 1

here,

the mass of block , m = 1 kg

the initial velocity , u = 5.2 m/s

s = 1.4 m

x = 0.16 m

the spring constant , K = 675 N/m

let the coefficient of kinetic friction between the block and plane be uk

using Work-energy theorm

- uk * m * g * (s + x) = 0.5 * K * x^2 - 0.5 * m * u^2

- uk * 1 * 9.81 * ( 1.4 + 0.16) = 0.5 * 675 * 0.16^2 - 0.5 * 1 * 5.2^2

solving for uk

uk = 0.32

the coefficient of kinetic friction between the block and plane is 0.32