9.1.1 Interactions and types of force

Forces come from interactions between objects

1. A force is a push or a pull that one object exerts on another, and it is measured in newtons, $N$.
2. A force never appears on its own, because it is produced by an interaction, so every force has an object that exerts it and an object that experiences it.
3. A force has both a size and a direction, so it is drawn as an arrow whose length shows the size and whose point shows the direction.
4. Interactions fall into two groups: those that act by contact, where surfaces touch, and those that act at a distance, where the objects are separated by a gap.
5. Naming the correct force is the first step in almost every forces question, because the mark is reserved for the precise name rather than for the word force on its own.

Non-contact forces act through fields

1. In a non-contact interaction the two objects are separated by a gap, and the force is carried across that gap by a field.
2. Three non-contact interactions are needed at this level: gravitational, electrostatic and magnetic.
3. A gravitational force acts between any two objects that have mass.
4. A tennis ball falling from a window is inside the Earth's gravitational field, so the ball is pulled towards the centre of the Earth while the ball pulls the Earth upwards with a force of the same size.
5. Gravitational forces are always attractive, and they become weaker as the two masses move further apart.
6. An electrostatic force acts between objects that carry an electric charge.
7. A polythene rod rubbed with a dry cloth gains electrons and becomes negatively charged, so it sits in its own electrostatic field and attracts small pieces of paper without touching them.
8. Electrostatic forces can attract or repel, because like charges repel and unlike charges attract.
9. A magnetic force acts between two magnets, or between a magnet and a magnetic material such as iron, steel, nickel or cobalt.
10. A bar magnet held a few millimetres above a steel paperclip lifts it through the magnetic field in the gap, and the paperclip pulls the magnet downwards with a force of the same size.
11. Magnetic forces can also attract or repel, because like poles repel and unlike poles attract.
12. To describe any non-contact interaction, name the field, name the property that puts the object into that field, which is mass, charge or magnetism, and then give the direction of the force.

Contact forces act where surfaces touch

1. A contact force acts only while two surfaces are touching, and it disappears the instant they separate.
2. The normal contact force is the push that a surface gives to an object resting on it, and the word normal means at $90^{\circ }$ to that surface.
3. A textbook lying on a desk is pulled down by its weight and pushed up by the normal contact force from the desk, so two arrows are drawn on the book pointing in opposite directions.
4. On a slope, such as a ramp, the normal contact force is still perpendicular to the surface, so it is no longer vertical.
5. Friction acts along the surfaces, in the direction that opposes sliding or the tendency to slide.
6. Pushing a heavy box across a hall floor to the right produces a friction force on the box that acts to the left.
7. Friction acts even when nothing is moving, so a box that will not budge has a friction force equal in size and opposite in direction to your push.
8. Friction is useful when a tyre grips a wet road or a brake pad grips a disc, and unwanted when it heats a machine and wears its moving parts away.
9. Pushes and pulls from a hand, a rope or a spring are also contact forces, because they stop the moment contact is lost.

Interactions produce pairs of forces

1. Whenever two objects interact, each one exerts a force on the other, so forces are always produced in pairs.
2. The two forces in a pair are equal in size, opposite in direction, of the same type, and they act on two different objects.
3. When a swimmer pushes backwards on the wall of a pool, the wall pushes forwards on the swimmer with a force of the same size, and that forward force on the swimmer is what starts the swim.
4. The two forces in a pair never cancel each other out, because they act on different objects, so only one of them is ever drawn on the object being studied.
5. Balanced forces are a different idea, because those act on the same object and add to a resultant of zero.
6. Each force in a pair is represented as a vector arrow drawn on the object it acts on, starting at that object and pointing along the direction of the force.
7. Every arrow is labelled with the name of the force, and arrow lengths are kept in proportion so that a longer arrow means a larger force.

9.1.2 Vector and scalar quantities

Scalar quantities have size only

1. A scalar quantity is fully described by a magnitude, which means a number together with a unit.
2. Nothing else is needed, so once you know a temperature is $18{}^{\circ }C$ you know everything that quantity carries.
3. Scalars used across the course include distance in $m$, speed in $m/s$, mass in $kg$, energy in $J$, time in $s$, temperature in ${}^{\circ }C$, density in ${kg/m}^3$ and power in $W$.
4. Scalars are combined by ordinary arithmetic, so walking $300m$ to the shop and $300m$ back gives a total distance of $600m$.

Vector quantities have size and direction

1. A vector quantity has a magnitude and a direction, and it is not fully described until both have been given.
2. A force of $20N$ is an incomplete description, while a force of $20N$ to the right is the complete vector.
3. Vectors used across the course include displacement in $m$, velocity in $m/s$, acceleration in ${m/s}^2$, force in $N$, weight in $N$ and momentum in $kg\; m/s$.
4. A vector is represented by an arrow, where the length is drawn to a scale to show the magnitude and the way the arrow points shows the direction.
5. Changing only the direction changes the vector, so a car driving north at $15m/s$ and a car driving south at $15m/s$ have the same speed but different velocities.
6. A direction can be given as a compass bearing, as left or right, as up or down, or as a positive or negative sign along a chosen line.
7. A negative sign in front of a vector therefore carries physical meaning, because a velocity of $-6m/s$ is a velocity of $6m/s$ in the opposite direction to the one chosen as positive.

Matched pairs of scalars and vectors

1. Several quantities come in pairs, one scalar and one vector, sharing a unit but not a meaning.
2. Distance is the total length of the path travelled, while displacement is the straight-line change in position together with its direction.
3. A runner who completes one lap of a $400m$ track has travelled a distance of $400m$ but has a displacement of $0m$, because the finish point is the start point.
4. Speed is how fast an object is moving, while velocity is speed in a stated direction.
5. A car driving round a roundabout at a steady $8m/s$ has a constant speed but a changing velocity, because its direction keeps changing.
6. Mass is the quantity of matter in an object, measured in $kg$, and it does not change when the object is moved somewhere else.
7. Weight is the gravitational force acting on that mass, measured in $N$, and it acts towards the centre of the planet or moon the object is near.
8. A $60kg$ astronaut still has a mass of $60kg$ on the Moon, but weighs about one sixth as much there, because the Moon's gravitational field strength is smaller.

9.1.3 Vector diagrams and free body diagrams

Adding forces with a scale vector diagram

1. Because a force is a vector, two forces that do not act along the same line cannot be added as plain numbers.
2. A scale vector diagram solves this by drawing each force as an arrow whose length is fixed by a stated scale, such as $1cm=10N$.
3. The arrows are joined tip to tail, so the tail of the second arrow is placed at the tip of the first while each arrow keeps its own direction.
4. The resultant is drawn from the tail of the first arrow to the tip of the last arrow, measured with a ruler and converted back into newtons using the scale.
5. Its direction is measured with a protractor and quoted as an angle from a stated reference, such as $53^{\circ }$ north of east.
6. The full method runs as follows.
   1. Choose a scale that makes the longest arrow fill most of the space available, and write it on the diagram.
   2. Draw the first force arrow accurately, to scale and in the correct direction.
   3. Draw each remaining arrow starting at the tip of the arrow before it.
   4. Join the tail of the first arrow to the tip of the last arrow and label that line as the resultant.
   5. Measure its length in centimetres and multiply by the scale to get the force in newtons.
   6. Measure its angle and quote the answer as a magnitude with a unit and a direction.
7. At this level the answer is expected from the scale drawing itself rather than from trigonometry, so the accuracy of the construction is what is being assessed.

Equilibrium and the closed vector diagram

1. An object is in equilibrium when all the forces acting on it add to a resultant of zero.
2. On a scale vector diagram that shows up as a closed shape, because the tip of the last arrow lands exactly on the tail of the first and there is no resultant arrow left to draw.
3. Three forces in equilibrium therefore form a closed triangle when they are drawn tip to tail.
4. Equilibrium does not mean that nothing is happening, because the object is either stationary or moving at a constant velocity, and both mean zero acceleration.
5. A mass hanging still on a spring is in equilibrium, because the upward force from the stretched spring is equal in size and opposite in direction to the downward weight.
6. Pull that mass further down and release it and the spring force is now larger than the weight, so there is an upward resultant force and the mass accelerates upwards.
7. Push it above the equilibrium position and the weight is now larger than the spring force, so the resultant force acts downwards.
8. The reasoning also runs backwards, so if a question states that an object is stationary or moving at a steady speed in a straight line, you may write down that the resultant force is zero and use it.

Resolving one force into two components

1. Resolving is the reverse of adding, because one force is replaced by two forces at right angles that together have exactly the same effect.
2. The two replacement forces are the components, and they are usually chosen to be horizontal and vertical, or parallel and perpendicular to a slope.
3. On a scale drawing, draw the original force to scale and then complete a rectangle that has this arrow as its diagonal.
4. The two sides of that rectangle are the components, so measuring each side and converting with the same scale gives the size of each one.
5. A sledge pulled by a rope held at an angle is the standard case, because the horizontal component drags the sledge forwards while the vertical component lifts part of its weight off the snow.
6. Each component is always smaller than the original force, so a component that comes out larger than the force itself shows that the drawing is wrong.

Free body force diagrams

1. A free body force diagram strips a situation down to one object and shows every force acting on that object.
2. The object is drawn as a simple box or a dot, and each force is drawn as an arrow starting on the object and pointing the way the force acts.
3. Every arrow carries a label naming the force, and the lengths are drawn in proportion so the diagram shows at a glance whether the forces balance.
4. Forces that the object exerts on other things are left out, because those forces act somewhere else.
5. The forces most often needed are listed below.
   1. Weight, the gravitational force on the object, drawn vertically downwards from its centre of mass.
   2. Normal contact force, drawn at right angles to the surface the object rests on.
   3. Friction, drawn along the surface, opposing sliding.
   4. Tension, drawn along a rope, cable or spring, away from the object.
   5. Air resistance, or drag in a liquid, drawn opposite to the direction of motion through the fluid.
   6. Thrust, or the driving force, drawn in the direction in which an engine or motor pushes.
   7. Upthrust, drawn vertically upwards on an object floating or submerged in a fluid.
6. A skydiver falling at a steady speed has just two arrows, weight downwards and air resistance upwards, and they are drawn the same length because the forces are balanced.

Forces on an isolated object or a system

1. The motion of an object depends on the resultant force acting on it, not on any single force taken by itself.
2. If the forces are unbalanced the resultant force is not zero, and the object accelerates in the direction of that resultant.
3. If the forces are balanced the resultant force is zero, and this is the special case of equilibrium.
4. A car on a level road has a forward driving force from the engine and backward resistive forces from friction and air resistance.
5. While the driving force is larger than the total resistive force the car speeds up, and the difference between them is the resultant force.
6. Air resistance grows as the car goes faster, so eventually the resistive forces match the driving force, the resultant becomes zero and the car settles at a steady top speed.
7. A system of connected objects can be treated as one body, so a car towing a caravan can be drawn with a single weight, a single driving force and a single total resistive force.
8. If the question asks for the force in the tow bar, the caravan has to be drawn on its own free body diagram, because the tension in the bar is then an external force acting on it.