Question

A block slides down a 40 degress incline. Its initial speed is 2.0m/s and after sliding a distance of 1.5 m it has a speed of 3.0 m/s. what is the coefficient of friction between the block and the incline?

The answer is 0.62, but I had trouble getting this.

Answer 1

here,

the initial speed , u = 2 m/s

the final speed , v = 3 m/s

distance , s = 1.5 m

let the coefficient of friction between the block and the incline be u

theta = 40 degree

using Work-energy theorm

work done by all forces = change in kinetic energy

Wg + Wf = 0.5 * m * (v^2 - u^2)

m * g * s * sin(theta) - uk * m * g * cos(theta) * s = 0.5 * m * ( v^2 - u^2)

9.81 * 1.5 * sin(40) - uk * 9.81 * cos(40) * 1.5 = 0.5 * ( 3^2 - 2^2)

solving for uk

uk = 0.62

the coefficient of friction between the block and the incline is 0.62