Question

A 64.7-kg skier coasts up a snow-covered hill that makes an angle of 23.0°

with the horizontal. The initial speed of the skier is 9.61 m/s. After coasting a distance of 2.08 m up the slope, the speed of the skier is 4.25 m/s. (a) Find the work done by the kinetic frictional force that acts on the skis. (b) What is the magnitude of the kinetic frictional force?

Answer 1

The work done by the kinetic frictional force is determined by the change in kinetic energy of the skier, and the magnitude of the frictional force is calculated by dividing this work by the distance traveled up the slope and the cosine of the hill's angle.

Step-by-step explanation:

To find the work done by the kinetic frictional force on a 64.7-kg skier, we can use the work-energy principle which states that the work done is equal to the change in kinetic energy. The initial kinetic energy (KE1) when the skier is moving at 9.61 m/s can be calculated using KE = 0.5 * m * v2, and the final kinetic energy (KE2) at a speed of 4.25 m/s is calculated the same way.

The work done by the frictional force (Wf) is then Wf = KE2 - KE1. To find the magnitude of the frictional force (f), we can use the work done by friction, which is distance * cos(θ), where θ is the angle of the hill, and the distance is 2.08 m. By calculating the work done and dividing it by the distance and the cosine of the angle, we find the magnitude of the frictional force.