UNit 5: (b) Density and Pressure

What is density?

Density is the mass per unit volume of a substance.

What is the formula for density?

ρ = m ÷ V

What is the SI unit of density?

kg/m³

What is the SI unit of mass?

kg

What is the SI unit of volume?

m³

What is the relationship between density, mass and volume?

Density = mass ÷ volume.

How do you calculate mass from density and volume?

mass = density × volume.

How do you calculate volume from mass and density?

volume = mass ÷ density.

What must mass be converted to when calculating density in SI units?

kg.

What must volume be converted to when calculating density in SI units?

m³.

What is 1 kg in grams?

1 kg = 1000 g.

What is 1 m³ in cm³?

1 m³ = 1,000,000 cm³.

What is 1 g/cm³ in kg/m³?

1 g/cm³ = 1000 kg/m³.

What happens to density if mass increases while volume stays the same?

Density increases.

What happens to density if volume increases while mass stays the same?

Density decreases.

Why does steel sink in water?

Steel has a greater density than water.

Why does wood float in water?

Wood has a lower density than water.

A metal block has a mass of 2.4 kg and volume of 0.0003 m³. What is its density?

8000 kg/m³.

What apparatus is used to measure the mass of a regular solid?

An electronic balance.

What apparatus is used to measure the dimensions of a regular solid?

A ruler.

How do you find the volume of a regular solid?

Volume = length × width × height.

How do you investigate the density of a regular solid?

Measure its mass with a balance, measure its length, width and height with a ruler, calculate volume using V = l × w × h, then calculate density using ρ = m ÷ V.

What apparatus can be used to measure the volume of an irregular solid?

A Eureka can and measuring cylinder.

How do you measure the volume of an irregular solid using a Eureka can?

Fill the Eureka can until water just runs out, place the object into the can, collect the displaced water and measure its volume in a measuring cylinder.

Why does the displaced water method give the volume of an irregular object?

The volume of water displaced is equal to the volume of the object.

What should you measure before calculating the density of an irregular solid?

The object's mass and its displaced volume.

What is pressure?

Pressure is the force acting per unit area.

What is the formula for pressure?

p = F ÷ A

What is the SI unit of pressure?

Pascal (Pa).

What is the SI unit of force?

Newton (N).

What is the SI unit of area?

m².

What is 1 Pascal?

1 Pa is 1 N acting on an area of 1 m².

What happens to pressure when force increases and area stays constant?

Pressure increases.

What happens to pressure when area increases and force stays constant?

Pressure decreases.

What is the relationship between pressure and area when force is constant?

Pressure is inversely proportional to area.

If the area doubles while force stays constant, what happens to pressure?

Pressure halves.

If the area triples while force stays constant, what happens to pressure?

Pressure becomes one third.

If the area halves while force stays constant, what happens to pressure?

Pressure doubles.

Why do high heels produce high pressure?

Their small contact area produces a high pressure for a given force.

Why do snowshoes produce low pressure on snow?

Their large area spreads the force over a larger area, reducing pressure.

Why does a sharp knife produce high pressure?

Its tiny contact area produces a high pressure.

Why do bulldozer tracks reduce pressure?

They spread the weight over a larger area.

A force of 800 N acts over an area of 2 m². What is the pressure?

400 Pa.

In which directions does pressure at a point in a liquid or gas act?

Equally in all directions.

Why does pressure in a liquid or gas act equally in all directions?

Particles move randomly and collide with surfaces from every direction, producing equal pressure.

What pressure does a diver experience underwater?

Pressure acts upwards, downwards and sideways simultaneously.

What is the formula for pressure difference in a liquid?

p = hρg

What does p represent in p = hρg?

Pressure difference in Pa.

What does h represent in p = hρg?

Depth or height in m.

What does ρ represent in p = hρg?

Density in kg/m³.

What does g represent in p = hρg?

Gravitational field strength in N/kg.

What value of g should normally be used for IGCSE calculations?

9.8 N/kg, unless the question instructs you to use another value such as 10 N/kg.

Why does liquid pressure increase with depth?

There is more liquid above you at greater depth, so its greater weight produces greater pressure.

What happens to liquid pressure as depth increases?

Liquid pressure increases.

What happens to liquid pressure as density increases?

Liquid pressure increases.

What happens to liquid pressure as gravitational field strength increases?

Liquid pressure increases.

What is the relationship between pressure difference and depth?

Pressure difference is directly proportional to depth.

What is the relationship between pressure difference and liquid density?

Pressure difference is directly proportional to density.

What is the relationship between pressure difference and gravitational field strength?

Pressure difference is directly proportional to gravitational field strength.

A diver is 5 m below water. Water density is 1000 kg/m³ and g = 9.8 N/kg. What is the pressure difference?

49,000 Pa.

What does directly proportional mean?

If one quantity doubles, the other also doubles, provided other factors remain constant.

What does inversely proportional mean?

If one quantity doubles, the other halves, provided other factors remain constant.

What quantity is density inversely proportional to when mass is constant?

Volume.

What quantity is pressure inversely proportional to when force is constant?

Area.

What quantity is liquid pressure directly proportional to?

Depth.

What quantity must be used in the density equation: mass or weight?

Mass.

What unit must mass have when using the density equation in SI units?

kg.

What is a common density calculation trap involving volume?

Forgetting to convert cm³ into m³ before substituting into the equation.

What area should be used in the pressure equation?

The contact area over which the force acts, not the total surface area of the object.

What unit must depth be in when using p = hρg?

Metres.

What does "pressure difference" mean in a liquid-pressure question?

The extra pressure due to the liquid only.

What is a common ruler-reading error in a density practical?

Reading the ruler at an angle.

How can ruler parallax error be reduced?

Read the ruler at eye level.

What is a common water-displacement error in a density practical?

Water spills from the apparatus.

How can water spilling be prevented?

Fill the Eureka can correctly and allow excess water to run out before collecting displaced water.

What is a common error caused by bubbles on an irregular object?

Air bubbles increase the measured displaced volume.

How can air-bubble error be reduced?

Remove air bubbles from the object before measuring.

What is a common balance error in a density practical?

The balance is not zeroed before measuring.

How can balance-zero error be reduced?

Tare or zero the balance first.

What is the formula for pressure difference in words?

Pressure difference = depth × density × gravitational field strength.

What is the formula for depth in words?

Depth = pressure difference ÷ (density × gravitational field strength).

What is the formula for density in words using p = hρg?

Density = pressure difference ÷ (depth × gravitational field strength).

What is the formula for gravitational field strength in words using p = hρg?

Gravitational field strength = pressure difference ÷ (depth × density).

What is the SI unit of pressure difference?

Pa.

What is the SI unit of depth?

m.

What is the SI unit of density?

kg/m³.

What is the SI unit of gravitational field strength?

N/kg.

What are the key density quantities and units to remember?

Density = kg/m³, mass = kg, volume = m³.

What are the key pressure quantities and units to remember?

Pressure = Pa, force = N, area = m².

What are the key liquid-pressure relationships to remember?

Liquid pressure is directly proportional to depth and density, and pressure acts equally in all directions in a fluid at rest.