What is a force?
A force is a push or a pull that one object puts on another. One force always needs two objects: the one that acts and the one that is acted on. This is called an interaction.
Forces are measured in newtons (N) with a spring balance (forcemeter). An apple weighs about 1 N.
- Contact forces need touching: push or pull by hand, friction, normal (support) force, tension in a rope, air resistance, buoyancy (upthrust).
- Non-contact forces act at a distance: gravity (weight), magnetic force, electric force.
Drawing forces: arrows and interaction diagrams
A force has four features, so we draw it as an arrow:
- Point of application: where the arrow starts.
- Line of action (direction): e.g. horizontal or vertical.
- Sense: which way along that line (left or right, up or down).
- Size (value): the arrow's length, using a scale like 1 cm = 10 N.
An object–interaction diagram shows the object in a circle and every other object that touches it or pulls it, joined by lines (solid for contact, dashed for non-contact). Example for a book on a table: book–table (contact), book–Earth (non-contact). Then you draw one arrow for each interaction.
Everyday forces: weight, normal force, friction, tension, buoyancy
Weight is the pull of the Earth on an object: W = m × g, with g ≈ 9.8 N/kg (often 10). Mass (kg) is the amount of matter and is the same everywhere; weight changes with gravity (on the Moon it is about 1/6). Gravity is one case of the gravitational force between any two masses; it gets weaker with distance.
Normal (support) force: a surface pushes up on what rests on it, at right angles to the surface.
Friction acts along surfaces and opposes sliding. It helps us walk and brake but wastes energy and wears parts. Rough surfaces give more friction; oil and wheels reduce it.
Tension is the pull in a stretched rope, string or spring, along the rope.
Buoyancy (upthrust) is the upward push of a liquid or gas. An object floats when upthrust equals its weight (a ship), and sinks when its weight is bigger (a stone).
What forces do: change motion and change shape
A force can:
- start or stop motion,
- make something faster or slower,
- change its direction,
- change its shape (deformation): squash, stretch, bend or twist.
A spring stretches in step with the load (up to a limit): double the weight, double the stretch. This is Hooke's law, F = k × x. If you go past the elastic limit the shape change stays (plastic deformation), like bent wire or kneaded dough.
Balanced forces, equilibrium and Newton's third law
Add forces along the same line: same direction → add; opposite → subtract. The result is the resultant (net) force.
- Net force = 0 → forces are balanced: a still object stays still; a moving one keeps the same speed in a straight line. A still object with balanced forces is in static equilibrium (book on a table: weight down = normal force up).
- Net force ≠ 0 → unbalanced: speed or direction changes.
Newton's third law: when A pushes on B, B pushes on A with an equal force in the opposite direction. The two forces act on different objects, so they never cancel each other. Feet push the ground back, the ground pushes you forward; a rocket pushes gas down, the gas pushes the rocket up.
Try it at home
Hang a rubber band from a hook and tie a small bag to it. Add coins one at a time (say 10 coins per step) and measure the stretch with a ruler. Is the stretch doubling when the load doubles? Then push a heavy book along a table with one finger: feel how the book does not move at first (friction balances you) and then suddenly slides.
Key formulas and definitions
- Unit of force: newton (N)
- Weight: W = m × g (g ≈ 9.8 N/kg on Earth, about 1.6 N/kg on the Moon)
- Resultant force: same direction → add; opposite → subtract
- Hooke's law: F = k × x (force = spring constant × extension)
- Balanced: net force = 0 → no change in motion
- Newton's third law: F(A on B) = − F(B on A)
Worked examples
1. Find the weight of a 50 kg student on Earth (g = 10 N/kg).
W = m g = 50 × 10 = 500 N.
2. The same student goes to the Moon (g = 1.6 N/kg). Mass and weight?
Mass stays 50 kg. Weight = 50 × 1.6 = 80 N.
3. Two children push a box to the right with 30 N and 20 N. Friction is 15 N. Net force?
Right: 30 + 20 = 50 N. Net = 50 − 15 = 35 N to the right, so the box speeds up.
4. A spring stretches 2 cm with 4 N. How much with 10 N (within the limit)?
Stretch per newton = 2 ÷ 4 = 0.5 cm/N. For 10 N: 10 × 0.5 = 5 cm.
5. A lamp hangs still from a cord. Its weight is 12 N. What is the tension?
It is in equilibrium, so tension up = weight down = 12 N.
6. A 3 N toy boat floats. What is the buoyant force on it?
Floating means balanced, so upthrust = weight = 3 N.
Common mistakes
- Mixing up mass (kg) and weight (N). Mass never changes; weight depends on gravity.
- Thinking a moving object needs a force to keep moving. With no friction it would keep going; a force is needed to change motion.
- Thinking the third-law pair cancels. The two forces act on different objects.
- Drawing the friction arrow in the direction of motion. Friction opposes sliding.