Need help with physics... Finiding the coeficient of kinetic and static friction when give: Mass Force Angle.?

Question

A 1000 N crate is being pushed across a level floor at a constant speed by a force of 500 N at an angle of 20.0° below the horizontal. Need help finding coeficient of kinetic friction between the floor and the crate. explanation would also be very helpful and appreciated.

Answer 1

Constant speed means the acceleration is 0, which means the net force is 0.

The vertical forces on the crate are its weight W, the normal force N, up from the floor, and the vertical component, Pv, of the pushing force.

The horizontal forces are the horizontal component Ph, of the pushing force and the frictional drag force D

The total pushing force and the angle are known so we can the numerical values of Ph and Pv.

Since the net force is 0 we have (choosing the signs correctly):

N = W + Pv
D = Ph

The drag force D is a function of the normal force and the coefficient of kinetic friction:

D = Ck x N

We can compute N and D so we can compute Ck.