Now we need to consider some specific forces – such as weight and friction.
When Isaac Newton was confined to his rural home to avoid the plague which was spreading uncontrollably in other parts of England, he is said to have noticed an apple fall to the ground. From this, he developed his theory of gravity that relates the motion of falling objects here on Earth to the motion of the Moon around the Earth, and the planets around the Sun.

Table 3.2: Some important forces.

Important situations	Force	Diagram
- pushing and pulling - lifting - force of car engine - attraction and repulsion by magnets and by electric charges	Pushes and pulls. You can make an object accelerate by pushing and pulling it. Your force is shown by an arrow pushing (or pulling) the object. The engine of a car provides a force to push backwards on the road. Frictional forces from the road on the tyre push the car forwards.
- any object in a gravitational field - less on the Moon	Weight. This is the force of gravity acting on the object. It is usually shown by an arrow pointing vertically downwards from the object’s centre of gravity.
- pulling an object along the ground - vehicles cornering or skidding - sliding down a slope	Friction. This is the force that arises when two surfaces rub over one another. If an object is sliding along the ground, friction acts in the opposite direction to its motion. If an object is stationary, but tending to slide – perhaps because it is on a slope – the force of friction acts up the slope to stop it from sliding down. Friction always acts along a surface, never at an angle to it.
- vehicles moving - aircraft flying - parachuting - objects falling through air or water - ships sailing	Drag. This force is similar to friction. When an object moves through air, there is friction between it and the air. Also, the object has to push aside the air as it moves along. Together, these effects make up drag. Similarly, when an object moves through a liquid, it experiences a drag force. Drag acts to oppose the motion of an object; it acts in the opposite direction to the object’s velocity. It can be reduced by giving the object a streamlined shape.
- boats and icebergs floating - people swimming  - divers surfacing - a hot air balloon rising	Upthrust. Any object placed in a fluid such as water or air experiences an upwards force. This is what makes it possible for something to float in water. Upthrust arises from the pressure that a fluid exerts on an object. The deeper you go, the greater the pressure. So there is more pressure on the lower surface of an object than on the upper surface, and this tends to push it upwards. If upthrust is greater than the object’s weight, it will float up to the surface.
- standing on the ground - one object sitting on top of another - leaning against a wall - one object bouncing off another	Contact force. When you stand on the floor or sit on a chair, there is usually a force that pushes up against your weight, and which supports you so that you do not fall down. The contact force is sometimes known as the normal contact force of the floor or chair. (In this context, normal means ‘perpendicular’.) The contact force always acts at right angles to the surface that produces it. The floor pushes straight upwards; if you lean against a wall, it pushes back against you horizontally.
- pulling with a rope - squashing or stretching a spring	Tension. This is the force in a rope or string when it is stretched. If you pull on the ends of a string, it tends to stretch. The tension in the string pulls back against you. It tries to shorten the string. Tension can also act in springs. If you stretch a spring, the tension pulls back to try to shorten the spring. If you squash (compress) the spring, the tension acts to expand the spring.

The force that caused the apple to accelerate was the pull of the Earth’s gravity. Another name for this force is the weight of the apple. The force is shown as an arrow, pulling vertically downwards on the apple (Figure 3.4). It is usual to show the arrow coming from the centre of the apple – its centre of gravity. The centre of gravity of an object is defined as the point where its entire weight appears to act.

Large and small

A large rock has a greater weight than a small rock, but if you push both rocks over a cliff at the same time, they will fall at the same rate. In other words, they have the same acceleration, regardless of their mass. This is a surprising result. Common sense may suggest that a heavier object will fall faster than a lighter one. It is said that Galileo dropped a large cannon ball and a small cannon ball from the top of the Leaning Tower of Pisa in Italy, and showed that they landed at the same time. The story illustrates that results are not always what you think they will be – if everyone thought that the two cannon balls would accelerate at the same rate, there would not have been any experiment or story.
In fact, we are used to lighter objects falling more slowly than heavy ones. A feather drifts down to the floor, while a stone falls quickly. But this is because of air resistance. The force of air resistance has a large effect on the falling feather, and almost no effect on the falling stone. When astronauts visited the Moon (where there is virtually no atmosphere and so no air resistance), they were able to show that a feather and a stone fell side-by-side to the ground.
As we saw in Chapter 2, an object falling freely close to the Earth’s surface has an acceleration of roughly $9.81\,m\,{s^{ - 2}}$, the acceleration of free fall g.
We can find the force causing this acceleration using $F = ma$. This force is the object’s weight. Hence, the weight W of an object is given by:

$weight = mass \times acceleration\,of\,free\,fall$

or

$W = mg$

On the Moon

The Moon is smaller and has less mass than the Earth, and so its gravity is weaker. If you were to drop a stone on the Moon, it would have a smaller acceleration. Your hand is about $1 m$ above ground level; a stone takes about $0.45 s$ to fall through this distance on the Earth, but about $1.1 s$ on the surface of the Moon. The acceleration of free fall on the Moon is about one-sixth of that on the Earth:

${g_{Moon}} = 1.6\,m\,{s^{ - 2}}$

It follows that objects weigh less on the Moon than on the Earth. They are not completely weightless, because the Moon’s gravity is not zero.

Mass and weight

We have now considered two related quantities, mass and weight. It is important to distinguish carefully between these (Table 3.3).

Figure 3.5 shows a vehicle used to travel on the moon, named a moon-buggy. If the moon-buggy breaks down, it will be no easier to get it moving on the Moon than on the Earth. This is because its mass does not change, because it is made from the same atoms and molecules wherever it is. From $F = ma$, it follows that if m does not change, you will need the same force F to start it moving.

However, your moon-buggy will be easier to lift on the Moon, because its weight will be less. From $W = mg$, since g is less on the Moon, it has a smaller weight than when on the Earth.