What is a force?
A force is a push or a pull. We cannot see a force, but we see what it does. A force can:
- start a still object moving,
- speed it up or slow it down,
- change its direction,
- change its shape (squeeze a ball of dough).
SI unit of force: newton (N). Force has size and direction, so it is a vector. We draw it as an arrow.
Balanced and unbalanced forces
When many forces act on a body, we add them up (with direction) to get the net force.
- Balanced forces: the net force is zero. The motion does not change. A still box stays still; a moving box keeps its speed and direction. Example: a tug of war where both teams pull equally.
- Unbalanced forces: the net force is not zero. The body speeds up, slows down or turns in the direction of the net force.
In the 3D: 5 N − 5 N = 0 N (balanced), then 10 N − 4 N = 6 N (unbalanced).
Friction
Friction is the force between two surfaces in contact that opposes sliding. It always acts opposite to the motion (or to the attempted motion).
- Rough surfaces give more friction; smooth surfaces (ice, oiled floor) give less.
- If you push a heavy almirah gently and it does not move, friction exactly balances your push.
- A ball rolling on the ground slows down and stops because of friction, not because "motion runs out".
Friction is useful (walking, brakes, writing) and also wasteful (wears out parts, heats machines). We reduce it with oil, grease, ball bearings and smooth shapes.
Newton's first law and inertia
First law: an object stays at rest, or keeps moving at the same speed in a straight line, unless an unbalanced force acts on it.
Galileo first saw this by rolling marbles down slopes: the smoother the surface, the farther they went. With no friction at all, a marble would never stop.
Inertia is the natural habit of a body to resist any change in its state of rest or motion. The first law is also called the law of inertia.
- Mass is the measure of inertia. A loaded truck is harder to start or stop than a bicycle.
- You jerk forward when a bus stops suddenly; you fall back when it starts suddenly.
- Flick a card from under a coin on a glass: the card flies away, the coin drops into the glass.
- Beating a carpet makes the dust fall off, because the dust stays behind when the carpet moves.
Momentum
Momentum (p) is the "amount of motion" in a body.
p = m × v
It is a vector, in the direction of velocity. SI unit: kg m/s.
A slow truck and a fast cricket ball can both hurt, because momentum depends on mass and velocity. To stop a body, we must remove its momentum, and that needs a force acting for some time.
Newton's second law: F = ma
Second law: the rate of change of momentum of a body is proportional to the unbalanced force on it, and happens in the direction of the force.
F ∝ (mv − mu) ÷ t = m(v − u) ÷ t = ma. Choosing units so that the constant is 1:
F = m × a
1 newton is the force that gives a 1 kg mass an acceleration of 1 m/s². So 1 N = 1 kg m/s².
- Same force, double mass → half acceleration (step 4 of the 3D).
- F × t = change in momentum. This is why a fielder draws his hands back: a longer time means a smaller force on his hands. High jumpers land on soft cushions for the same reason.
The first law is hidden inside the second: if F = 0, then a = 0, so velocity does not change.
Newton's third law: action and reaction
Third law: when one body pushes another, the second pushes back on the first with a force that is equal in size and opposite in direction.
- The two forces act on two different bodies, so they never cancel each other.
- They act at the same instant.
- Equal forces do not mean equal accelerations: the lighter body accelerates more (a = F/m).
Examples: you push the ground back to walk forward; a swimmer pushes water back; a boat moves back when a person jumps ashore; a gun recoils; a rocket pushes gas down and the gas pushes the rocket up.
Forces on a system of objects and conservation of momentum
A system is a group of bodies we look at together, like two trolleys and the spring between them.
- Internal forces act between the bodies inside the system. By the third law they come in equal and opposite pairs, so they add up to zero for the whole system.
- External forces come from outside (a push by your hand, friction from the floor).
So only external forces can change the total momentum of a system. If the net external force is zero, the total momentum stays the same. This is the law of conservation of momentum:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In the 3D both trolleys start at rest (total 0). After the spring pushes them: 1 kg × (−4 m/s) + 2 kg × (+2 m/s) = 0. The same idea explains gun recoil and a rocket launch.
If two bodies are joined or pushed together by an outside force, you can also treat them as one body: acceleration = total external force ÷ total mass.
Try it: inertia and third law at home
- Coin and card: put a playing card on a glass and a coin on the card. Flick the card quickly sideways. Predict first: where does the coin go? (It drops into the glass: inertia of rest.)
- Balloon rocket: tie a string across a room, pass it through a straw, tape a blown-up balloon to the straw and let the air out. Air rushes back, the balloon moves forward (third law).
- In the 3D: in free play, set F = 10 N. Change m from 1 kg to 5 kg. Predict how a changes, then push and check.
Key formulas and definitions
- Net force = sum of all forces (with direction)
- Momentum p = m × v (unit kg m/s)
- Second law: F = m × a = m(v − u) ÷ t
- 1 N = 1 kg × 1 m/s²
- Impulse: F × t = change in momentum = mv − mu
- Third law: F(A on B) = − F(B on A)
- Conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- Recoil: m_gun × v_gun = − m_bullet × v_bullet (starting from rest)
Worked examples
1. Two forces act on a trolley: 12 N to the right and 5 N to the left. Find the net force. Are the forces balanced?
Net force = 12 − 5 = 7 N to the right. The net force is not zero, so the forces are unbalanced and the trolley will accelerate to the right.
2. Find the momentum of a 0.15 kg cricket ball moving at 30 m/s.
p = m × v = 0.15 × 30 = 4.5 kg m/s, in the direction of the ball's motion.
3. What force is needed to give a 1200 kg car an acceleration of 2 m/s²?
F = m × a = 1200 × 2 = 2400 N.
4. A 20 N force acts on a 5 kg block on a smooth floor. Friction is 5 N. Find the acceleration.
Net force = 20 − 5 = 15 N. a = F ÷ m = 15 ÷ 5 = 3 m/s².
5. A 1000 kg car moving at 20 m/s is stopped by its brakes in 4 s. Find the braking force.
a = (0 − 20) ÷ 4 = −5 m/s². F = m × a = 1000 × (−5) = −5000 N. The braking force is 5000 N, opposite to the motion. (Or: change in momentum = 0 − 20000 = −20000 kg m/s; F = −20000 ÷ 4 = −5000 N.)
6. A 4 kg gun fires a 20 g bullet at 400 m/s. Find the recoil velocity of the gun.
Total momentum before = 0. After: 0.02 × 400 + 4 × v = 0 → 8 + 4v = 0 → v = −2 m/s. The gun moves back at 2 m/s.
7. A 2 kg trolley moving at 3 m/s hits a still 1 kg trolley and they stick together. Find their common velocity.
Momentum before = 2 × 3 + 1 × 0 = 6 kg m/s. After: (2 + 1) × v = 6 → v = 2 m/s in the same direction.
8. Two blocks of 3 kg and 2 kg touch each other on a smooth floor. A 10 N push acts on the 3 kg block. Find the acceleration and the force the 3 kg block puts on the 2 kg block.
Treat both as one system: a = 10 ÷ (3 + 2) = 2 m/s². The 2 kg block needs F = 2 × 2 = 4 N, so the 3 kg block pushes it with 4 N. By the third law, the 2 kg block pushes back on the 3 kg block with 4 N (an internal pair that cancels for the system).
Common mistakes
- Thinking a moving body needs a force to keep moving. It needs a force only to change its motion; things stop because of friction.
- Saying action and reaction cancel. They act on two different bodies, so they cannot cancel each other.
- Forgetting to subtract friction before using F = ma. Use the net force.
- Forgetting to change grams to kilograms (20 g = 0.02 kg) in momentum sums.