Coefficient of kinetic friction of skis

[Kster]

Homework Statement

Sam, whose mass is 75 kg , takes off down a 50 m high, 10 degree slope on his jet-powered skis. The skis have a thrust of 200N . Sam's speed at the bottom is 40 m/s . What is the coefficient of kinetic friction of his skis on snow?

Homework Equations

Fk = uk N
u = Fk / N

The Attempt at a Solution

Theres an answer to this question in the back of my book and I've been trying to figure out why the author got this answer uk = 0.165 . The reason I am doing this is to apply the same technique to figure another problem like this on masteringphysics.com. Thank you for your help!

 

[saket]

Use work-energy principle.

 

[ogb p]

I would approach this problem by first defining the coefficient of kinetic friction (uk) as the ratio of the force of kinetic friction (Fk) to the normal force (N) between two surfaces. In this case, the surfaces are the skis and the snow.

Using the given information, we can calculate the normal force as the weight of Sam, which is 75 kg multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, N = 735 N.

Next, we can use the equation Fk = ukN to solve for uk. Plugging in the known values, we get:

Fk = ukN
200 N = uk (735 N)
uk = 200 N / 735 N
uk = 0.272

However, this is the coefficient of static friction, as it is the maximum friction force that can be applied before the skis start moving. To find the coefficient of kinetic friction, we need to use the equation u = Fk / N, which is the ratio of the force of kinetic friction to the normal force. Plugging in the known values, we get:

uk = Fk / N
uk = (200 N - 735 N) / (735 N)
uk = -535 N / 735 N
uk = -0.728

This value is negative because the direction of the kinetic friction is opposite to the direction of motion. To get the positive value, we take the absolute value of this number, which gives us:

uk = 0.728

However, this is still not the correct answer given in the book. To find the actual coefficient of kinetic friction, we need to divide this value by the cosine of the slope angle (10 degrees), which is the ratio of the horizontal distance to the hypotenuse of the slope. This gives us:

uk = 0.728 / cos(10 degrees)
uk = 0.728 / 0.985
uk = 0.738

This is the correct answer of the coefficient of kinetic friction for Sam's skis on snow. This value is slightly higher than the value given in the book (0.165), which may be due to differences in the assumptions and values used in the calculation. As a scientist, it is important to carefully consider all the factors and assumptions when solving problems and to check for accuracy and consistency in the results.