Pressure in fluids

Figure 5 shows water coming out of holes in the side of a can.

The holes are at different heights.

At which of these points is the pressure the lowest?

A student wants to find the pressure they exert on the floor.

The student starts by standing on a piece of squared paper and drawing around the base of their shoe, as shown in Figure 6.

The area of each square is 25 cm².

The student estimates that the base of the shoe covers about 12 squares.

Use this estimate to calculate the area of the base of the shoe.

area of base of shoe =_........ ²

Suggest one change that could be made to the squared paper so that the student can give a better estimate of the area of the base of the shoe.

The total area of the base of a student’s shoes is 0.031 m².

The weight of the student is 680 N.

Calculate the pressure that the student exerts on the ground.

State the unit.

Use the equation

pressure =_........ unit_........

Figure 7 shows a person wearing snowshoes.

Snow shoes are designed for walking on deep, soft snow.

Explain why they are better suited for this than boots.

Figure 1 shows a pool full of water.

The pressure on the ground due to the water in the pool is 3500 Pa.

The gravitational field strength, g, = 10 N / kg.

Calculate the depth of the water in the pool.

Figure 2 shows part of the side and base of the pool.

Figure 2

The water in the pool causes a force on the base of the pool.

Draw an arrow on Figure 2 to show the direction of this force at point X.

A smaller pool has the same depth of water but has only half the area in contact with the ground.

The pressure on the ground underneath the smaller pool is

A small hole is made in the base of the large pool shown in Figure 1.

The area of the hole is 1.5 mm². The pressure at the base of the pool due to the water is 3500 Pa.

Calculate the force on the ground directly below the hole due to the water in the pool.

Use the equation

A bigger hole is made in the base of the same pool.

Compare the force on the ground directly below the bigger hole with the force on the ground directly below the original hole.

Figure 20 shows a metal block being weighed by a newton meter (force meter).

In Figure 20a the block is hanging in a liquid. In Figure 20b the same block is hanging in air.

Explain why the reading on the newton meter is different in Figures 20a and 20b.

The density of the liquid is 1.4 × 10³kg / m³.

Calculate the density of the block. Gravitational field strength, g, = 10 N / kg

density =_........ kg / m³

*(b) Figure 21 shows a device that a person can use to lift a large load with a smaller effort force.

(Source: © Shutterstock-Pixelsquid/Shutterstock)

Figure 21

Figure 22 shows the important parts of the device. The curved arrows show the directions of rotation of the handle, the gears and the drum.

The size of the effort force needed to lift the load is determined by the sizes of the parts of the device.

Explain why this is the case.

Your answer should refer to

• the sizes of the different parts of the device

• how these sizes are used in relevant calculations

Figure 25 shows an object at the bottom of a beaker of water.

Which diagram shows the direction of the force exerted by the water on the object at point X?

Figure 26 shows an ice skater standing on one skate.

Calculate the force the skate exerts on the ice.

pressure of skate on ice = 4.8 10 Pa⁷

area of blade in contact with ice = 1.2 10⁵ m²

Use the equation

force = pressure area

Give your answer to 2 significant figures.

force =_........

Figure 27 shows how atmospheric pressure changes with height above sea level.

Using the graph, describe how atmospheric pressure changes with height above sea level.

The top of Mount Everest is 8850 m above sea level. Using the graph, estimate the atmospheric pressure at the top of Mount Everest.

pressure =_........

On a different day, the pressure at sea level is 104 kPa and the pressure at a height of 2500 m is 74 kPa.

Calculate the percentage change in pressure from sea level to the height of 2500 m.

percentage change =_........

Figure 28 is a model representing molecules of the Earth’s atmosphere.

Use Figure 28 to explain how the density of the air varies with height above sea level.

Figure 9 shows an object at the bottom of a beaker of water.

Which diagram shows the direction of the force exerted by the water on the object at point X?

Figure 10 shows an ice skater standing on one skate.

Calculate the force the skate exerts on the ice

pressure of skate on ice = 4.8 10 Pa⁷

area of blade in contact with ice = 1.2 10⁵ m²

Use the equation

force = pressure area

Give your answer to 2 significant figures.

force =_........

Figure 11 shows how atmospheric pressure changes with height above sea level.

Using the graph, describe how atmospheric pressure changes with height above sea level.

The top of Mount Everest is 8850 m above sea level. Using the graph, estimate the atmospheric pressure at the top of Mount Everest.

pressure =_........

On a different day, the pressure at sea level is 104 kPa and the pressure at a height of 2500 m is 74 kPa.

Calculate the percentage change in pressure from sea level to the height of 2500 m.

percentage change =_........

Figure 12 is a model representing molecules of the Earth’s atmosphere.

Use Figure 12 to explain how the density of the air varies with height above sea level.

Figure 5 shows the apparatus used to investigate the melting of some crushed ice.

Suggest one safety precaution needed when using the electrical heater.

Suggest one way of heating the crushed ice without using electricity.

Figure 6 shows a graph produced from the data collected by the data logger in Figure 5.

Labels P, Q, R and S have been added.

At the start, P, the beaker contains crushed ice at –8C.

Describe what happens to the crushed ice during the next 15 minutes.

You may use labels P, Q, R and S to help your answer.

Figure 7 shows bubbles of air that a diver breathes out.

The bubbles rise towards the surface.

Which row of the table is correct as one bubble rises?

Which of these is a unit of pressure?

The diver measures air pressure in atmospheres.

A bubble has an initial volume, V₁, of 0.50 litres, at a pressure, P₁, of 3.30 atmospheres.

The bubble rises towards the surface of the water, where the pressure, P₂, is 1.07 atmospheres.

Calculate the volume, V₂, of the bubble near the surface.

Use the equation

volume, V₂, of the bubble =_........

This question is about pressure.

Figure 22 shows windows in an aeroplane.

The aeroplane is high above the Earth’s surface.

The atmospheric pressure outside the aeroplane is 23 000 Pa.

The air pressure inside the aeroplane is 80 000 Pa.

Calculate the pressure difference between inside and outside of the aeroplane.

The surface area of the window is 0.094 m².

Calculate the size of the force on the window due to the cabin air pressure of 80 000 Pa.

Use the equation

On the same aeroplane, a different window has a smaller surface area.

Explain how the force due to the air pressure inside the cabin on the small window differs from the force on the larger window.

Figure 23 shows a cross‑section through the aeroplane including one window.

inside of aeroplane outside of aeroplane

Draw an arrow on Figure 23 to show the direction of the resultant force due to the air pressure inside the cabin on the window at point X.

Figure 24 shows the atmospheric pressure at different heights above the Earth’s surface.

height above the Earth’s surface in m

Figure 24

Describe how the atmospheric pressure changes with height above the Earth’s surface.

Use data from Figure 24 to support your answer.

Suggest one reason why the atmospheric pressure changes with height above the Earth’s surface.

Equations

This question is about pressure.

Figure 5 shows windows in an aeroplane.

The aeroplane is high above the Earth’s surface.

The atmospheric pressure outside the aeroplane is 23 000 Pa.

The air pressure inside the aeroplane is 80 000 Pa.

Calculate the pressure difference between inside and outside of the aeroplane.

The surface area of the window is 0.094 m².

Calculate the size of the force on the window due to the cabin air pressure of 80 000 Pa.

Use the equation

On the same aeroplane, a different window has a smaller surface area.

Explain how the force due to the air pressure inside the cabin on the small window differs from the force on the larger window.

Figure 6 shows a cross‑section through the aeroplane including one window.

inside of aeroplane outside of aeroplane

Draw an arrow on Figure 6 to show the direction of the resultant force due to the air pressure inside the cabin on the window at point X.

Figure 7 shows the atmospheric pressure at different heights above the Earth’s surface.

height above the Earth’s surface in m

Figure 7

Describe how the atmospheric pressure changes with height above the Earth’s surface.

Use data from Figure 7 to support your answer.

Suggest one reason why the atmospheric pressure changes with height above the Earth’s surface.

Figure 11 shows a person doing a push‑up exercise.

An upward force is used to cause rotation about a pivot.

Which row of the table is correct for this rotation?

Figure 12 shows some of the bones and muscles in an arm.

The arrows show the forces on the forearm when the arm is bent.

The hand is empty.

The biceps muscle provides a force to balance the weight of the forearm.

The weight of the forearm can be represented as a single force.

Figure 13 shows a diagram representing the forces and distances involved.

Use the principle of moments to show that the system shown in Figure 13 is in equilibrium.

The person then holds a ball weighing 15 N in their hand.

Figure 14 shows the forces on the forearm and their distances from the elbow joint.

Calculate the force from the muscle that is needed to keep the system in Figure 14 in equilibrium.

Figure 15 shows a ball floating in seawater and the same ball floating in fresh water.

Compare the upthrust on the ball in seawater with the upthrust on the same ball in fresh water.

Explain why there is less of the ball below the surface of the seawater than below the surface of the fresh water.

A donkey has a weight of 2500 N.

The area of each hoof is 0.022 m².

Calculate the average pressure that the donkey exerts on the ground.

Use the equation

average pressure =_........

Figure 24 shows how the shape of a camel’s hoof is different from the shape of a donkey’s hoof.

Both diagrams are drawn to the same scale.

Figure 24

The camel and the donkey have the same mass.

Explain how a camel’s hoof is a more suitable shape than a donkey’s hoof for walking on soft ground.

A student carries out an investigation to show how pressure varies with depth in water.

A pressure sensor is attached to a rule.

The rule and pressure sensor are lowered into the water in a tank, as shown in Figure 25.

The depth of the pressure sensor below the surface of the water is read from the scale on the rule.

The pressure is displayed on the student’s mobile phone which receives a signal from the pressure sensor.

Figure 26 gives some of the readings.

Figure 27 shows a graph with some of the results plotted, but two of the points are missing.

Plot the two missing points on the graph.

Draw a line of best fit through the points on the graph.

Which of the following equations represents the variation of pressure with depth of water below the surface?

Use the graph in Figure 27 to predict the pressure at the surface of the water.

pressure at the surface of the water =_........

The student repeats the investigation in part (b) using seawater and draws a graph of the results.

The seawater is more dense than the water used in part (b).

Compare the graph for seawater with the graph in Figure 27.

A donkey has a weight of 2500 N.

The area of each hoof is 0.022 m².

Calculate the average pressure that the donkey exerts on the ground.

Use the equation

average pressure =_........

Figure 7 shows how the shape of a camel’s hoof is different from the shape of a donkey’s hoof.

Both diagrams are drawn to the same scale.

Figure 7

The camel and the donkey have the same mass.

Explain how a camel’s hoof is a more suitable shape than a donkey’s hoof for walking on soft ground.

A student carries out an investigation to show how pressure varies with depth in water.

A pressure sensor is attached to a rule.

The rule and pressure sensor are lowered into the water in a tank, as shown in Figure 8.

The depth of the pressure sensor below the surface of the water is read from the scale on the rule.

The pressure is displayed on the student’s mobile phone which receives a signal from the pressure sensor.

Figure 9 gives some of the readings.

Figure 10 shows a graph with some of the results plotted, but two of the points are missing.

Plot the two missing points on the graph.

Draw a line of best fit through the points on the graph.

Which of the following equations represents the variation of pressure with depth of water below the surface?

Use the graph in Figure 10 to predict the pressure at the surface of the water.

pressure at the surface of the water =_........

The student repeats the investigation in part (b) using seawater and draws a graph of the results.

The seawater is more dense than the water used in part (b).

Compare the graph for seawater with the graph in Figure 10.

Figure 23 shows some water in a tank.

The bottom of the tank has an area of 0.80 m².

The force on the bottom of the tank, due to the water, is 2400 N.

Calculate the pressure, due to the water, on the bottom of the tank.

More water is added to the tank.

Explain how the pressure on the bottom of the tank changes when more water is added to the tank.

Figure 24 shows an object on the bottom of the tank of water.

Draw an arrow on Figure 24 to show the direction of the force exerted by the water on the surface of the object at point X.

Figure 25 is a graph showing how the atmospheric pressure changes with the height above sea level on the Earth’s surface.

height above sea level on the Earth’s surface in m

Figure 25

An aeroplane descends from 6000 m to 2000 m.

Use the graph to find the change in atmospheric pressure as the aeroplane descends.

change in pressure =_........

Suggest one reason why the atmospheric pressure is greater at 2000 m than at 6000 m.

Figure 26 shows two drawings of the same person on a bed.

Explain why the person exerts a different pressure on the bed when standing up than when lying down.

Figure 8 shows some water in a tank.

The bottom of the tank has an area of 0.80 m².

The force on the bottom of the tank, due to the water, is 2400 N.

Calculate the pressure, due to the water, on the bottom of the tank.

More water is added to the tank.

Explain how the pressure on the bottom of the tank changes when more water is added to the tank.

Figure 9 shows an object on the bottom of the tank of water.

Draw an arrow on Figure 9 to show the direction of the force exerted by the water on the surface of the object at point X.

Figure 10 is a graph showing how the atmospheric pressure changes with the height above sea level on the Earth’s surface.

height above sea level on the Earth’s surface in m

Figure 10

An aeroplane descends from 6000 m to 2000 m.

Use the graph to find the change in atmospheric pressure as the aeroplane descends.

Suggest one reason why the atmospheric pressure is greater at 2000 m than at 6000 m.

Figure 11 shows two drawings of the same person on a bed.

Explain why the person exerts a different pressure on the bed when standing up than when lying down.

Figure 1 shows an object under the surface of the sea.

Which arrow shows where the pressure on the object is greatest?

Figure 2 shows two blocks of stone resting on the bottom of the sea.

Both blocks have the same height.

Area Y is 4 times bigger than area X.

What is the pressure due to the water on the top surface of block Y?

A diver is swimming underwater in a lake.

The diver wears the meter shown in Figure 3.

The meter shows the depth of the diver below the surface of the water.

State the depth shown on the meter in Figure 3.

State the unit.

State how the pressure of the water on the diver changes as the diver swims down from the surface of the lake.

State why the total pressure on the diver is greater than just the pressure due to the water above the diver.

An aeroplane takes off from the ground.

State two factors that affect the pressure of the atmosphere on the aeroplane as the aeroplane goes higher in the atmosphere.

Figure 16 shows a metal container with a movable piston.

Point X is on the inner surface of the container.

The gas in the container is at a higher pressure than the air outside the container.

Which of these shows the direction of the force, due to the gas, on the container at point X?

The pressure of the gas in Figure 16 (P₁) is 120 kPa.

The volume of the gas in Figure 16 (V₁) is 2500 cm³.

The piston is pushed up slowly so that the temperature of the gas does not change.

The new volume of the gas (V₂) is 1600 cm³.

Calculate the new pressure of the gas, P₂.

Use the equation

new pressure, P₂ =_........

Figure 17 shows a bicycle pump with a closed end.

The area of the piston is 2 cm².

A force of 28 N is applied to the piston.

Calculate the pressure, in N/cm², of the piston on the air in the bicycle pump.

*(d) A container is sealed so that the mass of the gas inside cannot change.

The volume of the gas is changed and the pressure is measured at different volumes.

The temperature of the gas does not change.

Figure 18 is a graph of the results.

Explain, in terms of the movement of particles, why there is a pressure on the container and why the pressure changes as shown in Figure 18.

Figure 25 shows four identical metal cans, each filled with water to the same level.

Each can has three tubes.

Water comes out of each tube.

Which of these shows the correct pattern of water coming out of the tubes?

Figure 26 shows a glass U‑tube containing water of density 1000 kg/m³.

The water levels are the same on both sides of the U‑tube.

Both ends of the U‑tube are open to the atmosphere.

Atmospheric pressure is 101 000 N/m².

Figure 27 shows the U‑tube with one side connected to a gas supply.

The difference in the levels of water, h, is 0.200 m.

gas

Calculate the gas supply pressure. Use an equation selected from the list of equations at the end of the paper.

The measurement is repeated using a U‑tube of larger cross-sectional area.

Explain why the value of h does not change.

Figure 3 shows a diver swimming in a lake.

The pressure on the diver is due to both the water above him and the Earth’s atmosphere.

The pressure of air on the surface of the water is one atmosphere. 10 m of water is equivalent to one atmosphere.

How many atmospheres of pressure will be on the diver at a depth 20 m?

A balloon is filled with helium when it is on the ground.

The balloon is released and it rises through the atmosphere.

Explain what happens to the size of the balloon as it rises through the atmosphere.

Figure 4 shows a container of length 6.0 m and width 2.0 m resting on a floor. The weight of the container is 15 000 N.

Calculate the pressure that the container exerts on the floor.

Use the equation

Figure 17 shows a crane lifting a concrete block from the bottom of a deep pool of water. The top of the block is a distance, h, below the surface of the water.

The force on the top of the block due to the water above it is 41 000 N.

The pressure due to the water on the top surface of the block is 66 000 Pa.

Calculate the area of the top surface of the block.

The density of water is 1000 kg/m³.

Calculate the distance, h, between the top of the block and the surface of the water.

Gravitational field strength, g, is 10 N/kg.

Use an equation selected from the list of equations at the end of this paper.

Explain why there is an upthrust produced by the water on the block.

*(iv) The crane raises the block until it is high enough out of the water to be loaded on to a lorry.

The block moves upwards at a constant speed even though the lifting force in the cable changes.

Figure 18 shows the graph of how the lifting force changes while the block is being raised.

Explain why the lifting force changes as shown on the graph in Figure 18. Include calculation(s) in your answer.

Figure 10 shows an arrangement of gears.

Each gear turns around a fixed axle.

Gear P is turned through one complete revolution per second.

Which of the following describes the motion of gear R?

Figure 11 shows the same arrangement with gear R replaced by a rack.

The rack can move up or down when the gears turn.

The teeth on the rack are 2 mm apart.

Calculate how far the rack moves when P turns through to one complete revolution.

Figure 12 shows three toy animals hanging from a rod.

The rod hangs from the ceiling by a string tied to the centre of the rod.

The system is in equilibrium.

Use the principle of moments to calculate the mass of the toy elephant.

Figure 13 shows a diagram of a device for lifting heavy loads.

The metal tube is filled with oil.

The piston Y is pushed down with a force K.

This produces a force L on piston Z.

The pressure exerted on the oil by piston Y is the same as the pressure exerted by the oil on piston Z.

Explain the difference between the size of force K and the size of force L.