Forces in Motion

What is left over

Newton gets three laws in most textbooks and they are usually learned as three separate things. They are not three things. Nothing that has ever moved responded to one force. A car has the engine pushing it forwards, friction and air resistance pushing it backwards, its weight pulling it down and the road pushing it up. What it actually does depends on the single force left over when all of those are added up, which is called the resultant. So there is one question, and it has two answers. Is the resultant zero? If it is, the velocity does not change at all. That covers a parked car and it equally covers a car doing seventy on a motorway, which surprises people. If it is not zero, the object accelerates in the direction of the resultant, by an amount that depends on its mass. Carry that one question through: what is the resultant here, and is it zero? How springs stretch is the other module on this topic.

Five words, and a diagram worth drawing

The first is the one the whole module is about. The last is a habit rather than a word, and it is the single most useful thing you can do to a forces question before answering it.

Follow one skydiver down

Someone jumps from a plane, well before the parachute is opened. Put what happens into order.

• At the moment of jumping there is almost no drag, so the resultant is nearly the whole weight
• The resultant is downwards and large, so the skydiver accelerates downwards quickly
• As the speed rises, the drag from the air rises with it
• The resultant gets smaller, so the skydiver is still speeding up but less sharply
• Eventually the drag has grown until it exactly equals the weight
• The resultant is now zero, so the speeding up stops and the fall continues at a steady speed

Seventy on the motorway

A car is travelling along a flat, straight motorway at a steady seventy. A student says that since it is not speeding up or slowing down, there must be no forces acting on it. What is wrong with that?

• There are several forces acting, and they add up to zero. A zero resultant means the velocity does not change, which includes staying at a steady speed. Balanced is not the same as absent
• Nothing is wrong; an object moving at constant speed genuinely has no forces on it
• There must be a resultant force forwards, or the car could not keep moving
• The forces cancel, so nothing at all is happening to the car

Two answers to one question

Work out the resultant, then look at which column you are in. Almost every forces question in the examination is one of these two, and knowing which one you are in tells you what to say next.

Five situations, five reasons

Find the acceleration

A car of mass 1500 kilograms is driven forwards by a force of 4000 newtons. The resistive forces on it total 1000 newtons. Work out the resultant force, then use it to find the acceleration of the car.

Is the resultant zero

For each situation, decide what the resultant force is doing. Three lives.

Why stopping takes so far

Stopping distance is usually learned as a list of factors to recite. It is the resultant question again, asked about a car that has to lose all its speed. Thinking distance is how far the car travels before the brakes are even touched. There is no braking force acting yet, so the resultant is about zero and the speed does not change at all. It depends on the reaction time and on how fast the car was already going. Braking distance is what happens once the brakes are on and there is a large backwards resultant. It depends on the speed, on the brakes and on the road surface, and it grows far faster than the speed does. ⭐ The two are affected by different things, and that is where the marks are. Being tired or distracted lengthens the THINKING distance and leaves the braking distance untouched. Worn brakes or a wet road lengthen the BRAKING distance and leave the thinking distance untouched. Going faster lengthens both, which is why it matters so much more than either of the others.

Two claims to strike out

Five statements from a set of revision notes. Tap the TWO that are wrong.

• Weight is a force, and is the pull of gravity on a mass
• An object moving at a steady speed in a straight line has a resultant force of zero
• A resultant force is needed to keep an object moving at a steady speed
• At terminal velocity the forces on a falling object have stopped acting
• Drag on a falling object increases as the object goes faster

The boat on the river

A boat sits on a river with its engine off, and the current carries it downstream at whatever speed the river is going. Start the engine, point it upstream, and open the throttle until the bank stops moving past. The boat is now holding perfectly still. It would be absurd to say that nothing is pushing it. The river is pushing one way with everything it has, and the engine is pushing the other way just as hard. What decides where the boat goes is never one of those two on its own. It is whatever is left when you take one away from the other, and just now that happens to be nothing at all. Open the throttle a little further and the boat creeps upstream. Ease it back and it drifts down again. And here is the other half. Do exactly the same thing with a barge loaded to the gunwales and the response is far more sluggish. Same change of throttle, same river, and the heavier boat takes much longer to do anything about it.

Put the proper words back

When several forces act on an object, the single force that would have the same effect as all of them together is called the _____. The downward pull of gravity on an object is its _____, and the resistive force from the air on something falling is called _____. A falling object speeds up until those two are equal, after which there is nothing left over and it falls at a steady _____ velocity. Whenever the leftover force is not zero the object will _____, and how much it does so for a given force depends on its _____.

Changing the acceleration

A trolley is pulled along a bench by a steady force, and its acceleration is measured. Select every change that would INCREASE the acceleration.

• Increasing the pulling force while leaving the trolley as it is
• Taking some of the load off the trolley while pulling with the same force
• Reducing the friction between the trolley and the bench
• Adding more load to the trolley while pulling with the same force
• Pulling for a longer time with the same force

Four judgements to make

Four situations, each answered by working out what is left over. Each stage sets out where things stand and hands you the decision.

• A cyclist is freewheeling down a long hill and notices that after a while they stop getting any faster, although the hill goes on. Decide what has happened.
• A driving instructor is explaining why a car travelling twice as fast needs far more than twice the distance to stop. Decide what to say about the two parts of that distance.
• Two identical trolleys are pulled along a bench by identical forces, but one is loaded with extra masses. A student predicts they will accelerate equally because the forces are the same. Decide what to tell them.
• A student writes that at the top of its flight a thrown ball has no force on it, because it is momentarily not moving. Decide what is wrong.

Build the forces answer

Assemble the sentence that gets the marks whenever a question asks you to explain the motion of something.

Explain motion from one idea

Explain why a car can travel at a steady speed even though large forces act on it, and explain why a falling object reaches a terminal velocity instead of speeding up for ever. Use the idea of a resultant force throughout.

• Explain what a resultant force is, and say what you would draw before answering a forces question
• Explain what a resultant of zero means for the velocity, and why that includes moving at a steady speed
• Name the forces on a car cruising on a level road, and say how they are arranged
• Explain what happens to the drag on a falling object as it speeds up, and why
• Finish by explaining what is true of the forces at terminal velocity, being careful not to say that they have stopped