Unit 4 - Lesson 2: Density and Pressure Flashcards
What is density a measure of?
Density is a measure of compactness of an object. More appropriately, it’s a measure of the mass of particles per metre cubed (m^3).
What is the algebraic symbol for density?
The Greek letter, ρ, pronounced ‘rho’. Don’t confuse this with ‘p’.
What is the formula to find density (ρ)?
Density (ρ) = Mass (m) / Volume (V)
What is the unit of measurement for density (ρ), mass (m), and volume (V)?
Density (ρ) = kg/m^3
Mass (m) = kg
Volume (V) = m^3
What is the triangle for density, mass and volume, which helps us rearrange the equation?
Mass is at the top of the triangle.
Density is at the bottom left of the triangle.
Volume is at the bottom right of the triangle.
What is the densest object in the universe?
A neutron star. It has approximately one million billion tonnes of particles per metre cubed (m^3).
Although density is generally measured in kg/m^3, what can it also be measured in?
g/cm^3, where the mass would be in grams (g) and the volume in cm^3.
What is 1kg in grams?
1000 g
What is 1m^3 in cm^3?
1,000,000 cm^3
What is 1g in kg?
0.001 kg
What is 1cm^3 in m^3?
0.000001 m^3
PRACTICALS: Measuring the density of a solid.
If we are given the (length x width x height) of a cuboid, and the mass in grams (after using a balance to measure the mass), how can we calculate the density?
First, find the volume.
V = l x w x h
If your answer to that equation is not in cm^3, convert it to cm^3.
Secondly, find the mass given to you in the question.
Thirdly, fill in this formula:
ρ = m / V
Finally, you have your answer.
What can we use to find the density of an irregular shaped object like a rock?
A displacement can. This is sometimes called a eureka can.
What equipment should we use to find the mass of an object?
A balance.
How can we find the density of an irregular shaped object like a rock? Include what apparatus is needed.
Use a BALANCE to find the mass. Place a MEASURING CYLINDER under the spout of the DISPLACEMENT CAN. Fill the displacement can with water and place the object in the water. The water that pours into the measuring cylinder is the volume of rock. The density formula can then be used to calculate density.
When using the displacement can method to find the density of an irregular shaped object, how should you prevent parallax error, and what is parallax error?
You should always read the lowest point of the liquid’s surface (the meniscus) to prevent parallax error. Parallax error is the perceived shift in an objects position when viewed from different angles. Also, always read the scale on the measuring cylinder at head height (straight on).
What is pressure?
Pressure is the force exerted on a given area of surface. We say pressure is the force per unit area.
What is the formula to find pressure (P)?
Pressure (P) = Force (F) / Area (A)
What units of measurement do pressure (P), force (F), and area (A) use?
Pressure (P) = Pa (pascal)
Force (F) = N
Area (A) = m^2
What is the triangle for pressure, force, and area, that helps us rearrange the equation?
Force is at the top.
Pressure is at the bottom left.
Area is at the bottom right.
Force is measured in pascals (Pa). What is one pascal equivalent to in N/m^2?
1 N/m^2
What is 1000 Pa in kPa?
1000 Pa = 1 kPa
Why do ballet dancers standing on pointe shoes exert MORE pressure on the floor than if they stood with their feet flat?
This is because the same force (weight) is applied over a smaller area when standing on pointe.
More pressure is exerted if the same force is applied over a smaller area as a larger area. True or false?
True.
How were military tanks adapted to not sink easily into mud?
By having caterpillar tracks with a high surface area, we are reducing the pressure that vehicle places on the floor compared to a truck of the same weight.
Animals like elephants and camels have large, wide feet. Does this reduce or increase the pressure they exert on an area of ground?
Having large, wide feet REDUCES the pressure they exert on an area of ground.
Sometimes, we want to increase pressure. How do knives achieve this?
Knives work by having a very thin edge. This exerts more pressure when you press down on one.
Force comes in many forms. Most of the time it will be weight in your exam. What is the formula for weight?
Weight = mass x gravitational field strength
Using P=F/A may require you to find the area of certain shapes.
a) How do you find the area of a rectangle or square?
b) How do you find the area of a triangle?
c) How do you find the area of a cuboid (3d square or rectangle?
d) How do you find the area of an irregular 2D shape?
a) Area = length x width
b) Area = 1/2 x base x height
c) Add together the area of each side. In a cube, this is the same as multiplying the area of one side by 6 (as all sides have the same area).
d) Trace the image on to squared paper and count the squares. Each square will be worth, for example, 25cm^2. Multiply the amount of squares by the size of the square.
How does pressure in fluids (a liquid or gas) that are at rest (not moving) act?
Pressure in fluids that are at rest acts equally in all directions.
Pressure in fluids that are at rest acts equally in all directions. What does this mean for when water is pouring out of all the holes of a container?
This means water will pour out of all the holes of a container with equal pressure and similarly if an object is submerged in a liquid, pressure will act on the object equally in all directions.
The pressure of seawater will be exerted equally in all directions on the surface of a submarine or an underwater swimmer. True or false?
True.
Why don’t you feel air exerting a pressure on your body equally in all directions?
You don’t feel this as the pressure inside your body is about the same magnitude.
Otto Van Guericke was the first person to show that a vacuum could be created in which no air was present. What experiment did he carry out to show this? Explain the science behind the experiment.
In 1654, he carried out an experiment where two metal bowels were secured together before all the air inside was removed. He proved the bowls couldn’t be separated again by allowing horses to pull on each bowl at the same time. When the bowls had air removed, there was only air pressure exerting on the outside of the bowls. This air pressure prevented the horses from pulling them apart. When there was air inside, the pressure exerted inside was equal to that outside, which meant they could be pulled apart.
Pressure increases with depth. What does this mean if water is leaking from a lower hole and a higher hole in a container? Is one leaking faster?
Pressure increases with depth, so the speed of water leaking from the bottom hole is LARGER than that from the high one.
COMPLETE THE SENTENCE:
The (deeper/shallower) an object is in a fluid, the more pressure is exerted on it.
The DEEPER an object is in a fluid, the more pressure is exerted on it.
If we want to calculate the pressure in a fluid at a given depth, what formula can we use? State the units of measurement used for each component of the equation.
Pressure (P) = density (ρ) x gravitational field strength (g) x height (h)
Pa = kg/m^3 x N/kg x m
The pressure of a liquid depends on its…what?
Density.
The pressure of a liquid depends on its density.
REVISION SHEET 2: PRESSURE IN THE EXAM
REVISION SHEET 2: PRESSURE IN THE EXAM
What value should you use for ‘g’ (gravitational field strength or acceleration due to gravity)?
In calculations, ‘g’ is always 10.
What are the units for:
a) Pressure
b) Height
c) Gravity
d) Density
a) Pascal (Pa)
b) Metres (m)
c) Newtons (N)
d) Kilograms per Metre Cubed (kg/m^3)
Example Question:
A necklace in a first-class cabin of Titanic can feel 3.9x10^7 Pa at the bottom of the ocean. Seawater has a density of 1020kg/m^3. What is the depth of the Titanic in metres?
We want to calculate DEPTH. The formula must include depth or something that could represent depth (like height or distance).
We have pressure (I knew this because pressure is measured in Pascals (Pa)) and density.
What formula has pressure, density, and depth (or equivalent)?
Pressure = Height x Density x Gravitational Field Strength
39000000 = Height x 1020 x 10
39000000 = Height x 10200
39000000 / 10200 = Height
Height = 3823.52941176 m
Other than depth, what can represent depth in an equation?
Height or distance.
In most situations, use P=F/A (pressure = force/area) in word questions. However, if you are dealing with force acting down, what formula should be used then?
P=ρhg (Pressure = density x height x gravitational field strength)
Example Question:
A hot air balloon is filled with air through an opening.
The air is heated using a burner.
(e) As the balloon climbs higher, the air pressure outside it decreases.
(i) Suggest a reason for this change in the outside air pressure.
(ii) Suggest how the decrease in air pressure outside the balloon affects the hot air inside.
(i) At higher altitudes, temperatures decrease. Lower temperature reduces the kinetic energy of the air particles. They collide with the outside of the balloon less. Therefore, the force acting on the same area of the balloon is reduced. The pressure decreases.
(ii) Pressure outside the balloon is higher than inside. There’s a greater force pushing outwards, which pushes air out of the balloon and causes balloon to expand. This greater force has come from the greater number of particles colliding with the walls of the balloon over the same time.
CORE PRACTICAL: Investigate the density of an object from its mass & volume.
a) What apparatus do we need?
b) What’s the method?
c) How do you use a eureka can?
a) - Eureka Can
- Water
- Ruler
- Balance
b) 1. Using the balance, measure the object’s mass.
2. Calculate the volume of the object. Either by measuring the length, height and width (if it’s cuboid) or by using a eureka can if its an irregular shape.
3. Plug in the objects mass and volume into the formula for density.
c) Fill the eureka can with water up to the spout. Drop an object into the water. The volume of water that pours in to the measuring cylinder is the volume of the object.
