Physics- coeffficient of friction

Question

Dana uses a rope to pull a box that weights 300 N across a level surface with constant velocity. The rope makes an angle of 30 degrees above the horizontal and the tension in the rope is 100 N. What is the coefficient of friction?

Answer 1

N = normal force

T = tension = 100 N

W = weight = 300 N

θ = 30°

f = kinetic friction

μ = coefficient of kinetic friction = ?

 

Since there is no acceleration, the opposing force of friction must be in equilibrium with the horizontal pull of the rope.

 

f = T cosθ

f = μN ⇒

μN = T cosθ

 

N + T sinθ = W ⇒

N = W - T sinθ

 

μ(W - T sinθ) = T cosθ ⇒

 

μ = (T cosθ) / (W - T sinθ)

 

Plug in T, θ, and W, which were given to you, and get μ.  You can finish from here.