Forces, Year 9

45 m/s

HintEach train is closing the gap from its own end, so both speeds work together.

The whyWhen two things travel in opposite directions, the distance between them changes at the sum of their speeds. That is why a train going the other way flashes past so quickly, and why head-on collisions are so severe.

10

HintBoth vehicles head the same way, so only the difference between them matters.

The whyThe lorry driver sees you creep past at a slow cycling pace even though the road is rushing by at 70 mph. Travelling the same way, you subtract the speeds — which is why overtaking takes so long when two vehicles are closely matched.

You can only see how the two trains move relative to each other

HintAll your eyes have to go on is the carriage next door sliding past the window.

The whyThrough the window, "that train going forwards" and "my train going backwards" look exactly alike, because the gap between you changes in the same way. You find out which is true only by checking against something else, such as the platform or a building.

Neither car is moving relative to the other

HintAsk how quickly the gap between the two of you is changing.

The whyBoth cars cover the same ground in the same time and in the same direction, so the distance between them stays fixed. Measured against the road each does 70 mph; measured against each other, the speed is zero. Whether something is "moving" always depends on what you measure it against.

Each measured it relative to something different

HintAsk what the passenger is sitting on, and what the other person is standing on.

The whyA speed has no meaning until you say what it is measured against. The passenger measures against the carriage, the person outside measures against the ground, and the two honest answers differ by exactly the speed of the train. There is no single "real" speed hiding behind them.

The steady 30 mph stretch

HintLook for the part where nothing about the motion is altering.

The whyPulling away is acceleration because the speed is rising, and braking counts too because the speed is falling. Only when nothing about the motion is changing is there no acceleration — however fast the bus happens to be going.

Car A

HintBoth end up equally fast; ask which one got there sooner.

The whyAcceleration is about how quickly speed changes, not how much speed you end up with. Both cars gain the same speed, but A does it in less than half the time, so its speed is changing faster throughout.

Its speed is not changing

HintCompare the car one moment with the car a moment later — is anything about its motion different?

The whyEveryday speech uses "accelerating" to mean "going fast". Physics keeps the word for a change in motion: getting faster, getting slower or changing direction. A car holding 200 mph along a straight is very fast and is not accelerating at all.

opposite

HintThink which way a strong headwind pushes on a cyclist.

The whyA force is needed to change how fast something moves, and its direction decides what the change is: a resultant force along the motion speeds the object up, one against the motion slows it down. Brakes, friction and air resistance all push backwards on a car that is travelling forwards.

6 N m

HintA turning effect needs two things multiplied together: how hard, and how far out.

The whyMoment = force × perpendicular distance from the pivot, so 20 × 0.3. The unit is the newton metre, written N m, because a force in newtons has been multiplied by a distance in metres.

8

HintLook at the unit the answer has been asked for before you multiply anything.

The whyThe distance must be in metres to give newton metres: 80 cm is 0.8 m, and 10 × 0.8 gives the answer. Handles are fitted far from the hinge on purpose — the same pull produces a much bigger turning effect out there.

The moment of a force

HintIn everyday speech the same word means a very short time.

The whyA push or pull does more than shove an object along — applied away from a pivot, it tries to turn it. Opening a door, tightening a nut and sitting on a seesaw are all about this turning effect, which depends on both the size of the push and how far from the pivot it acts.

moments

HintIt is not the two weights that have to match — it is each weight multiplied by something.

The whyThis is the principle of moments. One side tries to turn the beam one way and the other side tries to turn it back; when the two turning effects match, the beam stays level. What has to match is force × distance on each side, which is why where you sit matters as much as how heavy you are.

600 N m; 400 N

HintWork out the first child's turning effect, then ask what force at the shorter distance would match it.

The whyThe first child's moment is 300 × 2 newton metres. The second child must produce the same moment from 1.5 m, so their weight is that moment ÷ 1.5. Sitting closer to the pivot, they have to be heavier.