Work done by constant force:
formula and worked example

What work means in physics

In physics, work is energy transferred by a force moving something. Holding a heavy box still is tiring for a person but, strictly, does zero work on the box because it does not move. Pushing it across a floor does work, and the amount is the force applied multiplied by the distance covered.

This makes work the bridge between forces and energy. Once you know the work done on an object, you know how much its energy changed, which is how engineers size motors, hoists and pumps.

The formula and the conditions behind it

• Force: the constant force in newtons, acting in the same direction as the displacement.
• Distance: the distance in metres the point of application moves while the force acts.

One newton acting through one metre transfers one joule, so the unit comes out of the inputs on its own. If the force acts at an angle θ to the direction of travel, the general version is force × distance × cos θ. The simple product here is the special case where θ is zero.

The force must also stay constant. A spring or a variable engine thrust changes with position, and then you need to average it or integrate, not just multiply.

A 150 N push over 4 metres

1. 1Identify the force along the motion: 150 N.
2. 2Identify the distance moved: 4 m.
3. 3Multiply: 150 × 4 = 600.
4. 4Assign the unit: newton-metres, written as 600 J.

As a sense check, 600 J is about the energy needed to raise a mass of roughly 61 kg by one metre (600 ÷ 9.81 ≈ 61). If your intuition says the push was a light one, the numbers should look modest like this.

How to interpret joules of work

The answer tells you how much energy moved from the source of the force into the object, or into heat and deformation along the way. If the object had no friction and started at rest, 600 J would become kinetic energy. With friction present, part of it is lost as heat, and the object ends up with less.

• Positive work: the force speeds the object up or lifts it.
• Zero work: the force is perpendicular to motion, or there is no displacement.
• Negative work: the force opposes the motion, which is how friction and braking remove energy.

Dividing work by the time taken gives power. Doing 600 J in 2 s is 300 W, while doing it over 20 s is 30 W. The work is the same; the machine needed is not.

What a larger force does to the total

Work is directly proportional to force when distance is fixed, so a 10% rise in force from 150 N to 165 N lifts the work from 600 J to 660 J, exactly 10% more. There is no hidden amplification, unlike speed in kinetic energy.

The same holds for distance. Stretching the push to 8 m would double the work to 1,200 J. The practical message is that you can trade force for distance: a ramp lets you use a smaller force over a longer path to do the same work against gravity.

Common slips with work calculations

• Using the force's magnitude when it acts at an angle, such as pulling a sled by a rope, and skipping the cos θ.
• Counting time or speed in the product: work does not depend on how fast the distance was covered.
• Forgetting that a force held without movement does no work.
• Mixing units, such as force in kilogram-force or distance in centimetres, then labelling the answer joules.

A short checklist before you trust the figure

1. 1Is the force constant over the whole distance?
2. 2Does it act along the direction of travel, or do you need the angle?
3. 3Are force and distance in newtons and metres?
4. 4Do you want work done by one force, or net work from all forces including friction?

Answering these four questions turns a bare multiplication into a statement you can defend, and it makes it far easier to compare the work against a motor's rated energy or a battery's capacity.