A 61 kg skier on level snow coasts 184 m to stop from a speed of 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 coefficent of kinetic friction between the skiers skis and the snow

i did the left side of the equation = 4392

and the right side i got 109995.2

so i did 4392/109995.2 = .039929

sorry about that...

I got your 1/2 m v^2=mu*mg*distance

so I did 1/2(61kg)(12.0 m.s)^2 = mu * (what do i put for mg) and distance is 184 m right?

so its the 61(9.8)

so then the final formula would look like
1/2(61kg)(12.0 m.s)^2 = mu * (61kg)(9.8m/s^2)(184m)

solve for mu right?

m is mass, itis given as 61kg, g is 9.8m/s^2

correct.

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

A) For the first part of the question, we have a 61 kg skier coasting 184 m to stop from a speed of 12.0 m/s. The work done by friction is negative because it acts in the opposite direction of motion.

The work done by friction can be calculated using the equation W = -μ * N * d, where W is the work done by friction, μ is the coefficient of kinetic friction, N is the normal force, and d is the distance.

The normal force is equal to the weight of the skier, which is given as mg (mass * gravity). So, N = 61 kg * 9.8 m/s².

Since the skier comes to a stop, the final kinetic energy is zero. The initial kinetic energy can be calculated using the equation KE = 0.5 * m * v², where KE is the kinetic energy, m is the mass, and v is the velocity.

Using the work-energy principle, we can say that the work done by friction is equal to the change in kinetic energy: W = ΔKE.

Writing out the equation: -μ * N * d = 0.5 * m * v² - 0.5 * m * 0².

Substituting the values, we get: -μ * 61 kg * 9.8 m/s² * 184 m = 0.5 * 61 kg * 12.0 m/s² * 12.0 m/s².

Now, we can solve for the coefficient of kinetic friction (μ) by rearranging the equation: μ = (0.5 * m * v²) / (N * d).

Calculating the values on the right side: (0.5 * 61 kg * 12.0 m/s² * 12.0 m/s²) / (61 kg * 9.8 m/s² * 184 m).

After simplifying, you should find the coefficient of kinetic friction (μ).

B) For the second part of the question, we have a 75 kg skier with twice the starting speed coasting the same distance before stopping.

Using the same steps as in part A, we calculate the coefficient of kinetic friction (μ) by substituting the new values for mass (75 kg) and velocity (2 * 12.0 m/s) into the equation and solving.

Following these steps, you should be able to find the coefficient of kinetic friction between the skier's skis and the snow for both scenarios.

Didn't I go through this with you before? Set initial KE equal to mu*mg*distance.

If you don't understand that, explain. I can't read minds.