Forces and motion, Year 11: Newton's laws

Nothing has yet pushed them backwards to slow them down

提示The brakes grip the wheels, not the people.

为什么This 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

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

为什么With 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

提示A steady velocity tells you what the resultant force must be.

为什么The 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

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

为什么Many 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

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

为什么Every 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

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

为什么Resultant 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

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

为什么Newton'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

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

为什么F = 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

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

为什么The 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

提示Something the calculation ignores is opposing the pull of the string.

为什么The 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

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

为什么Push 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

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

为什么Whenever 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

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

为什么The 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

提示Swap the roles of the two objects named in the question.

为什么A 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

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

为什么The 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

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

为什么Balanced 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.