Question

1. Elmer Fudd pulls a 65.0 kg wooden crate of mass m across the floor with a force F at an angle of 34.0°. The coefficient of friction between the surfaces is m = 0.235. If the crate moves at a constant speed, what is the magnitude of the applied force F?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the wooden crate = m = 65 kg

Force applied by Elmer = F

Angle at which the force is applied = = 34^o

Normal force on the wooden crate from the floor = N

Coefficient of friction between the crate and the floor = = 0.235

Friction force on the crate = f

The crate moves at a constant speed meaning the acceleration is zero therefore all the forces on the crate area balanced.

From the free body diagram,

N = mg - FSin

f = N

f = (mg - FSin)

f = mg - FSin

FCos = f

FCos = mg - FSin

F(Cos + Sin) = mg

F[Cos(34) + (0.235)Sin(34)] = (0.235)(65)(9.81)

F = 156.02 N

Magnitude of the applied force = 156.02 N