Pascal's principle
You squeeze a full water bottle with several holes in its walls, and the water shoots out of all of them at once, even the holes that are far from your hands. How does the water at the other end find out that you are squeezing it?
Pressure is transmitted throughout the liquid
If you fill a plastic bag with water, tie it shut, prick fine holes all over it with a pin and press the neck, the jets come out with the same force and speed from every hole, no matter how far away it is. Why does the push from your hand not lose strength as it travels through the liquid?
In the bottle with holes, when you squeeze you increase the pressure at the point where you press, but that increase reaches every hole just as strongly: that is why the water shoots out of all of them at once, not only the nearest one.
Write Pascal's principle in your own words: explain what happens to the pressure exerted at a point in an enclosed liquid and how it is transmitted through its interior.…
Write Pascal's principle in your own words: explain what happens to the pressure exerted at a point in an enclosed liquid and how it is transmitted through its interior. Then give an everyday example of its application.
You fill a plastic bottle with water, poke several holes in its sides and squeeze the bottle with your hands, as shown in the figure: water shoots out of all the holes…
You fill a plastic bottle with water, poke several holes in its sides and squeeze the bottle with your hands, as shown in the figure: water shoots out of all the holes at the same time, including those far from your hands.
Which principle explains this? What can you say about the pressure received by the water at each hole?
Hydraulic presses use a liquid (oil) and not air. Thinking about whether liquids and gases can be compressed, explain why a liquid is much more effective than a gas at…
Hydraulic presses use a liquid (oil) and not air. Thinking about whether liquids and gases can be compressed, explain why a liquid is much more effective than a gas at transmitting force and motion between the pistons.
The hydraulic press: multiplying a force
In a hydraulic press, a force of $100\ \text{N}$ is exerted on the small piston, which has a surface area of $0,01\ \text{m}^2$, as shown in the figure. a) What pressure…
In a hydraulic press, a force of $100\ \text{N}$ is exerted on the small piston, which has a surface area of $0,01\ \text{m}^2$, as shown in the figure.
- a) What pressure is exerted on the liquid?
- b) According to Pascal's principle, what pressure reaches the large piston?
In a hydraulic press, the liquid transmits a pressure of $20\,000\ \text{Pa}$ to the large piston, which has a surface area of $0,5\ \text{m}^2$. With what force does…
In a hydraulic press, the liquid transmits a pressure of $20\,000\ \text{Pa}$ to the large piston, which has a surface area of $0,5\ \text{m}^2$. With what force does the liquid push this piston?
In a hydraulic press, the small piston has a surface area of $5\ \text{cm}^2$ and the large one $100\ \text{cm}^2$. You push the small piston with a force of…
In a hydraulic press, the small piston has a surface area of $5\ \text{cm}^2$ and the large one $100\ \text{cm}^2$. You push the small piston with a force of $50\ \text{N}$.
- a) Express both surface areas in $\text{m}^2$.
- b) Calculate the pressure exerted on the liquid.
- c) Calculate the force exerted by the large piston. By what factor has your force been multiplied?
Applications: jacks, brakes and chairs
When pressing the brake pedal, a car brakes all four wheels at the same time. Explain the role of the brake fluid and which physical principle makes it possible for the…
When pressing the brake pedal, a car brakes all four wheels at the same time. Explain the role of the brake fluid and which physical principle makes it possible for the force from your foot to reach all wheels almost instantly.
State which of these machines operate by applying Pascal's principle and which do not, justifying each answer: a) A garage hydraulic jack. b) A mattress spring. c) A…
State which of these machines operate by applying Pascal's principle and which do not, justifying each answer:
- a) A garage hydraulic jack.
- b) A mattress spring.
- c) A dentist's elevating chair.
- d) A bicycle cable brake.
You want to lift a $1\,200\ \text{kg}$ car using the garage hydraulic jack, as shown in the figure. The small piston has a surface area of $8\ \text{cm}^2$ and the large…
You want to lift a $1\,200\ \text{kg}$ car using the garage hydraulic jack, as shown in the figure. The small piston has a surface area of $8\ \text{cm}^2$ and the large one $400\ \text{cm}^2$. Take $g = 10\ \text{m/s}^2$.
- a) Calculate the weight of the car.
- b) Using $\frac{F_1}{S_1} = \frac{F_2}{S_2}$, calculate the force that must be applied to the small piston to lift it.
- c) Compare this force with the weight of the car and explain where the "extra force" comes from.
When braking, the pedal pushes the main piston of the brake circuit ($S = 2\ \text{cm}^2$) with a force of $200\ \text{N}$, as shown in the figure. On one of the wheels,…
When braking, the pedal pushes the main piston of the brake circuit ($S = 2\ \text{cm}^2$) with a force of $200\ \text{N}$, as shown in the figure. On one of the wheels, the piston that squeezes the brake pad has a surface area of $10\ \text{cm}^2$.
- a) Calculate the pressure reached by the brake fluid.
- b) Calculate the force with which the brake pad on that wheel is squeezed.
- c) Why is it advantageous for the surface area of the brake pad piston to be larger than that of the pedal piston?