D. Structures and Mechanisms · Systems in ActionForce, Displacement and Work
D2.4 D2.5 A1.2About 45 minutes
Learning goals- I can use the scientific terms force, displacement, work and energy to describe everyday experiences.
- I can explain when work is done on an object and when it is not.
- I can calculate work using W = F × d, and find a missing force or displacement.
- I can explain how work changes when the force or the displacement changes.
Words to know
force
A push or a pull, measured in newtons (N).
displacement
How far an object moves from its starting point in a certain direction, measured in metres (m).
work
What is done when a force moves an object in the direction of the force. Work = force × displacement.
joule (J)
The unit for work and energy. 1 J is the work done when a force of 1 N moves an object 1 m (1 J = 1 N·m).
energy
The ability to do work. Doing work on an object transfers energy to it.
weight
The force of gravity on an object. On Earth, weight in newtons is about mass in kilograms × 9.8.
Hook: is homework really work?
You spend an hour solving math problems. You are tired. Did you do a lot of work? In everyday language, yes. In science, no! A scientist would say you did almost no work, because you barely moved anything.
But when you shovel the driveway, pull a toboggan up a hill or lift groceries onto the counter, you do real scientific work. In science, work has an exact meaning.
Pulling a toboggan uphill is real scientific work: a force moves the toboggan through a displacement in the direction of the pull. AI-generated imageRemember from earlier grades
In Grade 7 you described forces by their magnitude, direction, point and plane of application, and you used weight (N) ≈ mass (kg) × 9.8. You will use that again today to find the force needed to lift something.
The scientific meaning of work
Work is done when a force makes an object move in the direction of the force.
- Force (F): the push or pull, in newtons (N).
- Displacement (d): how far the object moves in the direction of the force, in metres (m).
- Work (W): force × displacement, in joules (J).
W = F × d
Two things must both be true for work to be done:
- A force acts on the object.
- The object moves in the direction of that force (or partly in that direction).
If either one is missing, the work done by that force is zero.
| Situation | Is work done on the object? | Why |
|---|
| Lifting a bag of groceries onto the counter | Yes | upward force, upward motion |
| Pulling a toboggan along a flat, snowy path | Yes | forward pull, forward motion |
| Holding a heavy bag perfectly still | No | force, but no displacement (d = 0) |
| Pushing hard on a brick wall that does not move | No | force, but no displacement |
| Carrying a backpack along a flat hallway at a steady speed | No work by your upward holding force | your force is up, but the backpack moves sideways |
| A hockey puck sliding on ice after it leaves the stick | No work by you | you are no longer pushing it |
Work and energy
Energy is the ability to do work. When you do work on an object, you transfer energy to it. Lifting a box onto a shelf gives it gravitational potential energy (stored energy because of its height). Pushing a toboggan to get it moving gives it kinetic energy (energy of motion). Work and energy are both measured in joules.
Your energy for doing work comes from the food you eat. A machine's comes from fuel, electricity or another energy source.
How work, force and displacement are related
Because W = F × d:
- Double the force (same distance): the work doubles.
- Double the distance (same force): the work doubles.
- Same work, more distance: less force is needed. This is the secret of machines like ramps, which you will study in the next lessons.
You can rearrange the formula: F = W ÷ d and d = W ÷ F.
Worked exampleExample 1: Pulling a toboggan
You pull a toboggan with a steady forward force of 60 N along a flat path for 25 m. How much work do you do on the toboggan?
- The force and the motion are in the same direction (forward).
- W = F × d = 60 N × 25 m
- W = 1 500 J
Worked exampleExample 2: Lifting a bag of flour
You lift a 2 kg bag of flour from the floor to a shelf 1.5 m high. How much work do you do?
- First find the force needed to lift it: its weight. F ≈ 2 kg × 9.8 = 19.6 N.
- The force is upward and the bag moves upward 1.5 m.
- W = 19.6 N × 1.5 m = 29.4 J.
Worked exampleExample 3: Finding a missing force
A worker does 900 J of work sliding a crate 6 m across a warehouse floor. What force did the worker push with?
- Rearrange: F = W ÷ d.
- F = 900 J ÷ 6 m = 150 N.
- Check: 150 N × 6 m = 900 J. ✓
The worker pushed with 150 N.
Watch out!
- Use newtons for force, not kilograms. If you are given a mass, multiply by 9.8 to get the weight in newtons.
- Use metres for displacement. Change centimetres to metres first: 75 cm = 0.75 m.
- Only the displacement in the direction of the force counts.
Just for funNext time someone tells you to do your homework, you could point out that in science, sitting still and thinking does almost zero work on anything. (We do not recommend trying this argument on your teacher.)
Hands-on activityWork detective
You need: a measuring tape, a calculator, a few labelled grocery items (for example a 1 kg bag of sugar, a 2 L jug of milk, which is about 2 kg, a 4 L jug of milk, about 4 kg), a staircase, a pencil and paper.
Safety: lift with your knees bent and the item close to your body. Ask an adult before lifting anything heavier than 4 kg. Walk, do not run, on stairs.
- Measure the height of your kitchen counter and of one high shelf in metres.
- For each item, find its weight: mass × 9.8.
- Calculate the work to lift each item from the floor to the counter, then to the high shelf.
- Stair challenge: measure the height of one step and count the steps. Multiply to get the total height. Ask an adult for your approximate mass (or use 45 kg). Calculate the work you do against gravity climbing the stairs: your weight × height.
- Climb the stairs slowly, then quickly. Is the work different? (No: the same force and the same height. Climbing fast feels harder because you do the work in less time.)
What to look for: correct use of W = F × d with newtons and metres. Example: a 2 kg jug lifted to a 0.9 m counter: 19.6 × 0.9 = 17.64 J. A 45 kg student climbing 2.16 m: 441 × 2.16 ≈ 953 J.
Your turn
1You push a shopping cart with a forward force of 50 N for 20 m. How much work do you do?
W = 50 N × 20 m = 1 000 J.
2You lift a 3 kg box onto a shelf 1.2 m high. How much work do you do?
Force = 3 × 9.8 = 29.4 N. W = 29.4 N × 1.2 m = 35.28 J (about 35 J).
3You hold a 10 kg bag of potatoes still for one minute. How much work do you do on the bag?
0 J. The bag does not move, so d = 0 and W = F × 0 = 0.
4Pulling a sled 30 m takes 2 400 J of work. What force was used?
F = W ÷ d = 2 400 ÷ 30 = 80 N. Check: 80 × 30 = 2 400. ✓
5A 500 N student climbs stairs that rise 3 m. How much work does the student do against gravity?
W = 500 N × 3 m = 1 500 J.
6A force of 40 N does 280 J of work. How far did the object move?
d = W ÷ F = 280 ÷ 40 = 7 m.
7You push a box with the same force but twice as far. What happens to the work?
The work doubles, because work is force × displacement.
More practice: warm-up
1What is the formula for work?
W = F × d (work = force × displacement).
2What unit is work measured in?
3How much work is done by a 10 N force moving an object 2 m in the direction of the force?
4Is work done when you push on a wall that does not move?
No. There is no displacement.
The ability to do work. It is also measured in joules.
More practice: on your own
1Each shovelful of snow has a mass of about 4 kg. You lift each one 0.6 m to throw it on the snowbank. How much work do you do lifting 10 shovelfuls?
Force per shovelful = 4 × 9.8 = 39.2 N. Work per shovelful = 39.2 × 0.6 = 23.52 J. Ten shovelfuls: 23.52 × 10 = 235.2 J (about 235 J).
2Ana lifts a 20 N box 1.5 m. Ben slides a box with a 15 N push for 2 m. Who does more work?
Neither: they do the same work. Ana: 20 × 1.5 = 30 J. Ben: 15 × 2 = 30 J.
3A 45 kg student climbs 12 stairs. Each stair is 18 cm high. How much work does the student do against gravity?
Height = 12 × 0.18 m = 2.16 m. Weight = 45 × 9.8 = 441 N. W = 441 × 2.16 = 952.56 J (about 953 J).
4You carry a 5 kg backpack 100 m along a flat hallway at a steady speed. How much work does your upward holding force do on the backpack? Explain.
0 J. Your holding force points up, but the backpack moves sideways. There is no displacement in the direction of your force, so that force does no work on it. (You still get tired, because your muscles use energy to hold it up.)
5A snowplow pushes snow with a force of 4 000 N for 250 m. How much work does it do? Give your answer in joules and kilojoules.
W = 4 000 × 250 = 1 000 000 J = 1 000 kJ (1 kJ = 1 000 J).
Challenge
1You can lift a 600 N box straight up onto a truck bed 1 m high, or slide it up a smooth ramp 4 m long. Ignoring friction, how much work is done each way, and what force is needed on the ramp?
Lifting straight up: W = 600 × 1 = 600 J. On a frictionless ramp, the work is the same, 600 J, but it is spread over 4 m, so the force needed is F = 600 ÷ 4 = 150 N. The ramp trades a longer distance for a smaller force.
2An elevator lifts 8 people with a total mass of 560 kg up 30 m. How much work does it do on the people?
Weight = 560 × 9.8 = 5 488 N. W = 5 488 × 30 = 164 640 J (about 165 kJ).
3A student graphs work (vertical axis) against displacement (horizontal axis) for a box pushed with a steady force of 25 N. Describe the graph and find the work at 8 m.
The graph is a straight line through the origin (0, 0), because work increases at the same rate as distance. Each metre adds 25 J, so the steepness of the line equals the force. At 8 m: W = 25 × 8 = 200 J.
Quiz
1. Which formula gives the work done?
2. A 30 N force moves a box 4 m in the direction of the force. How much work is done?
3. In which situation is no work done on the object?
4. A force does 400 J of work moving an object 8 m. What is the force?
5. What is the unit of work and energy?
6. You lift a box with the same force but to three times the height. The work...
Big idea (D2.4, D2.5): Students use the terms displacement, force, work and energy and demonstrate an understanding of the relationships between work, force and displacement. The key formula is W = F × d, with force in newtons, displacement in metres and work in joules. Weight ≈ mass × 9.8 comes from earlier grades.
How to help: Turn chores into quick estimates: "How much work to lift the laundry basket onto the bed?" Weigh it on a bathroom scale, multiply by 9.8, multiply by the height. The stair activity also connects to Grade 8 math (rates and rearranging formulas).
Common difficulties:
- Using kilograms as the force. Remind your child to multiply by 9.8.
- Using centimetres. Convert to metres first.
- Thinking that being tired means work was done. In science, work needs movement in the direction of the force. Holding something still does zero work on it, even though your muscles use energy.