Answer:
0.47
Explanation:
Draw a free body diagram. There are 3 forces on the box:
Weight force mg pulling down,
Normal force N pushing up perpendicular to the ramp,
and friction force Nμ pushing up parallel to the ramp.
Sum of forces in the perpendicular direction:
∑F = ma
N − mg cos θ = 0
N = mg cos θ
Sum of forces in the parallel direction:
∑F = ma
mg sin θ − Nμ = ma
Substitute and solve for μ:
mg sin θ − (mg cos θ) μ = ma
g sin θ − g cos θ μ = a
g cos θ μ = g sin θ − a
μ = (g sin θ − a) / (g cos θ)
Plug in values and solve.
μ = (9.8 sin 32° − 1.3) / (9.8 cos 32°)
μ = 0.47
