A woman drags a 10.4 kg box of books at a constant speed, applying a 17.4 N force at 23.5°. What is the coefficient of friction?



Answer :

Answer:

0.168

Explanation:

According to Newton's second law, the net force on an object is equal to its mass times its acceleration. Drawing a free body diagram, there are 4 forces on the box: weight force mg pulling down, normal force N pushing up, friction force Nμ pushing left, and applied force F pulling up 23.5° above the horizontal.

Sum of forces in the y direction:

∑F = ma

F sin θ + N − mg = 0

N = mg − F sin θ

Sum of forces in the x direction:

∑F = ma

F cos θ − Nμ = 0

Nμ = F cos θ

μ = F cos θ / N

Substitute:

μ = F cos θ / (mg − F sin θ)

Plug in values and solve:

μ = 17.4 cos 23.5 / (10.4 × 9.8 − 17.4 sin 23.5)

μ = 0.168