Work, Power and Energy

Lessons

Senior 1 · Physics

Work, Power and Energy

5 lessons

Lesson 1 of 5

Work: Force and Distance

23 min

Hard work that is not work

Byiringiro pushes against the classroom wall as hard as he can for five minutes. He sweats and his arms ache, but the wall has not moved. Meanwhile Uwase pushes a wheelbarrow of bricks 20 m across a building site in Nyamirambo. In everyday speech both of them worked hard. In physics, only Uwase did any work. The scientific meaning is narrower and more useful: work is done only when a force moves something.

Definition

Work ( $W$ ) is done when a force moves the object it acts on. It equals the force multiplied by the distance moved in the direction of the force:

W = F \times d

where $F$ is the force in newtons (N) and $d$ is the distance moved in the direction of the force, in metres (m).

The SI unit of work is the joule (J): 1 J is the work done when a force of 1 N moves its point of action through 1 m in the direction of the force. $1\,\mathrm{J} = 1\,\mathrm{N\,m}$ . Larger units: $1\,\mathrm{kJ} = 1000\,\mathrm{J}$ , $1\,\mathrm{MJ} = 10^{6}\,\mathrm{J}$ .

When is work done?

Figure 1.1: In (a) the push is in the same direction as the motion, so it does work. In (b) the upward force holding the basket is at right angles (⟂) to the motion, so it does no work on the basket.

Work needs both a force and a movement in the direction of that force. So no work is done:

when the force does not move anything (Byiringiro pushing the wall);
when something moves with no force along its motion (a puck gliding on smooth ice);
when the force is at right angles to the motion (the upward force on a basket carried on the head along a level road).

Experiment: measuring work

You need: a wooden block with a hook, a newton meter, a metre rule, a load of known weight and a string.

Hook the newton meter to the block and pull it slowly along the bench at a steady speed. Read the force, for example 2.5 N.
Measure the distance pulled, for example 0.80 m. Work done against friction: $W = 2.5\,\mathrm{N} \times 0.80\,\mathrm{m} = 2.0\,\mathrm{J}$ .
Now hang a 5.0 N load on the newton meter and lift it slowly and steadily through 0.40 m. The force equals the weight, so $W = 5.0\,\mathrm{N} \times 0.40\,\mathrm{m} = 2.0\,\mathrm{J}$ .
Repeat each measurement three times and take the mean.

Important

Safety. Pull the block slowly so it does not shoot off the bench. Keep hanging loads low over the bench, and keep feet clear.

Definition

Work done against gravity. To lift a body of mass $m$ at a steady speed through a height $h$ , you must apply an upward force equal to its weight, $m g$ . The work done is

W = m g h

Example: lifting a 2.0 kg bag of sugar onto a 1.5 m shelf needs $W = 2.0 \times 9.8 \times 1.5 = 29.4\,\mathrm{J}$ .

Worked example 1: a wheelbarrow of bricks

Uwase pushes a wheelbarrow with a steady horizontal force of 150 N for 20 m. How much work does she do?

W = Fd = 150\,\mathrm{N} \times 20\,\mathrm{m} = 3000\,\mathrm{J} = 3.0\,\mathrm{kJ}

Worked example 2: lifting a jerrycan of water

A 20 L jerrycan full of water has a mass of 20 kg. Keza lifts it from the ground onto her head, a height of 1.5 m. How much work does she do on the jerrycan?

W = mgh = 20\,\mathrm{kg} \times 9.8\,\mathrm{N\,kg^{-1}} \times 1.5\,\mathrm{m} = 294\,\mathrm{J}

She then walks 500 m along a level path. The upward force of her head on the can does no more work, because it is at right angles to the motion.

Ramps and pulleys: the same work, a different force

Loading a 50 kg bag of cement (weight $50 \times 9.8 = 490\,\mathrm{N}$ ) onto a lorry bed 1.2 m high can be done in two ways.

Figure 1.2: A single fixed pulley only changes the direction of the pull: you still pull 490 N, for 1.2 m of rope. A ramp lets you use a smaller force, 196 N, but over a longer distance, 3.0 m. If friction is ignored the work is 588 J either way.

Worked example 3: the force needed on a ramp

Find the push needed to slide the 490 N bag up the 3.0 m ramp to the 1.2 m lorry bed, if friction can be ignored.

Work done along the ramp = work done lifting straight up:

F \times 3.0\,\mathrm{m} = 490\,\mathrm{N} \times 1.2\,\mathrm{m} = 588\,\mathrm{J}

F = \frac{588\,\mathrm{J}}{3.0\,\mathrm{m}} = 196\,\mathrm{N}

With real friction the push is a little larger, so a little more work is done than 588 J.

Warning

Watch the distance and the units

Use the distance moved in the direction of the force: for lifting, the vertical height, not the length of the path.
Convert to newtons and metres first. A 250 g mass is 0.25 kg; a 40 cm lift is 0.40 m. Using 250 and 40 gives an answer 100 000 times too big.
Mass is not force: to lift a 20 kg load, the force is $20 \times 9.8 = 196\,\mathrm{N}$ , not 20 N.

Work on Rwanda's hills

Rwanda is called the land of a thousand hills, and its roads show how engineers use the ramp idea. The road up to Kigali's Rebero hill, or the switchbacks between Musanze and Rubavu, zig-zag instead of climbing straight up. A lorry climbing the same height along a longer, gentler road needs a smaller driving force, which its engine can supply. Terraces on hillsides, and the ramps at the Nyabugogo taxi park, apply the same physics.

Tip

Three checks for every work question: Is there a force? Did the object move? Was the movement along the force? If any answer is no, the work done by that force is zero.

Work and power (Khan Academy). Watch the first part for the definition W = Fd and for the examples where a force does no work.

✦

Practice

Define work and give its SI unit.
A pupil pushes a desk with a force of 80 N through 3.0 m. How much work does he do?
State whether work is done in each case, and why: (a) holding a bag of rice still above your head; (b) pushing a stalled car along a road; (c) a satellite's weight as it moves in a circle round the Earth.
How much work is done in lifting a 5.0 kg box onto a shelf 2.0 m high?
A force of 250 N does 1500 J of work. How far does the object move along the force?
A 400 g book is lifted from the floor onto a table 75 cm high. Find the work done.
A 600 N barrel is rolled up a 4.0 m ramp onto a platform 1.0 m high. Ignoring friction, what force is needed along the ramp? Why does a ramp not save work?

Show answersHide answers

Work is done when a force moves an object; it equals force × distance moved in the direction of the force. SI unit: the joule (J).
$W = 80 \times 3.0 = 240\,\mathrm{J}$
(a) No: no movement. (b) Yes: the push moves the car along the push. (c) No: the weight points to the Earth's centre, at right angles to the motion.
$W = mgh = 5.0 \times 9.8 \times 2.0 = 98\,\mathrm{J}$
$d = \frac{W}{F} = \frac{1500}{250} = 6.0\,\mathrm{m}$
$m = 0.40\,\mathrm{kg}$ , $h = 0.75\,\mathrm{m}$ : $W = 0.40 \times 9.8 \times 0.75 = 2.94\,\mathrm{J}$
$F \times 4.0 = 600 \times 1.0 \Rightarrow F = 150\,\mathrm{N}$ . The force is smaller, but it acts over a longer distance; the work, 600 J, is the same (and a little more with friction).

Key points

Work is done only when a force moves an object along the direction of the force: $W = F d$ .
The unit of work is the joule: $1\,\mathrm{J} = 1\,\mathrm{N\,m}$ .
Lifting a body at steady speed: $W = m g h$ , using the vertical height.
Ramps and pulleys change the force needed, not the work done.

Sources and credits

7.1: Work: The Scientific Definition, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Consulted for the physics; no text was copied.
Video: Work and power | Physics | Khan Academy, Khan Academy, embedded from YouTube.

Written by Ganzaa: the lesson text, the experiment, diagrams, worked examples, Rwandan applications and practice exercises.

1Hard work that is not work

2When is work done?

3Experiment: measuring work

4Ramps and pulleys: the same work, a different force

5Work on Rwanda's hills

Hard work that is not work

When is work done?

Experiment: measuring work

Ramps and pulleys: the same work, a different force

Work on Rwanda's hills