# 6.1.2 Work & Efficiency

### Work Done

• In Physics, work is done when an object is moved over a distance by an external force applied in the direction of its displacement

• In the diagram below, the man’s pushing force on the block is doing work as it is transferring energy to the block (increasing its kinetic energy)

Work is done when a force is used to move an object over a distance

• When work is done, energy is transferred from one object to another
• Work done can be thought of as the amount of energy transferred, hence its units are in Joules (J)
• Usually, if a force acts in the direction that an object is moving then the object will gain energy
• If the force acts in the opposite direction to the movement then the object will lose energy

#### Worked Example

The diagram shows a barrel of weight 2.5 × 103 N on a frictionless slope inclined at 40° to the horizontal.

A force is applied to the barrel to move it up the slope at constant speed. The force is parallel to the slope.

What is the work done in moving the barrel a distance of 6.0 m up the slope?

A.     7.2 × 103 J               B.     2.5 × 104 J              C.     1.1 × 104 J               D.     9.6 × 103 J

#### Exam Tip

A common exam mistake is choosing the incorrect force which is not parallel to the direction of movement of an object. You may have to resolve the force vector to find the component that is parallel. The force does not have to be in the same direction as the movement, as shown in the worked example.

### Work Done by a Gas

• When a gas expands, it does work on its surroundings by exerting pressure on the walls of the container
• This is important, for example, in a steam engine where expanding steam pushes a piston to turn the engine

The gas expansion pushes the piston a distance s

• The diagram shows a gas of pressure P inside a cylinder of cross-sectional area A
• The cylinder is closed by a piston and the gas pushes the piston a distance s
• The amount of work done on the gas depends on the force F exerted by the piston
• From the definitions for pressure and work done:
• F = P × A and W = F × s
• We can deduce:
• W = PΔV where ΔV = A × s
• This is assuming that the pressure P does not change as the gas expands

### Efficiency of a System

• The efficiency of a system is the ratio of the useful energy output from the system to the total energy input
• If a system has high efficiency, this means most of the energy transferred is useful
• If a system has low efficiency, this means most of the energy transferred is wasted
• Multiplying this ratio by 100 gives the efficiency as a percentage

Efficiency equation in terms of energy

• Efficiency can also be written in terms of power (the energy per second):

Efficiency equation in terms of power

#### Exam Tip

Efficiency can be in a ratio or percentage format. If the question asks for an efficiency as a ratio, give your answer as a fraction or decimal. If the answer is required as a percentage, remember to multiply the ratio by 100 to convert it, e.g. Ratio = 0.25, Percentage = 0.25 × 100 = 25 %

### Solving Problems Involving Efficiency

• Recall the two equations for calculating efficiency are:

• Which to use will depend on whether you’re given a system calculating energies or power as shown in the examples below

#### Worked Example

The diagram shows a pump called a hydraulic ram.

In one such pump the long approach pipe holds 700 kg of water. A valve shuts when the speed of this water reaches 3.5 m s-1 and the kinetic energy of this water is used to lift a small quantity of water by height of 12m.

The efficiency of the pump is 20%.

Which mass of water could be lifted 12 m?

A. 6.2 kg               B. 4.6 kg               C. 7.3 kg               D. 0.24 kg

• The pump is what converts the water’s kinetic energy into gravitational potential energy. Since its efficiency is 20%, you would multiply the kinetic energy by 0.2 since only 20% of the kinetic energy will be converted (not 20% of the gravitational potential energy)

#### Exam Tip

Equations for kinetic and potential energies are important for these types of questions. Also familiarise yourself with the different equations for power depending on what quantities are given.

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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