Question

While water skiing behind her father’s boat, Letty is pulled at constant speed by a force of 164 N from the tow rope that makes an angle of 10.0° (from the horizontal). If Letty’s mass is 65.0 kg, what is the coefficient of friction between her skis and the water?

Answer 1

0.265

Step-by-step explanation:

Draw a free body diagram. There are four forces:

Normal force Fn pushing up.

Weight force mg pulling down.

Tension force T at an angle θ.

Friction force Fn μ pushing left.

Sum the forces in the y direction:

∑F = ma

Fn + T sin θ − mg = 0

Fn = mg − T sin θ

Sum the forces in the x direction:

∑F = ma

T cos θ − Fn μ = 0

Fn μ = T cos θ

μ = T cos θ / Fn

μ = T cos θ / (mg − T sin θ)

Given T = 164 N, θ = 10.0°, m = 65.0 kg, and g = 9.8 m/s²:

μ = (164 N cos 10.0°) / (65.0 kg × 9.8 m/s² − 164 N sin 10.0°)

μ = 0.265