Ip a 45-kg crate is placed on an inclined ramp. when the angle the ramp makes with the horizontal is increased to 24 ∘, the crate begins to slide downward.

There two problems related to this problem:

First is the coefficient of static friction between the map and the crate.

And the second one is at what angle does the crate begin to slide if the mass is doubled.

1. To look for the coefficient of static friction:

ΣF = 0

μ x m x g x cos θ = m * g * sin θ

μ = sin θ / cos θ = tan θ

μ = tan 24 = 0.45

2. At what angle ... the solution is:

The static friction or μ does not depend on mass, so the angle is still 24.