An object is placed on a ramp which makes an angle of 25º with the horizontal....

Question

An object is placed on a ramp which makes an angle of 25º with the horizontal. If the object accelerates at a rate of 3.0 m/s2 down the ramp, what is the coefficient of friction between the object and the ramp

Answer 1

The magnitude of the force of gravity down the ramp is

W = mg sinθ

It is opposed by the force of friction of magnitude

f = μmg cosθ

Therefore, the net acceleration down the ramp is

a = (W - f)/m = g(sinθ - μ cosθ)

a = g(sinθ - μ cosθ) ⇒

μ = (sinθ - a/g) / cosθ

You know the values of a, θ, and g. Now plug in the numbers and get μ.

Answer 2

Draw the FBD, coordinate system, sum forces = acceleration.