Pressure (Cambridge International IGCSE Physics): Exam Questions

Describe how the pressure beneath the surface of a liquid changes

(i) With depth.

(ii) With density of the liquid.

Extended tier only

Complete the word equation defining pressure in liquids.

Pressure in a liquid is the _________ of the liquid × gravitational field strength × change in _________.

Extract:

(From part a) (i) With depth:

• As depth increases, pressure increases / they are directly proportional. (ii) With density:
• As density increases, pressure increases / they are directly proportional.

(From part b) Pressure in a liquid is the density of the liquid × gravitational field strength × change in depth.

Fig. 1 shows two pairs of objects in a column of liquid.

For each pair identify the object which experiences the highest pressure and explain your reason.

Extract:

Pressure in a liquid is the density of the liquid × gravitational field strength × change in depth.

Extended tier only

A swimmer dives to the bottom of a swimming pool which is 2 m deep. Calculate the pressure on the swimmer. The density of the water in the pool is 1000 kg/m³.

A student is studying elephants. Fig. 2.1 shows an elephant.

The student measures the elephant and records the values, as shown in the table.

Complete the table by adding a suitable unit for each measurement. Choose the units from those shown in the box.

Extract:

| measurements | value | unit | | mass of elephant | 4000 | kg | | height of elephant | 3.0 | m | | surface area of elephant foot | 0.125 | m^2^ |

Using information from the table in (a):

(i) Calculate the weight of the elephant.

weight = ..................................................... N [3]

(ii) Calculate the pressure the elephant exerts on the ground when it is standing on four feet. Include a unit.

pressure = ......................................................... [4]

Complete the sentence defining pressure in solids.

Pressure is defined as the ________ per unit ________.

Extract:

Pressure is defined as the force per unit area.

Complete the word equation defining pressure in solids.

Pressure in a solid is the _______ ÷ _______.

Extract:

Pressure is defined as the force per unit area. Pressure in a solid is the force ÷ area.

The table shows some everyday examples of objects which exert a pressure.

For each one identify whether the object would exert high pressure or low pressure.

A student of weight 550 N is wearing shoes so that his two feet have a total area of 0.020 m².

Calculate the pressure exerted by the student on the ground when standing on both feet.

The weight of a car is 20 000 N. For each tyre, the area in contact with the road is 0.1 m².

For the car shown in Fig. 1, calculate the total area of the car tyres which are in contact with the road surface.

Extract:

The weight of a car is 20 000 N. For each tyre, the area in contact with the road is 0.1 m^2. Area = 0.1 × 4 = 0.4 m^2.

Calculate the total pressure exerted by the car on the road.

Extract:

Use the equation for pressure:

• P = F / A

Substitute the values from the question:

• P = 20 000 / 0.4 = 50 000

Round the answer to two sig figs and include the unit:

• P = 50 000 Pa / 50 kPa

The family who own the car are going on holiday. They add a roof-rack filled with heavy camping equipment.

State how this will affect the pressure which the car exerts on the road.

Extract:

The effect of adding weight to the car:

• Increases the pressure;

Explain your answer to part (c).

The weight of the skier shown in Fig.1 is 750 N. For each ski, the area in contact with the snow is 0.2 m².

Calculate the total area of the skis which is in contact with the snow.

Extract:

The weight of the skier shown in Fig.1 is 750 N. For each ski, the area in contact with the snow is 0.2 m^2. Area, A = 0.2 × 2 = 0.4 m^2

Calculate the total pressure exerted by the skier on the snow.

Extract:

The weight of the skier shown in Fig.1 is 750 N. For each ski, the area in contact with the snow is 0.2 m^2.

The skier has been told that using narrower skis will make her go faster.

She switches to skis which each have a surface area of 0.15 m².

State how this will affect the pressure which the skier exerts on the snow.

Extract:

The skier has been told that using narrower skis will make her go faster. She switches to skis which each have a surface area of 0.15 m^2. The effect of using skis with smaller surface area: Increases the pressure; Pressure = force ÷ area OR pressure and area are inversely proportional;

Explain your answer to part (c).

Fig.5.1 shows a glass bottle containing air. The bottle is sealed with a cap.

The air in the bottle becomes warmer.

(i) State what happens to the pressure of the air in the bottle.

(ii) Explain why the pressure of the air in the bottle changes. Use your ideas about gas molecules.

Extract:

Fig.5.1 shows a glass bottle containing air. The bottle is sealed with a cap.

The air in the bottle becomes warmer.

The bottle has a weight of 5.4 N and an area of 9.2 cm² in contact with the table.

Calculate the pressure produced by the bottle on the table. Give the unit.

pressure = .........................................................

Fig. 5.2 shows another bottle. The bottle is on a table. Part of the base of this bottle is not in contact with the table.

(i) The base of the bottle is circular. The radius of the outer circle is 4.0 cm as shown in Fig. 5.3. Calculate the area of this circle.

area = .................................................. cm² [1]

(ii) The bottle shown in Fig. 5.2 has the same mass as the bottle shown in Fig. 5.1.

Explain why the bottle shown in Fig. 5.2 exerts more pressure on the table than the bottle shown in Fig. 5.1.

Fig. 4.1 shows a pin. Fig. 4.2 shows a person pushing the pin into a wall.

The area of the top surface of the pin is 1.8 cm².

The person applies a force of 50 N.

Calculate the pressure exerted on the top surface of the pin.

pressure = ............................................. N / cm²

Extract:

The area of the top surface of the pin is 1.8 cm^2. The person applies a force of 50 N. pressure = 28 N / cm^2

The area of the top surface of the pin is 500 times larger than the area of the point.

Calculate the value of the pressure exerted by the point on the wall.

pressure = ............................................. N / cm²

Fig 2.1 shows liquid in a cylinder.

Table 2.1 gives some data about the cylinder and the liquid.

The cylinder containing liquid is placed on a digital balance that displays the mass in kg.

Calculate the reading shown on the balance.

reading ......................................................kg

Extended tier only

Fig. 2.2 shows a device called a manometer that measures the pressure of a gas.

(i) The pressure of the gas is 400 Pa greater than atmospheric pressure.

Calculate the density of the liquid.

density = ...........................................................[2]

(ii) With the gas supply connected, the top of the tube on the left of the device is sealed securely with a rubber stopper. The gas pressure is then increased.

State and explain what happens to the liquid in the manometer.

Extended tier only

On a particular day, the atmospheric pressure is 1.0 × 10⁵ Pa. A bubble of gas forms at a point 5.0 m below the surface of a lake. The density of water is 1000 kg/m³.

Determine

(i) the total pressure at a depth of 5.0 m in the water,

pressure = ...........................................................[3]

(ii) the pressure of the gas in the bubble.

pressure = ...........................................................[1]

Extract:

On a particular day, the atmospheric pressure is 1.0 × 10⁵ Pa. A bubble of gas forms at a point 5.0 m below the surface of a lake. The density of water is 1000 kg/m³.

(i) the total pressure at a depth of 5.0 m in the water,

(ii) the pressure of the gas in the bubble.

Extended tier only

As the bubble rises to the surface, the mass of gas in the bubble stays constant. The temperature of the water in the lake is the same throughout.

Explain why the bubble rises to the surface and why its volume increases as it rises.

Fig. 3.1 shows an archer pulling the string of a bow.

The archer uses a force of 120 N. The force acts on an area of 0.5 cm² on the archer’s fingers.

Calculate the pressure on the archer’s fingers.

pressure on fingers = ............................................ N/cm²

Extract:

The archer uses a force of 120 N. The force acts on an area of 0.5 cm^2 on the archer's fingers.

To calculate the pressure on the archer's fingers:

List the known quantities:

• Force, F = 120 N
• Area, A = 0.5 cm^2

Recall the equation linking pressure, force and area:

• pressure = force / area OR P = F / A

Substitute in known values:

• P = 120 / 0.5
• P = 240 N/cm^2

The archer’s other hand is pushing the bow with the same force of 120 N. This force acts on a larger area than the force in (a).

State whether the pressure on this hand is greater than, the same as or less than the pressure on the fingers holding the string.

Extract:

Fig. 3.1 shows an archer pulling the string of a bow.

State the energy store of the bow that energy is transferred into when the archer bends it as shown in Fig. 3.1.

The bottle has a weight of 5.4 N and an area of 9.2 cm² in contact with the table.

Calculate the pressure produced by the bottle on the table.

pressure = .............................................. N/cm²

A metal block has a weight of 24 N. The area of this metal block in contact with the ground is 4.0 cm².

Calculate the pressure of this block on the ground.

pressure = ............................................. N/cm²

Extended Tier Only

Fig. 2.1 shows water stored in a reservoir behind a hydroelectric dam.

The turbine is 150 m below the level of the water in the reservoir.

Atmospheric pressure is 1.0 × 10⁵ Pa. The density of water is 1000 kg/m³.

(i) Calculate the total pressure in the water at the turbine.

pressure = ......................................................... [3]

(ii) The turbine has a cross-sectional area of 3.5 m².

Calculate the force exerted on the turbine by the water.

force = .......................................................... [2]

The water in a hydroelectric dam flows to the turbine through a pipe of constant cross-sectional area.

Explain why the kinetic energy of the water in the pipe remains constant as it flows through the pipe.

Fig. 2.1 shows a concrete beam resting on the ground.

*Fig. 2.1 *

The weight of the concrete beam is 1540 N.

Calculate the pressure on the ground due to the concrete beam.

pressure = .............................................. N / cm²

Fig. 4.1 shows liquid in a cylinder.

The depth of the liquid is 10 cm and the radius of the cylinder is 3.0 cm. The weight of the liquid in the cylinder is 2.5 N.

Calculate the density of the liquid. You can assume that acceleration of free fall is 10 m/s².

density = ...........................................................

Extended tier only

Fig. 4.2 shows a device called a manometer that measures the pressure of a gas supply.

(i) The difference h between the two liquid levels is 2.0 cm. The density of the liquid is 800 kg/m³.

Calculate the difference between the pressure of the gas and atmospheric pressure.

pressure difference = ...........................................................[2]

(ii) A similar device with a tube of smaller cross-sectional area is connected to a gas supply at the same pressure.

State and explain any effect on the value of h.

A rectangular container has a base of dimensions 0.12 m × 0.16 m. The container is filled with a liquid. The mass of the liquid in the container is 4.8 kg.

Calculate

(i) the weight of liquid in the container

weight = ...........................................................[1]

(ii) the pressure due to the liquid on the base of the container

pressure = ...........................................................[2]

Extract:

(ii) To calculate the pressure due to the liquid on the base of the container:

List the known quantities:

• Dimensions of the base = 0.12 m × 0.16 m
• Weight = 47 N

Recall the equation linking pressure, force and area and substitute in known values:

• P = F / A
• P = 47 / (0.12 × 0.16)

Calculate P:

• P = 2450 Pa

Explain why the total pressure on the base of the container is greater than the value calculated in (a)(ii).

Extract:

A rectangular container has a base of dimensions 0.12 m × 0.16 m. The container is filled with a liquid. The mass of the liquid in the container is 4.8 kg.

Pressure, P = 2450 Pa

The depth of liquid in the container is 0.32 m.

Gravitational Field Strength, g = 9.81 m/s^2^

Extended tier only

The depth of liquid in the container is 0.32 m.

Calculate the density of the liquid.

density = ...........................................................

A scientist fills a container with seawater. The container has dimensions 30 cm × 30 cm × 40 cm. The density of seawater is 1020 kg/m³.

Calculate the mass of the seawater in the container.

mass = .........................................................

Extended tier only

Fig. 2.1 shows a submarine. The submarine is fully submerged in the sea.

(i) The atmospheric pressure is 100 kPa and the total pressure on the top surface of the submarine is 500 kPa.

Calculate the depth of the top surface of the submarine below the surface of the sea.

depth = ......................................................... [3]

(ii) A hatch (an opening door) on the top surface of the submarine has an area of 0.62 m².

Calculate the downward force on the hatch due to the total pressure on the top surface of the submarine.

force = ......................................................... [2]

Fig. 2.1 shows a hollow metal cylinder containing air, floating in the sea.

The density of the metal used to make the cylinder is greater than the density of seawater.

Explain why the cylinder floats.

Extract:

Fig. 2.1 shows a hollow metal cylinder containing air, floating in the sea.

The density of the metal used to make the cylinder is greater than the density of seawater.

Extended tier only

The cylinder has a length of 1.8 m. It floats with 1.2 m submerged in the sea. The bottom of the cylinder has an area of cross-section of 0.80 m².

The density of seawater is 1020 kg/m³. Calculate the force exerted on the bottom of the cylinder due to the depth of the seawater.

force = ...........................................................

Extract:

Length of the cylinder = 1.8 m Submerged length = 1.2 m Cross-sectional area of the cylinder = 0.80 m^2^ Density of seawater = 1020 kg/m^3^

force = 9600 N (calculated as the force exerted on the bottom of the cylinder due to the depth of the seawater)

There is no acceleration of the block so the forces must be balanced. The weight is the value calculated in part (b)

Deduce the weight of the cylinder. Explain your answer.

A cylindrical container has a base with diameter of 0.15 m and is filled with water to a depth of 0.35 m as shown in Fig. 1.1.

The mass of the water is 6.2 kg.

Calculate the weight of the water in the container.

Extract:

A cylindrical container has a base with diameter of 0.15 m and is filled with water to a depth of 0.35 m as shown in Fig. 1.1.

The mass of the water is 6.2 kg.

weight = 61 N

Calculate the pressure due to the liquid on the base of the container.

Extract:

To calculate the pressure due to the liquid on the base of the container:

Calculate the area of the base:

• Area, A = π r^2 = (π d^2)/4
• A = (π × 0.15^2)/4 = 0.018 m^2

Use the pressure equation and substitute in known values:

• P = F/A
• P = 61/0.018
• P = 3389

Write the answer to two sig figs and include the unit:

• P = 3400 Pa / 3.4 kPa

The water-filled cylinder is placed on a laboratory bench.

Suggest reasons why the total pressure on the bench is higher than the value calculated in part (b).

Extended tier only

A bead of hollow glass is dropped into the water and comes to rest floating 12 cm above the base of the cylinder as shown in Fig. 1.2.

Fig. 1.2

Calculate the total pressure on the bead.

Atmospheric pressure at sea level = 1.01 × 10⁵ Pa

Density of water = 1000 kg/m³