a 61 kg skier on level snow coasts 184 m to stop from a speed on 12.0 m/s. A) use the work energy principle to find the coefficient of kinetic friction between the skis and the snow. B) suppose a 75 kg skier with twice the starting speed coasted the same distance before stopping. Find the coefficient of kinetic friction between that skier's skis and the snow.

Original KE=work done by friction

1/2 m v^2=mu*mg*distance
solve for mu. Notice mass of the skier has nothing to do with it.

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

A) For the first scenario, where the skier has a mass of 61 kg and starting speed of 12.0 m/s, we need to find the work done to bring the skier to a stop.

The work done is equal to the change in kinetic energy, which can be calculated as:
Work = ΔKE = KE_final - KE_initial

The initial kinetic energy (KE_initial) can be calculated using the formula:
KE = (1/2) * m * v^2,
where m is the mass of the skier and v is the initial velocity.

KE_initial = (1/2) * 61 kg * (12.0 m/s)^2

Next, we have the final kinetic energy (KE_final) because the skier comes to a stop:
KE_final = 0, since the skier stops.

Therefore, the work done (W) is equal to the change in kinetic energy:
W = ΔKE = KE_final - KE_initial
W = 0 - (1/2) * 61 kg * (12.0 m/s)^2

Now, we can relate the work done to the work done by friction. The work done by friction is given by:
W_friction = -µ * N * d,
where µ is the coefficient of kinetic friction, N is the normal force, and d is the distance traveled.

Since the skier is on level snow, the normal force and the force of gravity are equal in magnitude but opposite in direction. Therefore:
W_gravity = -W_normal = -m * g * d,
where g is the acceleration due to gravity.

Since there is no external force acting on the skier in the horizontal direction, the work done by gravity is equal to the work done by friction, so we have:
W_gravity = -m * g * d = W_friction = -µ * N * d

Now, we can solve for the coefficient of kinetic friction (µ):
µ = (m * g) / N,

Substituting the given values:
µ = (61 kg * 9.8 m/s^2) / (61 kg * 9.8 m/s^2)

Thus, the coefficient of kinetic friction between the skis and the snow is 1.

B) For the second scenario, where the skier has a mass of 75 kg (twice the previous skier's mass) and twice the starting speed but the same distance is coasted before stopping, we need to find the new coefficient of kinetic friction.

Using the same formulas as before, we can find the new coefficient of kinetic friction (µ):

KE_initial = (1/2) * 75 kg * (2 * 12.0 m/s)^2

µ = (75 kg * 9.8 m/s^2) / (75 kg * 9.8 m/s^2)

Thus, the coefficient of kinetic friction between the skis and the snow for the second skier is also 1.