Question

A ski starts from rest and slides down a 30 ∘ incline 70 m long.

A)If the coefficient of friction is 0.075, what is the ski's speed at the base of the incline?

B)If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the ski = m

Angle of the incline = = 30^o

Length of the incline = L = 70 m

Height of the incline = H = LSin

Coefficient of friction = = 0.075

Normal force on the ski from the incline = N₁

Friction force on the ski on the incline = f₁

Speed of the ski at the base of the incline = V

By conservation of energy the initial potential energy of the ski is equal to the kinetic energy of the ski at the bottom of the incline plus the work done against friction.

V = 24.44 m/s

Normal force on the ski from the level snow at the foot of the incline = N₂

Friction force on the ski from the level snow = f₂

Distance the ski travels along the level snow = D

The kinetic energy of the ski at the bottom of the incline is lost to the work done against friction as moves along the level snow.

D = 406 m

A) Speed of the ski at the base of the incline = 24.44 m/s

B) Distance the ski will travel along the level = 406 m