Work and power

In physics, work is done when a force moves an object, and power measures how quickly work is done or energy is transferred. These concepts are essential in understanding how machines operate, how energy is used, and how forces affect motion in everyday life.

Work done = energy transfered

When a force moves an object, work is done on the object. The amount of work done is equal to the energy transferred to the object.

Equation for Work Done (Mechanical Work)

where:

• W = work done (Joules, J)

• F = force (Newtons, N)

• d = distance moved in the direction of the force (meters, m)

• ΔE = energy transferred (J)

Example Calculation:

A force of 10 N moves an object 5 m. Find the work done.

W = 10 × 5 = 50 J = 50 J

This means 50 Joules of energy have been transferred to the object.

Key Idea: The greater the force applied or the further the object moves, the more work is done.

Power

Power is the rate at which work is done or energy is transferred. In other words, it measures how quickly energy is converted from one form to another.

Equations for Power:

or

where:

• P = power (Watts, W)

• W = work done (J) 

• ΔE = energy transferred (J)

• t = time taken (s)

Example Calculation:

A machine does 200 J of work in 4 seconds. Find its power.

P = 200/4 = 50 W

This means the machine transfers 50 Joules of energy every second.

Power is measured in Watts (W), where 1 Watt = 1 Joule per second (J/s). A machine with a power rating of 1000 W (1 kW) transfers 1000 J of energy every second.

Work, power and energy and real life

The principles of work and power apply to various everyday activities and mechanical systems.

1. Lifting a Box

• Work Done: When lifting a box, work is done against gravity.

• Equation: 

• Power Calculation: The rate at which work is done can be calculated as: 

• Example: Lifting a 10 kg box to a height of 2 meters requires work to be done against gravity. The power output depends on how quickly it is lifted.

2. Pushing a Car

• Work Done: Work is done when a force is applied to move the car over a distance.

• Equation: 

• Power Calculation: 

• Example: If a person applies a 300 N force to push a car 10 m in 5 seconds, the power output can be calculated.

3. Running Up Stairs

• Work Done: Running upstairs requires energy to be transferred from chemical energy in muscles to gravitational potential energy.

• Equation: 

• Power Calculation: 

• Example: A person weighing 70 kg running up a staircase of height 3 m in 5 seconds can have their power output calculated.

4. Electrical Appliances

• Energy Transferred: Electrical devices use energy to perform work.

• Equation: 

• Where:

  • V = voltage (volts, V)

  • I = current (amperes, A)

  • t = time (seconds, s)

• Power Calculation: