Balanced and Unbalanced Forces, and Moments

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1. Key words

2. Forces and resultant force

A force is a push or a pull. Forces are measured in newtons (N) with a newton meter (force meter). In a diagram we draw a force as an arrow: the arrow points in the direction of the force, and a longer arrow means a bigger force.

Most objects have several forces acting on them at once. The resultant force is the single force that would have the same effect as all of them together:

• Forces in the same direction: add them.
• Forces in opposite directions: subtract the smaller from the larger. The resultant acts in the direction of the larger force.
• If the resultant force is zero, the forces are balanced. If it is not zero, they are unbalanced.

3. Balanced forces

When the forces on an object are balanced (resultant force = 0), its motion does not change:

• An object that is still stays still. A book on a table: its weight (down) is balanced by the support force of the table (up).
• An object that is moving keeps moving at the same speed in the same direction. It does not slow down and stop.

4. Unbalanced forces

When the forces are unbalanced, there is a resultant force and the motion changes. What happens depends on the direction of the resultant force:

The skydiver — balanced and unbalanced forces in one story. Checkpoint loves this example. Learn the five stages:

5. Turning forces: moments

A force can make an object turn around a fixed point called the pivot. Opening a door, using a spanner, riding a seesaw and lifting the lid of a tin with a spoon are all examples. The turning effect of a force is called its moment.

"Perpendicular distance" means the distance from the pivot to the force, measured at right angles to the force. In most Stage 8 questions the force pushes straight across the lever, so you just use the distance from the pivot to where the force acts.

To get a bigger moment you can use a bigger force, or apply the force further from the pivot. That is why:

• a long spanner undoes a tight nut more easily than a short one;
• a door handle is on the edge furthest from the hinges;
• it is easier to open a tin lid with a long spoon handle than with a coin;
• on a seesaw, a light child sitting far from the pivot can balance a heavier adult sitting near the pivot.

6. Balancing: clockwise and anticlockwise moments

A force on the left of a pivot pushing down turns the beam anticlockwise. A force on the right of a pivot pushing down turns it clockwise. If the total clockwise moment equals the total anticlockwise moment, the beam is balanced (it does not turn). This is called the principle of moments.

1. Anticlockwise moment (left) = 500 N × 1.2 m = 600 N m.
2. Clockwise moment (right) = 300 N × 2.0 m = 600 N m.
3. The moments are equal, so the seesaw is balanced — even though the forces are different. The lighter person balances the heavier one by sitting further from the pivot.

7. Worked examples

Worked example 1 — In a tug of war, team A pulls the rope to the left with 1200 N and team B pulls to the right with 1050 N. (a) Calculate the resultant force. [1] (b) Describe what happens to the rope. [1]

1. (a) Opposite directions, so subtract: 1200 − 1050 = 150 N to the left (give the direction!).
2. (b) The forces are unbalanced, so the rope (and team B) starts to move to the left, towards team A, and speeds up.
3. Common mistake: adding the forces (2250 N). Forces in opposite directions are subtracted.

Worked example 2 — A car moves at a constant speed. The driving force is 2000 N. (a) What is the total of air resistance and friction? [1] (b) The driver presses the accelerator and the driving force rises to 2600 N. What is the resultant force and what happens? [2]

1. (a) Constant speed → balanced forces, so air resistance + friction = 2000 N.
2. (b) Resultant = 2600 − 2000 = 600 N forwards (1), so the car speeds up (1).

Worked example 3 — A spanner is used to turn a nut. A force of 40 N is applied 0.25 m from the centre of the nut. (a) Calculate the moment. [2] (b) The nut needs a moment of 15 N m to turn. What force is needed at the same distance? [2]

1. (a) moment = force × distance = 40 × 0.25 = 10 N m.
2. (b) force = moment ÷ distance = 15 ÷ 0.25 = 60 N.
3. Tip: rearranging works just like the speed triangle: force = moment ÷ distance; distance = moment ÷ force.

Worked example 4 — A 250 N child sits 1.6 m from the pivot of a seesaw. Where must a 400 N adult sit on the other side to balance it? [2]

1. Anticlockwise moment = 250 × 1.6 = 400 N m (1).
2. Clockwise moment must also be 400 N m: 400 × d = 400, so d = 400 ÷ 400 = 1.0 m from the pivot (1).
3. Check: the heavier person sits closer to the pivot — sensible.

Worked example 5 — A plank is pivoted at its centre. On the left, a 6 N weight is 20 cm from the pivot. On the right, a 4 N weight is 25 cm from the pivot. Will the plank balance? If not, which way will it turn? [3]

1. Anticlockwise moment = 6 × 20 = 120 N cm (1).
2. Clockwise moment = 4 × 25 = 100 N cm (1).
3. The anticlockwise moment is bigger, so the plank is not balanced and turns anticlockwise — the left side goes down (1).

Worked example 6 — Explain why a book resting on a table does not move, using ideas about forces. [2]

1. The weight of the book acts downwards and the table pushes upwards with a support force (1).
2. These forces are equal and opposite / balanced, so the resultant force is zero and the book stays still (1).

Practice

All pages in this course

Start here

• Stage 8 Science: The Tests and How to Prepare
• Thinking and Working Scientifically: Models, Investigations and Analysing Results

Biology

• Joints and Antagonistic Muscles
• Blood and Its Components
• Breathing, Gas Exchange and Diffusion in the Lungs
• A Balanced Diet, Energy Stores and Lifestyle
• Aerobic Respiration
• Ecosystems, Bioaccumulation and Invasive Species

Chemistry

• The Structure of the Atom
• Purity, Concentration and Chromatography
• Word Equations, Exothermic and Endothermic Reactions
• The Reactivity of Metals
• Impure Products and Solubility of Salts

Physics

• Speed and Distance–Time Graphs
• Balanced and Unbalanced Forces, and Moments
• Pressure, Particles and Diffusion
• Reflection and Refraction
• Dispersion and Colour
• Magnetic Fields and Electromagnets

Earth and space

• The Earth's Magnetic Field and Earth's Resources
• Climate, Weather and Climate Change
• Galaxies and Asteroids

Practice tests

• Stage 8 Science — Practice Test 1
• Stage 8 Science — Practice Test 2
• Stage 8 Science — Practice Test 3