A 20 kg sled is being pulled along a horizontal stretch of snow covered ground by a horizontal force of 30 N. Starting from rest, the sled attains a speed of 2.0 m/s in 12 m. Using the work-energy theorem, find the coefficient of kinetic friction between the sled and the snow.

To find the coefficient of kinetic friction between the sled and the snow, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.

First, let's calculate the final kinetic energy of the sled. The formula for kinetic energy is given by:

Kinetic Energy (KE) = 1/2 * mass * velocity^2

Given that the sled has a mass of 20 kg and a final velocity of 2.0 m/s, we can calculate the final kinetic energy:

KE = 1/2 * 20 kg * (2.0 m/s)^2
= 20 J

Next, we need to calculate the work done on the sled. The work done by the horizontal force is equal to the force multiplied by the distance traveled. In this case, the force is 30 N and the distance traveled is 12 m:

Work (W) = force * distance
= 30 N * 12 m
= 360 J

Since the sled starts from rest, the initial kinetic energy is zero. Therefore, the work done on the sled is equal to the change in kinetic energy:

W = KE - KE_initial
360 J = 20 J - 0 J
360 J = 20 J

Therefore, the work done on the sled is equal to the change in kinetic energy.

Now, let's consider the work done against friction. Since the force of friction is in the opposite direction of the applied force, the work done against friction is negative. In other words:

Work against friction (Wf) = - force * distance

We need to find the force of friction, so rearranging the equation, we get:

force = - Wf / distance

The work done against friction is equal to the force of friction multiplied by the distance traveled. In this case, the distance traveled is 12 m:

360 J = - force * 12 m

Solving for the force of friction:

force = - 360 J / 12 m
force = - 30 N

The negative sign indicates that the force of friction is in the opposite direction of the applied force. Now we can calculate the coefficient of kinetic friction using the following equation:

force of friction = coefficient of kinetic friction * normal force

The normal force is the force exerted by the surface perpendicular to the sled. In this case, since the sled is on a horizontal surface, the normal force is equal to the weight of the sled which is given by:

weight = mass * acceleration due to gravity
= 20 kg * 9.8 m/s^2
= 196 N

Substituting the values into the equation:

-30 N = coefficient of kinetic friction * 196 N

Now we can solve for the coefficient of kinetic friction:

coefficient of kinetic friction = -30 N / 196 N
coefficient of kinetic friction ≈ -0.153

The coefficient of kinetic friction between the sled and the snow is approximately -0.153.