Question

A 64.4-kg skier coasts up a snow-covered hill that makes an angle of 21.7 ° with the horizontal. The initial speed of the skier is 8.43 m/s. After coasting a distance of 1.40 m up the slope, the speed of the skier is 4.07 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

(a) The work done by kinetic frictional force is -1,754.9 J.

(b) The magnitude of the kinetic frictional force is 1,350 N.

How to calculate the work done kinetic frictional force?

(a) The work done by kinetic frictional force is calculated by applying the following formula as shown below.

Using work energy theorem, the change in kinetic energy of the skier is equal to work done by friction.

W = ΔK.E

W = ¹/₂ x m x (v² - u²)

W = ¹/₂ x 64.4 x (4.07² - 8.43²)

W = -1,754.9 J

(b) The magnitude of the kinetic frictional force is calculated as follows;

W = -Fdcos(θ)

- 1,754.9 = - F x 1.4 x cos(21.7)

1,754.9 = 1.3F

F = 1,754.9 / 1.3

F = 1,350 N