Forces – GCSE Combined Science Physics

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Think about kicking a football. Your foot pushes the ball and it shoots away across the grass. Later it slows down, drops and rolls to a stop. A force caused every one of those changes.

A force is a push or a pull. Forces can start something moving, stop it, speed it up, slow it down or change its direction. They can also change its shape, like squashing a sponge or stretching a rubber band.

Here is a picture to hold on to. Imagine a tug of war between two teams. If one team pulls harder, the rope moves their way. If both teams pull equally hard, the rope stays still, even though everyone is pulling.

That tug of war is the big idea of this lesson. Forces have a size and a direction, and what matters is what is left over when they are all added up. The left-over force decides whether something speeds up, slows down or carries on as it was.

By the end you will be able to do three things. You will say what a force is and tell a vector from a scalar. You will work out the weight of an object and the resultant force on it.

You will also meet Newton's three laws of motion. They explain why things stay still, why they speed up and why every push has a push back. Two short equations finish the job, one for force and acceleration and one for work done. Nothing here needs more than multiplying and dividing.

What a force is, and why direction matters

A force is measured in newtons. We write newtons as N. A small apple pulling down on your hand with its weight is about 1 N, and a newton meter is the tool that measures it. Bigger forces have bigger numbers, so 100 N is a much stronger push than 5 N.

A force always has a size and a direction. Pushing a door open and pulling it open can use the same size of force. The direction is different, so the door ends up moving in a different way.

A quantity with both size and direction is called a vector. Force is a vector. Velocity is a vector too, because velocity is speed in a stated direction, such as 5 m/s north.

A quantity with size only is called a scalar. Mass, speed, time and temperature are scalars. You would never say that your mass is 50 kg upwards, because mass has no direction at all.

We draw a force as an arrow. The arrow points the way the force acts, and a longer arrow means a bigger force. Always label each arrow with the name of the force, such as push, weight or friction.

Contact forces, non-contact forces and force pairs

Some forces need things to touch. These are called contact forces. When you push a shopping trolley, your hands touch it, so your push is a contact force.

Friction is a contact force that tries to stop two surfaces sliding past each other. It is why your trainers grip the floor. Air resistance is friction with the air, and it slows a cyclist down.

Tension is the pull in a rope or string when it is stretched, like the rope in a tug of war. The normal contact force is the push of a surface on something resting on it. A book on a table is pushed up by the table, and the word normal here just means at right angles to the surface.

Some forces work with no touching at all. These are non-contact forces. Gravity pulls a dropped phone to the floor, a magnet can pull a paper clip across a gap, and a rubbed balloon can pull on your hair.

To tell them apart, ask one question. Is something touching? If yes, it is a contact force, and if no, it is a non-contact force. In the exam, name the force and say what it is acting on.

Every force comes from an interaction between two objects. When you lean on a wall, you push the wall and the wall pushes you. Newton's third law says that whenever two objects interact, the forces they exert on each other are equal and opposite. The two forces are the same size, they point in opposite directions and they are the same kind of force.

A swimmer pushes the water backwards, and the water pushes the swimmer forwards. The two forces in a pair act on different objects, so they can never cancel each other out. A book rests on a table. The table pushes up on the book, and the book pushes down on the table. Those two are a pair. The Earth pulls the book down, and the book pulls the Earth up. That is a second pair.

Forces that balance are a different idea. The weight of the book and the push of the table both act on the same book, so they can balance each other. They are not a third law pair. A pair is always one force on each of two objects.

Weight and mass

Mass is how much matter an object has. It is measured in kilograms, kg. A bag of sugar has a mass of 1 kg wherever it is in the universe.

Weight is the pull of gravity on an object. Close to the Earth, this force is due to the gravitational field around the Earth. Weight is a force, so it is measured in newtons, N. The same bag of sugar weighs about 10 N on Earth.

The gravitational field strength tells you how many newtons of pull there are on each kilogram. It is written g. Take g = 10 N/kg on Earth, which means every 1 kg is pulled down by 10 N. A 2 kg bag of rice is therefore pulled down by 20 N.

weight = mass × gravitational field strength, or W = m × g in symbols. Use it when you know the mass and want the weight. The mass must be in kg, and the weight comes out in N.

Mass does not change when you travel to the Moon, but weight does, because gravity there is weaker. The Moon's field strength is about 1.6 N/kg. A 10 kg bag weighs 100 N on Earth but only 16 N on the Moon.

Weight and mass are directly proportional. Double the mass and the weight doubles. We write this as W ∝ m. On a graph of weight against mass you get a straight line through the origin, and its gradient is the gravitational field strength.

Gravity pulls on every part of an object, but we draw the weight as one arrow. It starts from a single point called the centre of mass. For a regular object such as a ruler, that point is in the middle. Weight always points straight down.

Weight is measured with a newton meter, which is a calibrated spring balance. On Earth the real value of g is about 9.8 N/kg. A question tells you which value to use.

Resultant forces, balanced forces and Newton's first law

Usually more than one force acts on an object at the same time. The resultant force is the single force that would have the same effect as all of them together. In a tug of war, it is how much one team is winning by.

To find it, work along one straight line. Add forces that point the same way, and subtract forces that point in opposite directions. Then say which way the answer points, and never add two forces that pull against each other.

Here is an example. A car is driven forwards by 3000 N. Air resistance and friction push back with 1000 N in total. The resultant is 3000 − 1000 = 2000 N forwards.

When two forces are equal and opposite, the resultant force is zero. We say the forces are balanced. A book resting on a table has its weight pulling down and the table pushing up with exactly the same force.

Newton's first law says what happens when the resultant force is zero. A stationary object stays stationary. A moving object keeps moving at the same speed in the same direction, so its velocity does not change. The velocity of an object only changes if a resultant force acts on it.

A car cruising at a steady speed follows this law. The driving force balances the resistive forces, so the resultant force is zero. A zero resultant force does not mean that nothing is moving. It means that nothing is speeding up, slowing down or turning.

The first law also explains why things stop. A box slides across a rough floor and stops, because friction is a resultant force pointing backwards. On smooth ice, a puck slides much further. A force is only needed to change the motion.

Higher tier: inertia is the tendency of an object to stay at rest, or to keep moving at a steady velocity. When a bus brakes, your body carries on forward at the old velocity. The bigger the mass, the bigger the inertia.

Higher tier: to show the forces on one object, draw a free body diagram. Draw the object on its own, with one labelled arrow for every force acting on it and nothing else. If the arrows balance, the resultant force is zero.

Higher tier: a single force can be split into two forces at right angles, called components. A sledge pulled by a rope at an angle is pulled forwards by one component and lifted by the other. Together they have the same effect as the original force. To find the resultant of two forces at an angle, draw both to scale, head to tail. Then measure the line that completes the triangle.

Higher tier: an object is in equilibrium when the forces on it are balanced and the resultant force is zero. If you draw the forces head to tail in a vector diagram to scale, the arrows form a closed shape, such as a triangle. If the shape does not close, there is a resultant force, and its size and direction are given by the line that would close it.

A moon or satellite in a circular orbit keeps a constant speed, but its direction is always changing, so its velocity is changing. A changing velocity means there is a resultant force, and here it is the pull of gravity towards the centre of the orbit.

Newton's second law: resultant force and acceleration

If the resultant force is not zero, the velocity changes. The speed, the direction or both can change. We call a change in velocity acceleration, and a car pulling away from traffic lights is a good picture of it.

Acceleration is measured in metres per second squared, m/s². An acceleration of 2 m/s² means the speed goes up by 2 m/s every second. Slowing down is a negative acceleration, and speeding up quickly means a large one.

The link is Newton's second law. The acceleration of an object is proportional to the resultant force on it, and inversely proportional to its mass. As an equation, resultant force = mass × acceleration, or F = m × a in symbols. The force is in N, the mass is in kg and the acceleration is in m/s². Use it whenever a force makes something speed up or slow down.

Use it when you know two of the three quantities. To find the acceleration, rearrange it to a = F ÷ m. A bigger force gives a bigger acceleration, and a bigger mass gives a smaller one, which is why an empty trolley speeds up more easily than a full one.

Always use the resultant force, not one of the forces on its own. An engine pushes with 2400 N and 400 N pushes back, so the resultant is 2000 N. A mass of 800 kg then accelerates at 2000 ÷ 800 = 2.5 m/s².

Notice that when the resultant force is zero, a = 0 and the velocity does not change. That is Newton's first law again. It is the second law with nothing left over.

Higher tier: motion in a circle. An object moving in a circle at a steady speed is always changing direction, so its velocity is changing even though its speed is not. This means it is accelerating, so there must be a resultant force. The force acts towards the centre of the circle and is called the centripetal force. For the Moon it is gravity, for a car on a bend it is friction between the tyres and the road, and for a ball whirled on a string it is the tension in the string.

Work done

In physics, work is done when a force moves something. Pushing a car along a road does work. Pushing on a wall that does not move does no work, however tired you get.

Work done is energy transferred. The unit is the joule, J. One joule is the work done when a force of 1 N moves something 1 m, which is about lifting a small apple from the floor onto a table. So 1 joule = 1 newton-metre, and 30 N m is the same as 30 J.

work done = force × distance moved in the direction of the force. In symbols, W = F × s. The symbol W is also used for weight, so write the words in your working to keep the two apart.

A rope pulls a sledge with 25 N for 6 m. The work done is 25 × 6 = 150 J. Most of that energy ends up as heat, because of friction between the sledge and the snow.

The energy goes to a store. Lifting a box transfers energy to its gravitational potential store, and pushing a trolley transfers energy to its kinetic store. Work done against friction heats the surfaces, so the object and its surroundings get warmer. Rub your hands together hard and you can feel it.

The movement must be in the direction of the force. When you carry a heavy bag along a flat path, your arms push up but you move forwards. The upward force does no work on the bag, because the movement is at right angles to it.

Recap

A force is a push or a pull, measured in newtons. Force is a vector, so it has a size and a direction. Mass is a scalar, because it has a size and no direction.

Forces are contact forces, such as friction, tension and air resistance, or non-contact forces, such as gravity and magnetism. Newton's third law says that when two objects interact, they push or pull on each other with equal and opposite forces. The pair acts on two different objects, so it never cancels.

weight = mass × g, with g = 10 N/kg. Mass is in kg and never changes. Weight is a force in N, it is proportional to mass, and it is smaller on the Moon. It acts from the centre of mass.

The resultant force is all the forces added, with directions counted. Newton's first law: a zero resultant force means the velocity stays constant. Newton's second law: resultant force = mass × acceleration. Higher tier: inertia, free body diagrams and components build on the same ideas.

Work done = force × distance moved in the direction of the force, in joules, and 1 J = 1 N m. Springs follow a force rule of their own, and you meet it in the springs lesson.

How this is asked in an exam: you are often given a mass and told to take g = 10 N/kg, then asked for the weight. One mark is for the substitution and one for the answer with its unit. Another common question gives two forces and asks for the resultant first, then the acceleration. An explain question may describe a car at a steady speed. Say that the forces are balanced, so the resultant force is zero, so the velocity does not change. Show every line of working and always write the unit.