﻿ SmartLearner ## Work, Energy and Power

(This section must be read in conjunction with the CAPS, p. 117–120.)

### Work

• Define the work done on an object by a constant force F as: where (Work is done by a force on an object – the use of 'work is done against a force', e.g. work done against friction, should be avoided.)
• Draw a force diagram and free-body diagrams.
• Calculate the net/total work done on an object.
• Distinguish between positive net/total work done and negative net/total work done on the system.

### Work-energy theorem

• State the work-energy theorem:
The net/total work done on an object is equal to the change in the object's kinetic energy OR the work done on an object by a resultant/net force is equal to the change in the object's kinetic energy.
In symbols: • Apply the work-energy theorem to objects on horizontal, vertical and inclined planes
(for both frictionless and rough surfaces).

### Conservation of energy with non-conservative forces present

• Define a conservative force as a force for which the work done in moving an object between two points is independent of the path taken.
Examples are gravitational force, the elastic force in a spring and electrostatic forces (coulomb forces).
• Define a non-conservative force as a force for which the work done in moving an object between two points depends on the path taken. Examples are frictional force, air resistance, tension in a chord, etc.
• State the principle of conservation of mechanical energy: The total mechanical energy (sum of gravitational potential energy and kinetic energy) in an isolated system remains constant. (A system is isolated when the resultant/net external force acting on the system is zero.)
• Solve conservation of energy problems using the equation: • Use the relationship above to show that in the absence of non-conservative forces, mechanical energy is conserved.

### Power

• Define power as the rate at which work is done or energy is expended. In symbols: • Calculate the power involved when work is done.
• Perform calculations using: when an object moves at a constant speed along a rough horizontal surface or a rough inclined plane.
• Calculate the power output for a pump lifting a mass (e.g. lifting water through a height at constant speed).