Using Potential Energy Formula
Exercise. A stone is dropped from a height of 1 m. If it is 0.2 kg, find the kinetic energy just before it hits the ground. Assume that g = 10 m/s2. Answer. When it reaches the ground, all it potential energy is converted to kinetic energy. So its kinetic energy is equal to mgh = 0.2 x 10 x 1 = 5 J.
Exercise. A ball is bounced vertically off the ground. It leave the ground with a speed of 1 m/s. Find the maximum height that it reaches. Assume that g = 10 m/s2. Answer. At the maximum height, the stone is at rest for an instance. So the kinetic energy there is zero. That means all the kinetic energy when it leaves the ground is converted to potential energy. Therefore the potential energy mgh = mv2/2. The height is then h = v2/(2g) = 12 / (2 x 10) = 0.05 m.
Exercise.
A ball is dropped from a height of 2 m.
It bounces off the ground and reaches a new height of 1 m.
If it is 0.1 kg, find the heat produced. Assume that g = 10 m/s2.
Answer.
The new height is lower, so some potential energy is lost. This is converted to
heat on hitting the ground. The heat produce is equal to the decrease in
potential energy. Potential energy at 2 m is mgh = 0.1 x 10 x 2 = 2 J.
Potential energy at 1 m is mgh = 0.1 x 10 x 1 = 1 J. So the heat produced
is 2 - 1 = 1 J.
Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 20 September 2010.