Forces and Newton's Laws

A force is a push or a pull, and the three laws Newton set out explain what forces do to motion. They are worth learning as a connected set rather than three separate facts, because each one answers a question the previous one raises, and because between them they account for most of the mechanics items you will meet.

The forces you will actually meet

Before the laws themselves, it helps to have the cast of characters. Some forces need contact: friction between surfaces that slide, the normal force from a surface holding something up, tension in a rope or cable being pulled taut, thrust from an engine, and drag from air or water resisting motion through it. Others act at a distance with nothing in between: weight, which is gravity pulling on mass, along with magnetic and electrostatic forces that later modules cover. All of them are measured in newtons and all of them have a direction, and a question that seems to be about something exotic is usually about these few in an unfamiliar arrangement.

The other idea to fix early is the net force — the single force that would have the same effect as all the real forces put together. Two 50-newton pushes in the same direction give a net force of 100 newtons; the same two in opposite directions give zero. It is always the net force that goes into the second law, never one force picked out of the set, and a question that lists an engine thrust and a drag figure separately is asking you to combine them first. Adding forces that are not in a straight line needs a little geometry, which a later lesson covers; for now every force in an example points along the same line.

The first law: things carry on as they are

An object at rest stays at rest, and an object moving stays moving at the same velocity, unless a net force acts on it. The word "net" is doing heavy lifting there and it will come back in a later lesson: several forces can act at once and still add up to nothing, in which case the motion does not change. The property being described is inertia — the reluctance of matter to have its motion altered — and the more mass something has, the more inertia it has.

The half of this law that clashes with intuition is the moving half. Everyday experience says that things stop unless you keep pushing, so it feels as though motion needs a continuous force to sustain it. What experience is actually showing you is friction and air resistance quietly doing their work; remove them, as space does, and an object keeps going indefinitely with nothing pushing it at all. Getting this straight now matters, because an answer option offering "a forward force is needed to keep it moving at constant speed" appears repeatedly and is always wrong.

The second law: force, mass and acceleration

If a net force does act, the object accelerates, and how much depends on how hard you push and how much mass you are pushing.

Read it as a statement about proportions before treating it as arithmetic. For a fixed mass, doubling the force doubles the acceleration. For a fixed force, doubling the mass halves it. And because the newton is defined as exactly the force that accelerates one kilogram at one metre per second squared, the equation needs no conversion factor — the units were chosen to make it come out clean. Rearranged, it gives $m = \frac{F}{a}$ and $a = \frac{F}{m}$, derived by the same dividing-both-sides move from the units lesson.

It is worth being explicit about what the equation does not say. It says nothing about how fast the object is going — only about how quickly that speed is changing. A spacecraft coasting at enormous velocity with its engines off has no net force on it and therefore no acceleration, and there is no contradiction in that. Equally, an object can be momentarily stationary and still have a large force on it and a large acceleration, which is exactly the case of the ball at the top of its throw from the next lesson. Force goes with change of motion, never with motion itself.

The third law: forces come in pairs

For every force there is an equal and opposite force. The detail that decides most exam questions is that the two act on different objects. When you push on a wall, the wall pushes back on you with exactly the same size of force in the opposite direction — but one of those forces acts on the wall and the other on you, so they do not cancel each other. If they did, nothing could ever accelerate, since every force in the universe has a partner.

This is what makes walking, swimming and jet propulsion work. Your foot pushes backwards on the ground and the ground pushes forwards on you; a propeller throws air backwards and the air pushes the aircraft forwards. In each case the useful force is the reaction, acting on a different body from the action.

Drawing the forces out

Before calculating anything, it is worth drawing every force acting on the one object you care about, with each arrow pointing the way the force pushes. That drawing is called a free-body diagram, and it is the single most useful habit in mechanics — most wrong answers come from a force being forgotten or pointed the wrong way rather than from bad arithmetic.

One piece of vocabulary from that figure: the upward push from the surface is called the normal force, where "normal" is used in its geometric sense of perpendicular. It exists because the surface is solid and the block cannot pass through it, and on level ground with nothing else pressing down it is equal in size to the block's weight.

Putting it to work

Why it matters in aviation

Flight is normally described with four forces, and they are the same cast this lesson introduced: lift acting upwards, weight downwards, thrust forwards and drag backwards. In steady level flight at constant speed the net force is zero — lift matches weight, thrust matches drag — so the first law accounts for why the aircraft neither climbs nor accelerates while all four forces remain large. Nothing has been switched off; the sums simply cancel, which is the same point as the spacecraft coasting with its engines off.

The third law explains where thrust comes from in both propeller and jet installations. Each takes hold of a mass of air and accelerates it rearwards, and the reaction on the aircraft is what drives it forward — a propeller working on a large mass of air at modest speed, a jet on a smaller mass at high speed, but the mechanism identical. The second law then sets the price of weight. For a given thrust, a heavier aircraft accelerates more slowly, so it takes longer to reach its takeoff speed and needs more runway to get there. That is why takeoff performance is calculated for the actual weight on the day, along with the conditions that affect thrust, rather than read off one fixed figure for the type.

What the test asks

Three traps, one per law. For the first law, the option claiming steady motion requires a steady forward force. For the second, being handed the engine's total force when the question asked about the net force, with friction given separately and meant to be subtracted. For the third, the claim that action and reaction cancel out — they are equal and opposite, but they act on different bodies, and only forces on the same body can cancel.