On a frozen pond, a 11.7 kg sled is given a kick that imparts to it an initial speed of v0 = 2.01 m/s. The coefficient of kinetic friction between sled and ice is μk = 0.111. Use the work kinetic energy theorem to find the distance the sled moves before coming to rest.

1/2 mv^2 = Fd

F = (mu)mg
so d = v^2/2g(mu)

To find the distance the sled moves before coming to rest, we can use the work-kinetic energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

First, let's calculate the initial kinetic energy (KEi) of the sled using the equation:
KEi = 0.5 * m * v0^2

where m is the mass of the sled and v0 is the initial speed. Plugging in the values, we get:
KEi = 0.5 * 11.7 kg * (2.01 m/s)^2 = 23.45217 Joules (rounded to 5 decimal places)

Next, we need to calculate the work done by friction (Wfr) on the sled. The work done by friction is given by the equation:
Wfr = -μk * m * g * d

where μk is the coefficient of kinetic friction, m is the mass of the sled, g is the acceleration due to gravity (9.8 m/s^2), and d is the distance moved by the sled before coming to rest.

Since the sled moves until it comes to rest, the work done by friction will cause an equal decrease in the kinetic energy of the sled, so:

Wfr = ΔKE (change in kinetic energy) = - KEi

Equating the two equations, we get:
-μk * m * g * d = - KEi

Now, solve for d:
d = KEi / (μk * m * g)

Plugging in the values, we get:
d = 23.45217 Joules / (0.111 * 11.7 kg * 9.8 m/s^2)

Calculating this expression, the distance the sled moves before coming to rest is approximately 18.72 meters (rounded to 2 decimal places).