Module 6—Work and Energy

Module Summary

 

Work is a measure of the amount of energy transferred when a force acts over a given displacement. It is the product of the magnitude of the applied force and the displacement of the object in the direction of that force.

 

You have examined three forms of energy and their interactions in isolated and non-isolated environments:

A bungee jump begins with gravitational potential energy. On the way down, the energy is converted to kinetic energy and finally to elastic potential energy at the very bottom. On the way up, the process is reversed. With each bounce, some energy is lost from the system and eventually the motion stops.

 

Total mechanical energy (the sum of the potential energy and the kinetic energy) is conserved in an isolated environment. Any change in either potential or kinetic energy is associated with an equal but opposite change in the other energy. As an object slides down an incline, potential energy is converted into kinetic energy until all of the energy has been transferred from one form to the other. The forces acting in an isolated system are called conservative forces.

 

Mechanical energy is not conserved when friction is present, making the system non-isolated. In this case, some of the potential energy is lost due to the work done by friction rather than being converted to kinetic energy. Therefore, the mechanical energy decreases over time. By reducing the friction, the loss in mechanical energy can be minimized, which results in a greater conversion of potential energy into kinetic energy and a greater speed at the bottom of an incline. Forces acting on a non-isolated system from outside the system or from friction are called non-conservative forces.

In the presence of a conservative force (gravity), the work done in raising an object, such as a skier, through a vertical distance is equal to the gain in potential energy of that object. This is known as the work-potential energy theorem.

In the presence of both a non-conservative force (friction) and a conservative force (gravity), the work done raising an object vertically is equal to the sum of the gain in potential energy and the work done to overcome the non-conservative force. For example, the work done by a chairlift is not equal to the gain in mechanical energy of the riders since some energy is lost working against the force of friction. The longer the pathway, the more energy is lost to the non-conservative forces.

 

Power is the rate of doing work. It is the ratio of the work done to the time interval in which it is done. In the case of the chairlift, the motor does work on the riders, increasing their mechanical energy during the time they are moving up the hill. The energy created by the motor is also consumed doing work against non-conservative forces, such as friction. To counteract friction, more power is needed. Increasing the power (doing more work in the same time period) on a chairlift will cause it to move at a faster rate, moving more mass up the hill in less time.

 

Efficiency is the ratio of the energy output (useful work) to the energy input (total energy used). For a chairlift, the useful work is equal to the gain in potential energy of the riders once they reach the top of the lift. The total energy used is greater than this since some of the energy is consumed overcoming non-conserved forces, such as friction. Minimizing non-conserved forces will lead to greater efficiency.

 

Module 6 Assessment

 

You are expected to submit the following items to your teacher for marks:

Choose one of the Reflect on the Big Picture items from this module, and share it with your teacher.