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Three Quick Experiments
Three Quick Experiments
10 Min Experimental Design:
What data would you collect?
What relationships can you make?
Why is it so hard to visit the Titanic’s remains?
Why is it so hard to visit the Titanic’s remains?
Based on what we just saw, any guesses why it’s so tough to make submarines that can travel that deep?
You have five minutes to explore this phet. While exploring, you are seeking to find evidence to answer the following questions.
Tip: for 1 - 3, you should turn off the atmosphere for easy mathematical reasoning.
What is the relationship between pressure & depth within the water?
What relationship does density of the liquid have with pressure?
Does the shape of the container have an effect on the pressure?
What variable affects atmospheric pressure and what relationship does it have with atmospheric pressure?
Pressure
Pressure
Pressure is a measurement of the force exerted straight into an area. Only forces applied perpendicular to the surface will create a pressure.
The units for pressure include:
N / m2
Atm (atmospheric pressure)
Pa (pascals)
Pressure has an inverse relationship with area.
This means that a needle, which has a very small area at the tip, will cause a greater pressure than a pencil’s eraser, even if both are pushed into your arm with the same force.
The units for area are m2. The exact formula for area will depend on its shape.
Air can cause pressure when air molecules collide with an object. These microscopic collisions collectively create a large pressure in or on an object.
The more molecules in a space, the more collisions there will be with the containers of the wall. This is why when we blow up a balloon and fill it with a high density of air, there is a great pressure!
The conversion for these units can be found on the front page of your formula sheet.
Atmospheric Pressure:
Atmospheric Pressure:
Air can cause pressure when air molecules collide with an object. These microscopic collisions collectively create a large pressure in or on an object.
The more molecules in a space, the more collisions there will be with the containers of the wall. This is why when we blow up a balloon and fill it with a high density of air, there is a great pressure!
The air molecules above us and around us collide into us, generating atmospheric pressure.
When you go up, such as climbing a mountain or flying in an airplane, the pressure decreases. This is because the density of the air molecules decreases and less collisions happen between the molecules and you.
It also gets harder to breath because there are less molecules of oxygen.
Water Pressure
Water Pressure
When you are underwater, you will experience pressure from the water all around you. As you proceed deeper into the water, this pressure increases.
The equation shown to the right calculates for the absolute pressure experienced, based on the:
Atmospheric pressure above the water, P0
Density of the water, ρ
Gravitational acceleration, g
Height of the water above, h
When you are underwater, you will experience pressure from the water all around you. As you proceed deeper into the water, this pressure increases.
The equation shown to the right calculates for the absolute pressure experienced, based on the:
Atmospheric pressure above the water, P0
Density of the water, ρ
Gravitational acceleration, g
Height of the water above, h
Gauge Pressure
Gauge Pressure
Another option is to use the gauge pressure equation. This calculates the relative pressure without atmospheric pressure. In other words, the pressure resulting from just the liquid in question.
It is helpful to easily compare pressures under water columns without having to know atmospheric pressure.
Cup B is filled with liquid A, of density 1,200 kg/m3, to a height of 0.15 cm. How much more pressure does the bottom of cup A experience, as compared to cup B, which is empty?
Pressure is greatest on the lowest part
Pressure is greatest on the lowest part
Since pressure is greater with more liquid above, this means that the pressure experienced by a large object will vary depending on its depth.
If you stand at the bottom of a pool, your head will experience less force than your feet.
The net differences in the pressure forces is what results in the buoyant force.
Pressure Force Diagrams
Pressure Force Diagrams
Note the number of arrows at the top and bottom of the cylinder.
Note the length of the arrows around the sphere.
U-Shaped Tubes
U-Shaped Tubes
We often apply our understanding of pressure to u-shaped tubes, like the ones shown here. The water will reach to the same height on either side. So, the absolute pressure at a depth of h on either side is the same.
If there are two liquids with different densities, they will need different respective heights to exert the same pressure at a certain height.
Which liquid is denser?
How do you know?
Liquid A is denser (greater ρ) than liquid B.
ρAghA = ρBghB
Liquid B is denser (greater ρ) than liquid C.
ρCghC = ρBghB
Which liquid is denser?
How do you know?
Practice Problem 1
Practice Problem 1
Hoover dam is a large structure that holds back water. It is wider at the base than at the top.
Explain why it designed in such a manner. Specifically, why is it important for the bottom of the structure to be stronger than the top of the structure?
There is a lot more pressure at the bottom of the dam than at the top, due to the depth of the water! This means the bottom of the dam must be very strong to withstand all of that pressure.
I have a rectangular box, which has dimensions L x 2L x 2L. It has a mass of m.
Create an expression for the pressure the box exerts on the floor in terms of m, L, and fundamental constants, when…
… the box stands on its smaller size.
P = F / A P = mg / L*L P = mg / L2
… the box stands on its larger size.
P = F / A P = mg / (2L)*L P = mg / (2L2)
AP Classroom Student Workbook:
AP Classroom Student Workbook:
8.C Pressure in Cylinders.pdf8.D Pressure in Pipes.pdf8.G Balloon in Pool.pdfPage updated
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