Question

A mass, denoted M, slides downward along a rough plane surface inclined at angle of 25.94 in degrees relative to the horizontal. Initially the mass has a speed of 7.51 m/s, before it slides a distance of 1.0 m down the incline. During this sliding, the magnitude of the power associated with the work done by friction is equal to the magnitude of the power associated with the work done by the gravitational force. What is the coefficient of kinetic friction between the mass and the incline?"

Answer 1

μ = 0.486

Step-by-step explanation:

Data:

Angle of inclination, θ = 25.94°

Initial speed of the mass, v = 7.51 m/s

Distance traveled, d = 1.0 m

considering the given condition, we have

μNcosθ = Mgsinθ

where,

N is the normal reaction = Mg

M is the mass.

μ is the coefficient of the kinetic friction

on substituting the values, we get

μ × Mg × cos25.94° = Mg × sin25.94°

or

μ = tan25.94°

or

μ = 0.486