Forces and motion in machines
A force is a push or a pull. It is measured in newtons (N). If forces on a part are balanced, the part keeps doing what it was doing. If they are not balanced, the part speeds up, slows down or turns.
The leftover force is the net force. For a trolley: net force = push − friction.
Acceleration = net force ÷ mass (a = F ÷ m). A bigger force gives more acceleration. A bigger mass gives less. This is why a loaded truck is slow to start.
Friction in machines
Friction is the force that rubs against motion when two surfaces touch. It always points opposite to the motion. A simple rule: friction = μ × m × g, where μ is how rough the surfaces are (no unit), m is mass and g = 10 m/s² (about).
Friction is useful in brakes, belts and tyres. It is harmful in shafts and gears because it makes heat and wears parts. We reduce it with oil or grease, ball bearings and smooth surfaces.
If the push is not bigger than friction, the net force is zero and the machine part does not start moving.
Work, energy and power
Work is done when a force moves something. Work = force × distance (in the direction of the force). Unit: joule (J). Pushing a wall that does not move is no work in science.
Energy is the ability to do work. It is also in joules. Fuel and electricity give a machine energy; the machine changes it into work.
Power = work ÷ time. Unit: watt (W), 1 W = 1 J per second. A powerful machine does the same work faster. 1 kW = 1000 W.
Efficiency: energy that is wasted
No machine turns all its input energy into useful work. Some becomes heat and sound, mostly because of friction.
Efficiency = useful output ÷ input × 100%. An efficiency of 75% means 25% is wasted. Better lubrication and bearings raise efficiency.
Machines also trade force for distance: a lever gives more force over a smaller distance, but the work stays the same (see Mechanisms).
Try it: trolley and books
Tie a string to a toy car. Pull it with a rubber band stretched to the same length every time. Put 2 books in the car, then 4 books. Guess first: will it speed up less or more? Then rub the floor with a cloth or sprinkle sand and try again. You are repeating steps 1 to 3 of the 3D with real things.
Key formulas and definitions
- Net force = push − friction
- a = F ÷ m (m/s² = N ÷ kg)
- Friction = μ × m × g, g ≈ 10 m/s²
- Work W = F × d (joule, J)
- Power P = W ÷ t (watt, W)
- Efficiency = useful output ÷ input × 100%
Worked examples
1. A 20 N push moves a 4 kg trolley with no friction. Find the acceleration.
a = F ÷ m = 20 ÷ 4 = 5 m/s².
2. A 30 N push acts on a 6 kg cart. Friction is 12 N. Find the acceleration.
Net force = 30 − 12 = 18 N. a = 18 ÷ 6 = 3 m/s².
3. A 5 kg trolley has μ = 0.2. Find the friction force (g = 10 m/s²).
Friction = μ × m × g = 0.2 × 5 × 10 = 10 N.
4. A force of 50 N pushes a box 8 m. How much work is done?
W = F × d = 50 × 8 = 400 J.
5. A crane lifts a 500 N load up 6 m in 10 s. Find the work and the power.
Work = 500 × 6 = 3000 J. Power = 3000 ÷ 10 = 300 W.
6. A motor takes in 2000 J and gives 1500 J of useful work. Find the efficiency and the wasted energy.
Efficiency = 1500 ÷ 2000 × 100 = 75%. Wasted = 2000 − 1500 = 500 J (as heat).
Common mistakes
- Using the full push instead of the net force. Always subtract friction first.
- Thinking friction helps the motion. It always points against the motion.
- Mixing up work and power. Work is in joules; power is work per second, in watts.
- Forgetting that no distance means no work, even if you push hard.