You are pulling a wagon up a ramp at a constant velocity Please calculate the kinetic coefficient of friction between the wagon and the ramp?

Question

Ramp is at a 23 degree angle from the ground. The mass of the wagon is 20 kg. Fp=152N and the Fp is at an angle of 48 degrees.

Answer 1

The coefficient of kinetic friction is equal to the ratio of the kinetic force to the normal force.

Equation ⇒ μ_k = (F_k / F_N)

The normal force, F_N, is equal in size to the perpendicular component, F_⊥, of the weight, w, of the wagon. The kinetic force, F_k, is equal to the parallel component, F_||, of the pulling force, F_P, up the ramp.

We will use the angle of the ramp to calculate the normal or perpendicular force and the pulling angle to the ramp, assuming the pulling angle is relative to the surface of the ramp, to calculate the parallel component or kinetic force.

 

GIVEN:

SOHCAHTOA

Ramp θ = 23°

Pulling angle = 48°

mass of wagon = 20 kg

F_P = 152N

 

UNKNOWN:

μ_k = ?

 

SOLUTION:

Weight of wagon: w = mg = (20kg)(9.8m/s²) = 196N

Normal force = perpendicular force: F_N = F_⊥ = mg cos23° = (196N)cos23° = 180.4N

Kinetic force = parallel force: F_k = F_|| = F_P cos48° = (152N)cos48°= 101.7N

μ_k = (F_k / F_N) = (101.7N / 180.4N) = 0.564 (not using sig figs)