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# Forces and Pressure

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## Forces and Pressure

**Think about these two situations:**

- Pushing a drawing pin into a wall pointy end towards the wall.
- Pushing a drawing pin into a wall pointy end towards your thumb.

Two similar activities with two very different results.

The reason for this is the difference in pressure. Assuming the same force is applied, each case would have a different pressure acting on the thumb. In the first diagram the thumb pushes on a **large area** so the **force is spread out** and the **pressure is low.** In the second diagram the **force is concentrated** on a **small area** so the **pressure is much higher**.

**If a force is applied over a smaller surface area you get a larger pressure.**

**Pressure can be calculated using the following equation:**

Force will be in newtons, N.

Area will be in either m^{2} or cm^{2}.

If the area is in m^{2} then the pressure will be measured in Pascals or N/m^{2}. If the area is in cm^{2} then the pressure will be in N/cm^{2}.

**Example:**

**A lump of cheese of weight 20N stands on a table. It is a cubic lump with an area of 10cm ^{2}.**

**What pressure does it exert on the table?**

**Answer:**

* Note:* Don't forget the units!

When it comes to pressure in liquids, there are 3 rules that you need to remember:

**1. Pressure increases with depth **

Have you ever noticed that when you dive down to the bottom of a swimming pool, your ears start to hurt? The further you dive down, the more it hurts.

This is because the pressure in a liquid increases as you go further below the surface of the liquid.

A common example in exams is this - a can full of water with holes down the sides. Notice how the further down the hole is, the faster the water comes out because the higher the pressure is in that part of the can.

**Here are some other common examples. Can you explain them?**

**Water comes out of a downstairs tap faster than an upstairs tap.****Dam walls have to be thicker at the bottom than at the top.**

You always get these ideas in any movie that has a submarine in it. You can guarantee that at some stage during the film, the sub will go too deep! Alarms will sound, people start to sweat, look nervous and the sub will creek and groan. Sometimes, the water will burst in and the sub will **'implode'** (that means explode inwards rather than outwards).

This is due to the fact that the pressure from the water outside the submarine increases as the sub goes deeper and deeper until the structure of the sub isn't strong enough to resist - and it is crushed.

**2. Pressure acts equally in all directions **

**To illustrate this:**

- Grab a plastic bag.
- Fill it with water.
- Tie a knot in the top.
- Squeeze it.
- Then poke holes in the bag with a pin!

- Water goes everywhere! And that's the point.
- Water, from holes at the top of the bag, goes up.
- Water, from holes at the side of the bag, goes sideways.
- Water, from holes at the bottom of the bag, goes down.

This shows that the pressure in the water (which makes the water squirt out of the bag) **is acting in all directions** - not just downwards!

There's another example that helps to explain this. Remember when you are swimming at the bottom of the pool and your ears are hurting. It doesn't matter what you do with your head - turn left, right, twist it up or down - your ears hurt just as much. The water is pushing in on them from all sides equally - not just downwards.

**3. Pressure is transmitted through liquids **

You can't squash liquids. We say that they are **'incompressible'.**

Fill a syringe with water. Put your thumb over the nozzle and press the plunger. It won't move. The water in the syringe can't be compressed.

Do the same thing with a syringe full of air and you can easily squash it. Air is compressible.

The fact that you can't compress liquids is extremely useful. It means that **pressure can be transmitted through liquids.**

An example - you connect two syringes together with a pipe and then fill them with water. Press one plunger in - and the other one comes out. That's because you have **transmitted pressure **from one plunger to the other.

This is used in **hydraulics.**

**Hydraulics **

All hydraulics systems work because the pressure is the same throughout the system.

A really good example of this is a **car brake system.** You need to know all about this for your exams.

Think about it. If you are driving a car along a motorway, you can stop it quite quickly by pushing gently on the brake pedal.

Now here's an alternative. You are driving a car along a motorway and you decide to stop. So you open the door, and, using the same force as above, gently press down on the tarmac with your foot.

(P.S: In case you need to be told - don't try this!!!)

You won't be surprised to learn that the car doesn't stop nearly as quickly. And, you wreck your trainers!

**So how does the car turn the small force that you apply to the brake pedal into the huge force needed to stop a speeding car?**

If you look at the above diagram, you can see that the brake cylinder by the pedal (the master cylinder) that the driver presses is very narrow.

But the cylinders by the brakes (the slave cylinders) are very wide.

This means they apply a much larger force.

**Why?**

Because the pressure in the liquid is the same everywhere. So if the area is bigger in the slave cylinders the applied force must be bigger too.

This is easier to see with an example.

If you push the master cylinder with a force of 12N and it has an area of 3cm^{2}.

**Using the equation:**

This means the pressure in the master cylinder must be:

Now, because pressure is the same throughout the system, that means that the pressure in the slave pistons must also be 4N/cm^{2}.

If the slave cylinders have an area of 12cm^{2}, using the equation:

- Force = Pressure x area
- Force = 4 x 12
- Force = 48N

(* Note:* The pressure stayed the same.)

Although gases are compressible (squashy) they exert a pressure because of the **gas particles bouncing off things.** The pressure the air exerts at the surface of the Earth is about 100,000 Pa. Luckily, our bodies have evolved to cope with that pressure, or we would be squashed.

The diagram below illustrates how **gas particles exert more pressure when the gas is squashed.**

Both cylinders have the same number of particles in - and both sets of particles are going the same speed.

Notice that the particles in the small cylinder **hit the walls more frequently **- because there is less distance for the particles to cross from the top to the bottom of the cylinder.

Now remember that it is the **collisions that cause the pressure - more collisions means more pressure**. So the fact that there are more collisions in the small container means that the pressure is higher in the small container.

**Boyle's Law**

The diagram above explains why **changing the volume of a gas sample changes the pressure** of the gas. **Boyle's Law** is a way of calculating how much the pressure changes when the volume changes.

An eighteenth century scientist called Robert Boyle discovered that for a fixed mass of gas the pressure x the volume of the gas stays the same.

In other words, as you squeeze a gas its pressure will go up and its volume will get less.

* Important point:* The temperature and mass of gas must stay the same for this to be true!

**We can write this as:**

pressure x volume = constant

**or **

P_{1}V_{1} = P_{2}V_{2}

**where:**

P_{1} is the pressure of the gas at the start,

V_{1} the volume of the gas at the start and

P_{2} and V_{2} the pressure and volume of the gas at the end.

**This tells us if we double the pressure of a gas its volume will halve. If we reduce the pressure by one half, the volume will double.**

**Example:**

**Imagine a balloon full of air. The air's pressure is 10N/cm ^{2} and its volume is 300cm^{3}.**

**You squash the balloon to 200cm ^{3} without any air escaping. **

**What is the pressure of the air inside the balloon?**

**Answer:**

**Write down the formula:**

P_{1}V_{1} = P_{2}V_{2}

(* Remember:* P

_{1 }is the pressure at the start, V

_{1}is the volume at the start, etc)

**Plug in the numbers:**

10 x 300 = P_{2} x 200

**Rearrange the equation to give:**

**so**

P_{2} = 15 N/cm^{2}.

* Remember:* The temperature and mass of gas must remain the same for this to work!