## 2.2 Force (ESBKH)

### What is a force?(ESBKJ)

A force is anything that can cause a change to objects. Forces can do things like:

change the shape of an object,

accelerate or stop an object, and

change the direction of a moving object.

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A force can be classified as either a contact force or a non-contact force.

A contact force must touch or be in contact with an object to cause a change. Examples of contact forces are:

the force that is used to push or pull things, like on a door to open or close it

the force that a sculptor uses to turn clay into a pot

the force of the wind to turn a windmill

Figure 2.1: Contact forces
Figure 2.2: Contact forces

A non-contact force does not have to touch an object to cause a change. Examples of non-contact forces are the forces due to:

gravity, like the Earth pulling the Moon towards itself;

electricity, like a proton and an electron attracting each other; and

magnetism, like a magnet pulling a paper clip towards itself.

Figure 2.3: Non-contact forces

The unit of force in the international system of units (S.I. units) is the newton (symbol N). This unit is named after Sir Isaac Newton who first defined force. Force is a vector quantity and so it has a magnitude and a direction. We use the symbol $$\overrightarrow{F}$$ for force.

This chapter will often refer to the resultant force acting on an object. The resultant force is simply the vector sum of all the forces acting on the object. It is very important to remember that all the forces must be acting on the same object. The resultant force is the force that has the same effect as all the other forces added together.

### Different types of forces in physics (ESBKK)

A lot of the physics topics you will study revolve around the impact or effect of forces. Although there are many different forces, will learn some fundamental principles for approaching the problems and applications in this book no matter which force applies

Physics is the study of the natural world and you probably know a lot more physics than you think. You see things happening everyday that are governed by the laws of physics but you probably aren"t thinking about physics at the time. If you throw a stone up in the air it eventually falls to the ground. A lot of physics can be learnt by analysing an everyday situation.

We are going to learn about some forces in the next few sections but before we start lets describe an everyday situation in which they all play a role so you can visualise what is happening. You need a table and a three books that all have different masses. Take any book and put it on the table. Nothing happens, the book just rests on the table if the table is flat. If you slowly lift one side of the table so that the top of the table is tilted the book doesn"t move immediately. As you lift the table more and more the book suddenly starts to slide off the table. You can repeat this with all three books and see how much you have to tilt the table before the books start to slide.

This real world situation illustrates a lot of the physics we want to learn about in this chapter.

The normal force

When an object is placed on a surface, for example think of the case of putting a book on a table, there are a number of forces acting. Firstly, if the table were not there the book would fall to the floor. The force that causes this is gravity. The table stops the book falling to the floor. The only way this can happen is for the table to exert a force on the book. The force that the table exerts on the book must balance out the force of gravity. This tells us a few things immediately! Gravity is a force pulling the book down, it is a vector. The force that the table exerts must balance this out and it can only do this if it has the same magnitude and acts in the opposite direction.

This occurs often, gravity pulls a person towards the earth but when you are standing on the ground something must be balancing it, if you put a heavy box on the ground the gravitational force is balanced. If you put a brick on water it will sink because nothing balances the gravitational force. We give the force that a surface (any surface) exerts to balance the forces on an object in contact with that surface the normal force.

The normal force is a force that acts on the object as a result of the interaction with the surface and is perpendicular to the surface. This last part might be seem unexpected (counter-intuitive) because if we tilt the table slightly the direction of the gravitational force hasn"t changed but the direction of the normal force has a little (the normal is not always directly opposite gravity). Don"t panic, this will all make sense before the end of this chapter. Remember: the normal force is always perpendicular (at a right angle) to the surface.

Normal forceThe normal force, $$\vec{N}$$, is the force exerted by a surface on an object in contact with it.
Friction forces

Why does a box sliding on a surface eventually come to a stop? The answer is friction. Friction arises where two surfaces are in contact and moving relative to each other.

For an everyday example, press your hands together and move one backwards and forwards, we have two surfaces in contact with one moving relative to the other. Your hands get warm, you will have experienced this before and probably rub your hands together in winter to warm them up. The heat is generated through friction.

Friction arises because the surfaces interact with each other. Think about sandpaper with lots of bumps on the surface. If you rub sandpaper the bumps will slot into any groove .

When the surface of one object slides over the surface of another, each body exerts a frictional force on the other. For example if a book slides across a table, the table exerts a frictional force onto the book and the book exerts a frictional force onto the table. Frictional forces act parallel to surfaces.

Frictional forceFrictional force is the force that opposes the motion of an object in contact with a surface and it acts parallel to the surface the object is in contact with.

The magnitude of the frictional force depends on the surface and the magnitude of the normal force. Different surfaces will give rise to different frictional forces, even if the normal force is the same. Frictional forces are proportional to the magnitude of the normal force. \

For every surface we can determine a constant factor, the coefficient of friction, that allows us to calculate what the frictional force would be if we know the magnitude of the normal force. We know that static friction and kinetic friction have different magnitudes so we have different coefficients for the two types of friction:

$$\mu_s$$ is the coefficient of static friction$$\mu_k$$ is the coefficient of kinetic friction

A force is not always large enough to make an object move, for example a small applied force might not be able to move a heavy crate. The frictional force opposing the motion of the crate is equal to the applied force but acting in the opposite direction. This frictional force is called static friction. When we increase the applied force (push harder), the frictional force will also increase until it reaches a maximum value. When the applied force is larger than the maximum force of static friction the object will move. The static frictional force can vary from zero (when no other forces are present and the object is stationary) to a maximum that depends on the surfaces.

For static friction the force can vary up to some maximum value after which friction has been overcome and the object starts to move. So we define a maximum value for the static friction: $$f_s^{max} = \mu_sN$$.

When the applied force is greater than the maximum, static frictional force, the object moves but still experiences friction. This is called kinetic friction.For kinetic friction the value remains the same regardless of the magnitude of the applied force. The magnitude of the kinetic friction is: $$f_k = \mu_kN$$.

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Remember that static friction is present when the object is not moving and kinetic friction while the object is moving. For example when you drive at constant velocity in a car on a tar road you have to keep the accelerator pushed in slightly to overcome the friction between the tar road and the wheels of the car. However, while moving at a constant velocity the wheels of the car are rolling, so this is not a case of two surfaces “rubbing” against each other and we are in fact looking at static friction. If you should break hard, causing the car to skid to a halt, we would be dealing with two surfaces rubbing against each other and hence kinetic friction. The higher the value for the coefficient of friction, the more "sticky" the surface is and the lower the value, the more "slippery" the surface is.

Friction is very useful. If there was no friction and you tried to prop a ladder up against a wall, it would simply slide to the ground. Rock climbers use friction to maintain their grip on cliffs. The brakes of cars would be useless if it wasn"t for friction!