Question

A sled of mass m is given a kick on a frozen pond. The kick imparts to the sled an initial speed of v. The coefficient of kinetic friction between sled and ice is µk.Use energy considerations to find the distance the sled moves before it stops. (Use any variable or symbol stated above along with the following as necessary: g.)

Answer 1

Given

Mass of the sled - m

Initial speed of the the sled - v

Coefficient of kinetic friction - µ_k

Acceleration due to gravity - g

Solution

The normal force acting on the object

N = mg

The friction resisting the movement

F = µ_kN

F = µ_kmg

The initial kinetic energy

E = ½ mv²

The friction will resist the movement of the sled, but the sled will try and move as long as it can perform the work against friction. It will come to rest when all of its kinetic energy is spent on doing work against friction

Work done = energy spent

W = E

Fd = E

µ_kmgd = ½ mv²

d = v²/2µ_kg