Work, Energy and Power
Explore the fundamental concepts of work done by forces, the different forms of energy, the law of conservation of energy, and power as the rate of doing work.
Work Done by a Force
In physics, work is done when a force causes an object to move through a displacement. Work is a scalar quantity measured in joules (J). One joule is the work done when a force of 1 newton moves an object 1 metre in the direction of the force.
Work Formula
W = Fs cos θ
where W = work (J), F = force (N), s = displacement (m), θ = angle between force and displacement
θ = 0°
Force parallel to displacement
W = Fs (maximum work)
θ = 90°
Force perpendicular to displacement
W = 0 (no work done)
θ = 180°
Force opposite to displacement
W = -Fs (negative work)
Key insight: A force perpendicular to an object's displacement does zero work. This is why the normal force on a flat surface and the centripetal force in circular motion do no work.
Kinetic and Potential Energy
Energy is the capacity to do work. It exists in many forms, but two of the most fundamental in mechanics are kinetic energy (energy of motion) and gravitational potential energy (energy of position).
Kinetic Energy
Ek = ½mv2
The energy an object possesses due to its motion. Depends on mass (m) and velocity (v). Always positive or zero.
Gravitational Potential Energy
Ep = mgh
The energy stored in an object due to its height (h) above a reference point. Depends on mass (m), gravitational field strength (g) and height (h).
Conservation of Mechanical Energy
In an isolated system with no external forces doing work (no friction, air resistance, etc.), the total mechanical energy remains constant:
Ek(initial) + Ep(initial) = Ek(final) + Ep(final)
Top of fall
Max Ep, Min Ek
Mid-fall
Ep converting to Ek
Bottom
Min Ep, Max Ek
Power
Power is the rate at which work is done (or energy is transferred). It is a scalar quantity measured in watts (W). One watt equals one joule per second (1 W = 1 J s-1).
Power Formulae
P = W / t
Power = work done divided by time taken
P = Fv
Power = force multiplied by velocity (for constant force and velocity)
Efficiency
No real machine is 100% efficient. Some energy is always lost, usually as heat due to friction.
Efficiency = (useful energy output / total energy input) × 100%
Key Vocabulary
Work
The energy transferred when a force moves an object through a displacement. Measured in joules (J). W = Fs cos θ.
Kinetic Energy
Energy possessed by an object due to its motion. Ek = ½mv2. Measured in joules (J).
Conservation of Energy
Energy cannot be created or destroyed, only transformed from one form to another. Total energy in an isolated system is constant.
Power
The rate at which work is done or energy is transferred. P = W/t. Measured in watts (W), where 1 W = 1 J s-1.
Worked Examples
A student pushes a 15 kg box 4.0 m across a floor with a horizontal force of 50 N. How much work is done?
Known: F = 50 N, s = 4.0 m, θ = 0° (force is horizontal, displacement is horizontal)
Using: W = Fs cos θ = 50 × 4.0 × cos 0° = 50 × 4.0 × 1
W = 200 J
A 2.0 kg ball is dropped from a height of 5.0 m. What is its speed just before hitting the ground? (g = 9.8 m s-2)
Using conservation of energy: Ep(top) = Ek(bottom)
mgh = ½mv2 → the mass cancels
v2 = 2gh = 2 × 9.8 × 5.0 = 98
v = 9.9 m s-1
A motor does 6000 J of work in 12 seconds. What is its power output?
Known: W = 6000 J, t = 12 s
Using: P = W / t = 6000 / 12
P = 500 W
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What are the SI units of work?
Question 2
If a force is applied perpendicular to an object's displacement, the work done is:
Question 3
A 3.0 kg object has a velocity of 4.0 m s-1. What is its kinetic energy?
Question 4
As a ball falls freely (ignoring air resistance), which statement is true?
Question 5
A machine does 1500 J of work in 5.0 seconds. What is its power?
Key Concepts Summary
- ●Work = Fs cos θ. Work is zero if force is perpendicular to displacement.
- ●Kinetic energy Ek = ½mv2; Gravitational potential energy Ep = mgh.
- ●The law of conservation of energy states that total energy in an isolated system remains constant.
- ●Power = W/t = Fv, measured in watts (W).
- ●Efficiency compares useful energy output to total energy input, always less than 100% in real systems.