Question

a block accelerates at 3.3 m/s^2 down a plane inclined at an angle of 27°. find the kinetic friction coefficient between the block and inclined plane. acceleration due to gravity is 9.8 m/s^2

Answer 1

Answer:

0.13

Explanation:

Draw a free body diagram.  There are three forces:

Weight force mg pulling down.

Normal force N pushing perpendicular to the incline.

Friction force Nμ pushing parallel up the incline.

Sum of the forces perpendicular to the incline:

∑F = ma

N − mg cos θ = 0

N = mg cos θ

Sum of the forces parallel down the incline:

∑F = ma

mg sin θ − Nμ = ma

mg sin θ − mgμ cos θ = ma

g sin θ − gμ cos θ = a

gμ cos θ = g sin θ − a

μ = (g sin θ − a) / (g cos θ)

Given a = 3.3 m/s² and θ = 27°:

μ = (9.8 m/s² sin 27° − 3.3 m/s²) / (9.8 m/s² cos 27°)

μ = 0.13