Question

25 points!
A boy with a mass 50 kg walks up the stairs from the ground to the top of a spiral water slide in 1 minute. The height of the slide is 11.5 m above the ground. As the boy slides down the slide and reaches the bottom, his speed is 12 m/s and the distance traveled along the slide is 108 m.

Find the mechanical energy lost by the boy in sliding down the slide.
What is the average frictional force acting on the boy?

Answer 1

Refer to the diagram shown below.

At A, the boy begins walking up the stairs.

At B, the boy is at the top of the slide. He has acquired PE (potential energy).
The value of the PE is
(50 kg)*(9.8 m/s²)*(11.5 m) = 5635 J

At C, the boy has KE (kinetic energy).
The value of the KE is
(1/2)*(50 kg)*(12 m/s)² = 3600 J

Energy is lost between B and C due to friction.
The lost energy is
5635 - 3600 = 2035 J

The distance traveled along the slide is 108 m.
If F =  the average frictional force, then
(F N)*(108 m) = 2035 J
F = 18.84 N

Answers:
(a) The mechanical energy lost by sliding is 2035 J.
(b) The average frictional force is 18.84 N