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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you should be able to explain what Pascal's principle is, including providing the equation that represents it. You should also be able to provide examples of Pascal's principle in action and solve problems using the equation.

Fluids are cool and super useful. If you've ever filled up a water balloon to throw at your friends or blown up an air mattress, you'll probably have some intuitive understanding of how **fluids** (liquids or gases) work. If an air mattress is half blown-up, and you lay on it, or screw up part of it, pushing all the air into one corner, you'll feel the air pushing hard on the walls of the mattress. By squeezing on one side of the mattress, you can apply a force to the opposite side. Your force can transmit all the way through the mattress. This is how fluids work, and this vitally important property is explained in Pascal's principle.

**Pascal's principle** says that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. Thanks to Pascal's principle, we can lift huge trucks and cars with only human muscles, pump blood around the body, and stop a bike by just pressing a button. All through the power of fluids.

Mathematically, pressure is force, F, measured in Newtons, divided by area, A, measured in meters squared (F / A). So Pascal's principle says that the pressure, F divided by A, is the same when it's transmitted across a fluid. So F1 divided by A1 is equal to F2 divided by A2 (F1 / A1 = F2 / A2). What this means is that if you push with a small force across a small area that can lead to a large force being applied over a large area. This is amazingly useful; so next, let's talk about some of the ways we can use this principle in everyday life.

**Hydraulics** is defined as the branch of science and technology concerned with the conveyance of liquids through pipes and channels, especially as a source of mechanical force or control. And this is by far the most common application of Pascal's principle. There are many, many uses of the principle, but nearly all of them boil down to hydraulics.

Car brakes are the most commonly used hydraulic system. A liquid in a tube takes the pressure you apply on the brake pedal and transfers it all the way to wheels to apply a force there. What's more, by pushing that fluid against a larger area, A, your little push of the pedal can lead to a much larger braking force.

If that doesn't convince you that Pascal's principle is powerful, let's take a look at a car lift. We can lift cars and trucks in the air through hydraulics. By pushing down on a small area, with a small force, we can apply a large force over a large area at the other end of the lift, pushing the car upwards.

Okay, one more example. The human heart also works on Pascal's principle. By enclosing a fluid - in this case, your blood - in blood vessels under pressure, your heart can apply relatively minor force and pump blood all the way around your body!

Hold on! I hear you say. Doesn't all of this break conservation of energy? Surely, you can't get something for nothing. And that's true. The work you do in, say, lifting a car isn't actually decreased. Work is force times distance. If you apply a smaller force, you have to push for a larger distance. So when you push down on your lever to raise the car into the air, you'll have to pump a lot of times to get it to lift. But your muscles are only capable of applying a certain force. This way, you can apply a small force for a long while, and lift a huge, heavy car, whereas, without the hydraulic lift, your muscles wouldn't be strong enough to lift the car at all.

Okay, time to do a quick example problem. Let's say you're lifting a car, like we talked about. The area of the lever you're pushing is 0.1 meters squared, and the area of the lift under the car is 5 meters squared. If you push with a force of 5 Newtons, how much force will be applied to the car?

First, write down what you know. We'll call the lever 1 and the lift 2. We know that the area of the lever, A1 = 0.1, and the area of the lift, A2 = 5. Last of all, we know that the force applied on the lever, F1 = 5 Newtons. Plug all of that into our equation.

5 / 0.1 = F1 / 5

Do some algebraic rearranging to make F2 the subject and we find that:

F2 = 5 (5 / .1)

Type that into a calculator and you get 250 Newtons. So your little 5 Newton push leads to a force of 250 Newtons on the car. Pretty impressive!

**Pascal's principle** says that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. Mathematically, pressure is force, F, measured in Newtons, divided by area, A, measured in meters squared (F / A). So Pascal's principle says that the pressure, F divided by A, is the same when transmitted across a fluid. So:

F1 / A1 = F2 / A2

What this means is that if you push with a small force across a small area that can lead to a large force being applied over a large area. Applications of this principle include the human heart pumping blood around the body, car lifts, car and bike brakes... really, anything that works on hydraulics is based on Pascal's principle.

After reviewing this lesson, you should have the ability to:

- Describe Pascal's principle
- Identify the equation for Pascal's principle
- Explain everyday examples that operate according to Pascal's principle

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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

- Go to Vectors

- Go to Kinematics

- Pressure: Definition, Units, and Conversions 6:21
- Hydrostatic Pressure: Definition, Equation, and Calculations 7:14
- Applications of Pascal's Principle 5:21
- Fluid Mass, Flow Rate and the Continuity Equation 7:53
- Bernoulli's Principle: Definition and Examples 5:21
- Bernoulli's Equation: Formula, Examples & Problems 7:14
- Go to Fluids in Physics

- Go to Relativity

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