Forces and motion, Year 11: Newton's laws

Nothing has yet pushed them backwards to slow them down

HintThe brakes grip the wheels, not the people.

The whyThis is Newton's first law: an object keeps moving at the same speed in the same direction unless a resultant force acts on it. The brakes slow the bus, but the passengers carry on at the old speed until the floor, a handrail or a seat in front supplies a force on them too.

The first law

HintWith almost no friction, hardly any resultant force acts on the puck.

The whyWith no resultant force, a moving object carries on at the same speed in a straight line — it needs no push to keep going. On rougher ground friction supplies a resultant force, which is the only reason things usually seem to 'run out' of motion.

800

HintA steady velocity tells you what the resultant force must be.

The whyThe velocity is not changing, so by Newton's first law the resultant force is zero. The resistive forces (friction and air resistance) must therefore exactly balance the driving force. The speed of 20 m/s plays no part in the answer.

resultant

HintIt is the single force left over when all the forces on the object are combined.

The whyMany forces can act on an object and still leave its motion unchanged, as long as they cancel. What matters is the overall force once they are all added together as vectors. A change of velocity can mean a change of speed, of direction, or of both.

Inertia

HintIt is why a loaded trolley is hard to get going and just as hard to stop.

The whyEvery object resists having its motion changed: left alone, it carries on doing whatever it was doing. This is the idea behind Newton's first law, given a name. It is not a force, and nothing has to act to keep it going.

3 m/s²

HintThe F in the equation is what is left over once the opposing forces have been set against each other.

The whyResultant force = mass × acceleration, or F = m a; AQA expects this equation to be recalled. First find the resultant force: 2000 − 500 = 1500 N forwards. Then a = F ÷ m = 1500 ÷ 500. The F is always the resultant force, never just the biggest one.

It halves

HintIn a = F ÷ m, the number you divide by has just become twice as big.

The whyNewton's second law says acceleration is proportional to the resultant force (a ∝ F) and inversely proportional to the mass (a ∝ 1 ÷ m). With F unchanged, twice the mass gives half the acceleration: the same push now has twice as much 'stuff' to get moving. Triple the mass and the acceleration falls to a third.

6

HintRearrange the equation so that the quantity you want stands alone, then divide.

The whyF = m a rearranges to m = F ÷ a, so the mass is 30 ÷ 5 kilograms. Check by putting it back: that mass × 5 m/s² gives the 30 N you started with.

Move a mass from the trolley to the hanging stack

HintThe slotted weights on the string are being accelerated too, so they count as part of what is moving.

The whyThe force is the weight of the hanging masses, and it is the independent variable; the acceleration is the dependent variable. The trolley, the string and the hanging masses all speed up together, so the control variable is their total mass. Passing masses across from the trolley changes the force while that total stays fixed.

Friction acting against the trolley's motion

HintSomething the calculation ignores is opposing the pull of the string.

The whyThe calculation assumes the pull of the hanging masses is the resultant force. In practice friction at the wheels and the pulley, and a little air resistance, act the other way, so the resultant force is slightly smaller and so is the acceleration. Tilting the runway very slightly can compensate for this.

Inertial mass

HintIt is the m in F = m a, described by what it does.

The whyPush two objects with the same force: the one that accelerates less has more of this. Rearranging Newton's second law gives m = F ÷ a, so it can be found by measuring a force and the acceleration it produces, without weighing anything.

The third law

HintLook for a pair of forces, one acting on each of two different things.

The whyWhenever one object pushes on a second, the second pushes back on the first with an equal force in the opposite direction. The two forces act on different objects — her push is on the water, the water's push is on her — which is why they do not cancel and she moves.

Neither — the two forces are equal

HintNewton's third law takes no notice of how massive either partner is.

The whyThe lorry pushes on the car exactly as hard as the car pushes on the lorry, in opposite directions. The car comes off worse because that same-sized force acts on a much smaller mass, so its motion changes far more violently.

The book pulls the Earth upwards with a force of 5 N

HintSwap the roles of the two objects named in the question.

The whyA third-law pair always involves the same two objects with their roles exchanged: if A pulls B, then B pulls A. Both forces are of the same type — here both are gravitational. The table's upward push on the book is a different interaction, between the book and the table.

equal; opposite

HintOne word compares how big the two forces are; the other compares which way they point.

The whyThe law holds whether the objects are still, moving steadily or accelerating, and whatever their masses. The two forces always act on different objects, one on each, and are of the same type.

different; same

HintAsk how many things are involved, and what kind of push or pull each one is.

The whyBalanced forces both act on one object and can be of different types — a book's weight and the table's push, say. A third-law pair is one force on each of two objects, and both forces are the same kind, such as two gravitational pulls or two contact pushes. Because they act on different objects, a third-law pair can never cancel.