Work, Energy and Power · Lesson 2 of 16
Work by a Constant Force
“Distinguish physical work from effort and calculate signed work force by force.”
• Calculate positive, negative and zero work. • Identify the body, force and displacement. • Distinguish third-law force pairs from their work.
Work is an energy transfer through force
In ordinary speech, holding a heavy bag or studying for an examination is work. In mechanics we ask a more specific question: how much energy does a particular force transfer to a particular body as it moves? A large force alone is insufficient. Holding a stationary load gives zero mechanical work on the load, even though muscles consume chemical energy internally. The body and the energy account must be named.
Read the sign from the displacement
When you raise a bucket slowly, the upward rope tension does positive work and downward gravity does negative work. Equal magnitudes cancel in the net work because the bucket’s speed is unchanged. When a block slides down a rough slope, sliding friction acts up the slope and does negative work. A pulling force on a box moving steadily across a rough floor does positive work even though the net work is zero. Work describes each force separately before the contributions are added.
Three ways to get zero work
Work vanishes if the force is zero, the relevant displacement is zero, or the force is perpendicular to every small displacement. A stationary wall has no displacement. Gravity does no work on a horizontally moving load at fixed height. A radial force in a perfectly circular orbit is perpendicular to the instantaneous tangential displacement and does zero work. A force may therefore change direction of motion without changing speed. For a curved path, apply perpendicularity locally rather than comparing the force with the overall start-to-finish chord.
Problem
A 50 N force pulls a suitcase 6 m horizontally at 60° above the horizontal. Find its work.
- 1.The displacement is horizontal, so the contributing component is 50 cos60° = 25 N.
- 2.Work is 25×6 = 150 J.
- 3.The upward component does zero work over this horizontal displacement. The result is the work of the pull, not automatically the net work.
Action and reaction do not imply cancelling work
Newton’s third law gives equal and opposite forces on different bodies. Their displacements need not be equal. Therefore their work contributions need not cancel. A skidding cycle can move 10 m while the ideal rigid road remains stationary. The road’s force does negative work on the cycle; the cycle’s equal opposite force does no macroscopic work on the stationary road in this idealisation. Real contact heats and deforms the materials, so a complete energy account includes those effects.
Problem
A 200 N road force opposes a bicycle’s 10 m displacement. What is the work on the bicycle, and on an ideal stationary road?
- 1.On the bicycle, W = 200×10 cos180° = −2000 J.
- 2.On the stationary road, the displacement at the ideal contact surface is zero, so its macroscopic mechanical work is zero.
- 3.The force magnitudes are equal; the two work magnitudes differ because different bodies move differently.
Units and dimensions
| Quantity or unit | Equivalent or dimension |
|---|---|
| Work / energy | [M L² T⁻²] |
| 1 joule | 1 N m = 1 kg m² s⁻² |
| 1 erg | 10⁻⁷ J |
| 1 electron volt | 1.602 × 10⁻¹⁹ J |
| 1 calorie | about 4.186 J |
| 1 kilowatt-hour | 3.6 × 10⁶ J |
Use metres, newtons and seconds before calculating in SI. A kilowatt-hour is power multiplied by time, hence energy. The symbol W can mean work in an equation or watt as a unit; context distinguishes them. Negative work means energy is removed from the body’s kinetic-energy account by that force, not that energy itself is a vector.
Check your understanding
Quiz
A stationary lifter holds a load for 30 s. Work on the load is
Explanation: The load does not move.
Gravity does what work on a rising bucket?
Explanation: Force and displacement are opposite.
For uniform circular motion, a purely radial force does
Explanation: It is perpendicular to the instantaneous motion.
Third-law forces have
Explanation: The forces act on different bodies with potentially different displacements.
One kWh is a unit of
Explanation: It is a power-time product.
Key Takeaways
• Always specify the force, body and displacement. • A zero net work does not mean each force does zero work. • Perpendicular force changes direction without transferring kinetic energy.