Work & Power (AQA A Level Physics)

• The work done by a force is equivalent to a transfer of energy
  • The units of work done are newton metres
  • 1 N m = 1 J
• The work done by a resultant force on a system is equal to the change in energy in that system

• Mechanical work is defined as

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

• If a constant force is applied 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)

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

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

• When pushing a block, work is done against friction and energy is transferred from the man to the block
• Some of the energy is dissipated to the surroundings by heating and as sound

• 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 of the object
  • When θ is 0 (the force is in the direction of motion) then cos θ = 1 and W = Fs

• For horizontal motion, cos θ is used
• For vertical motion,  sin θ is used
  • 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