Question

A body starts from rest on a long inclined plane of slope 45°. The coefficient of friction between the body and the plane varies as µ = 0.3 x, where x is distance travelled down the plane. The body will have maximum speed (for g = 10 m/s²) when x = ______.

Options

• 9.8 m

• 27 m

• 12 m

• 3.33 m

Answer 1

A body starts from rest on a long inclined plane of slope 45°. The coefficient of friction between the body and the plane varies as µ = 0.3 x, where x is distance travelled down the plane. The body will have maximum speed (for g = 10 m/s²) when x = 3.33 m.

Explanation:

a = g sin θ - µg cos θ  

a = g sin θ - 0.3 xg cos θ

= `"g"/sqrt2-(0.3"g"x)/sqrt2=5sqrt2-0.3(5sqrt2)x=5sqrt2-1.5sqrt2x`

Velocity will increase until a = 0 and when v = v_max, then a = 0

0 = `5sqrt2-1.5sqrt2x`

x = `(5sqrt2)/(1.5sqrt2)`

x = 3.33 m