Work and conservation of energy (3.3.1)
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Work done is defined as the energy transferred when a force moves an object through a distance:
Where:
- is the displacement in metres , and
- is the average force in the direction of the displacement in newtons .
Work done is measured in joules, One joule is the work done when a force of one newton moves an object one metre in the direction of the force.
For an object to move at a constant velocity, the net force acting on it must be zero. If an object has an opposing force, such as friction or gravity, it will require a continuous applied force to move at a constant velocity.
For an object moving at constant velocity, the work done by the applied force is equal to the work done against opposing forces like friction or gravity.
Question walkthrough
Calculating Work Done Lifting an Object
Uses W = mgh to find the work done lifting a 300kg object at constant velocity through a height of 10m.
Question walkthrough
Verifying Work Done via Two Methods
Calculates the work done by a 5N force pushing an object against 3N of friction, first directly via W=Fx, then by summing the separate contributions from acceleration and friction.
The direction of the force and the displacement of an object may not be the same. Generally, work done is given by:
Where:
- is displacement,
- is the average force, and
- is the angle between and
is the component of the force acting in the direction of motion.
Carefully note the direction of the force when calculating the work done,
Question walkthrough
Calculating Work Done at an Angle
Uses W = Fd cos θ to find the work done lifting a box at constant velocity along a displacement inclined at 30° to the horizontal.
The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred or transformed from one form to another.
For example, for an ideal pendulum, gravitational potential energy is converted to kinetic energy and vice versa during each swing, but the total energy stays the same.
The principle of conservation of energy is best illustrated in an isolated system.
- Isolated system: energy or matter cannot be exchanged with the surroundings. In an isolated system, the total energy remains constant.
- Closed system: matter cannot be exchanged with the surroundings, but energy can be.
- Open system: energy and matter can be exchanged with the surroundings.
Wasted energy is simply defined as energy that is not useful. Wasted forms of energy typically include heat, light and sound.
For instance, in any real mechanical system, useful energy output is always less than the total energy input because friction between a machine’s moving parts generates heat and sound.
Question walkthrough
Finding Work Done Against Friction
Uses the work-energy principle to find the energy lost to friction when a force accelerates an object over a known distance, then finds the corresponding average frictional force.
Energy exists in many forms. Common examples of energy pathways include:
Energy can be transferred from one object to another or from one form to another, in accordance with the principle of conservation of energy.
Energy exists in many forms. Common examples of energy stores include:
Energy can be transferred from one object to another or from one form to another, according to the principle of conservation of energy.
Question walkthrough
Energy Transfers in a Mass-Spring System
Describes how elastic potential energy converts into kinetic and gravitational potential energy as a vertically oscillating mass moves from its stretched position back toward equilibrium.
Doing work on an object transfers energy to it. For example, lifting a weight increases its gravitational potential energy, which equals the work done in lifting it.
The greater the magnitude of a force or the distance over which it is applied, the more energy is transferred:
Question walkthrough
Finding Height Gained from Energy Transfer
Uses the work done by a piston force to split transferred energy between heating water and lifting a platform and scooter, then finds the height gained using W = mgh.