# 4.6.1 Work & Power

### Work & Power

• Work is defined as

The amount of energy transferred when an external force causes an object to move over a certain distance

• If the force is parallel to the direction of the object’s displacement, the work done can be calculated using the equation:

#### W = Fs

• Where:
• W = work done (J)
• F = average force applied (N)
• s = displacement (m)

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

• When pushing a block, work is done against friction to give the box kinetic energy to move
• The kinetic energy is transferred to other forms of energy such as heat and sound
• 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
• Sometimes the direction of motion of an object is not parallel to the direction of the force
• If the force is at an angle θ to the object’s displacement, the work done is calculated by:

#### W = Fs cos θ

• Where θ is the angle, in degrees, between the direction of the force and the motion
• When θ is 0 (the force is in the direction of motion) then cos θ = 1 and W = Fs
• This may not always be cos θ, since this is just for horizontal motion
• For vertical motion, it would be sin θ
• Always consider the horizontal and vertical components of the force
• The component needed is the one that is parallel to the displacement When the force is at an angle, only the component of the force in the direction of motion is considered for the work done

#### Power

• Power is the rate of doing work or the rate of energy transfer
• Power is calculated by the equation: •  Where:
• P = power (W)
• ΔW = change in work done (J)
• Δt = change in time (s)

• The equation shows that the power is increased if:
• There is a greater energy transfer (work done)
• The energy is transferred (work is done) over a shorter period of time
• If an object is moving at constant velocity with a constant force, the power can also be calculated by:

#### P = Fv

• Where:
• F = force (N)
• v = velocity (m s–1)
•  The force must be in the direction of the velocity
• Otherwise, the component of the force in the direction of the velocity must be used instead

#### 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 first in order 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. ### 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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