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.)

d = v² / (2μ g)

Explanation:

In the work relationship is equal to the variation of energy,

W = ΔEm

The work is defined by

W = F. d = F d cos θ

In this case the outside is the force of friction, which always opposes

to the movement, so the angle is 180 °

W = - fr d

The force of friction can be found with Newton's second law

fr = μ N

Y Axis

N - W = 0

N = mg

fr = μ m g

We substitute in the expression of work

W = - μ mg d

Now we use the relationship of work and energy

-μ mg d = 0 - ½ m v²

d = v² / (2μ g)