Physical quantities & units

A student plays a game using a single dice.

The student decides to determine the density of the dice by measuring its mass and volume.

Describe how the student could accurately measure the mass of the dice.

The dice is not a regular shape.

The student decides to measure the volume of the dice using a displacement method.

The student places the dice into a measuring cylinder containing water.

The diagram shows the water in the measuring cylinder before and after the dice is fully submerged.

The measuring cylinder gives volume in units of cm³.

Using the diagram, determine the volume of the dice.

The dice has a mass of 9.2 g.

Calculate the density of the dice using the formula

Give a suitable unit.

The photograph shows a mechanism that can be used to open a gate.

(Source: © Photimageon / Alamy Stock Photo)

The diagram shows the gate mechanism when the handle is being pulled to the right.

The bolt is connected to the handle. When the handle is pulled to the right, the bolt also moves to the right and the gate can be opened.

The spring is compressed when the bolt moves to the right. When the handle is released, the spring pushes the bolt back to its original position.

When the handle is pulled to the right, the spring applies a force on the handle to the left.

The vertical distance between the spring and the pivot point of the handle is 22 cm.

The force from the spring is 5.2 N.

Show that the force from the spring produces a moment of approximately 1 Nm.

State what is meant by the term principle of moments.

Force F acts on the handle to keep the handle stationary so that the gate can be opened.

Force F acts at a vertical distance of 70 cm from the pivot point of the handle.

Calculate the magnitude of force F.

Give two changes to this gate mechanism that would make it easier to open the gate.

A tennis ball is dropped from a height above the ground.

Diagram 1 shows the tennis ball at the instant it is released.

Diagram 1

On diagram 1, draw a labelled arrow to show the force acting on the tennis ball at the instant it is released.

Diagram 2 shows the tennis ball at the instant it hits the ground.

Diagram 2

Just before hitting the ground, the tennis ball is moving downwards at a velocity of 2.5 m/s.

Just after hitting the ground, the tennis ball is moving upwards at a speed of 1.9 m/s.

The mass of the tennis ball is 0.057 kg.

Calculate the change in momentum of the tennis ball when it hits the ground.

Give the unit.

The ball is in contact with the ground for a time of 6.0 ms.

Calculate the force exerted on the ball by the ground.

Give the direction of this force.

The coefficient of restitution can be used to determine how high a ball will bounce. The higher the value of the coefficient of restitution, the higher the ball will bounce.

Diagram 3 shows a ball being dropped from a height (h₁) above the ground.

The ball hits the ground and bounces.

At the top of its bounce, the ball reaches a height (h₂) above the ground.

The coefficient of restitution can be determined using the formula

A student decides to do an investigation to compare the coefficient of restitution for different types of ball.

Design a method for the student’s investigation.

Your answer should include details of

• the variables in the investigation

• how to obtain accurate measurements

• how to obtain reliable results

You may add to diagram 3 or draw an additional diagram to help your answer.

Diagram 1 shows the apparatus a student uses to determine the specific heat capacity of a liquid.

Describe a suitable method the student could use to determine the specific heat capacity of the liquid.

The graph shows the student’s results.

What is happening to the liquid between points P and Q on the graph?

Use the graph to determine the change in temperature of the liquid after 15 minutes of heating.

The power of the heater is 48 W and the mass of the liquid is 0.53 kg.

Calculate the specific heat capacity of the liquid.

specific heat capacity =_........ J / kg °C

In 1947, the Railton Mobil Special was the first ground vehicle to achieve a speed of more than 400 miles per hour.

During a test, the vehicle travelled at a speed of 403 miles per hour.

Calculate a speed of 403 miles per hour in metres per second (m / s). [1 mile = 1600 m]

During the test, the vehicle travelled past two markers. The markers were placed a known distance apart.

Describe how these markers could be used to determine the speed of the vehicle.

The diagram shows the vehicle travelling at a constant speed.

One of the horizontal forces acting on the vehicle has been drawn.

Complete the diagram by drawing a labelled arrow for the other horizontal force acting on the vehicle.

A student investigates the voltage-current characteristics of an unknown component, X.

The student is given this equipment to investigate component X.

• battery

• variable resistor

• ammeter

• voltmeter

• connecting wires

The diagram shows an incomplete circuit containing the battery and component X.

Complete the diagram by drawing a circuit the student could use for their investigation.

The graph shows the results of the investigation.

Draw a line of best fit on the graph.

Calculate the resistance of component X when the voltage is 4.2 V.

Give the unit.

Which of these is equivalent to 4.2 V?

The student concludes that component X is a filament lamp.

Comment on the student’s conclusion.

The photograph shows a power bank used to recharge the battery in an electronic device.

The power bank stores charge.

The charge stored can be measured in amp-hours (Ah). 1 Ah is the amount of charge transferred by a current of 1 A in a time of 1 hour.

Calculate the charge stored in coulombs when the charge stored is 1 Ah.

Use the formula

charge stored = current × time taken

An electronic device is connected to the power bank.

Whilst recharging, the electronic device receives a constant current of 2.4 A and 3.8 × 10³C of charge is transferred.

Calculate the time taken to recharge the electronic device.

Give your answer in minutes.

The electronic device is connected to the power bank using a long cable.

Suggest how using a long cable affects the time taken to recharge the electronic device when compared with a short cable.

A student owns three electronic devices. Each electronic device stores a different amount of charge.

The table gives some information about the charge stored by the electronic devices and how often they need to be recharged.

The power bank stores a maximum charge of 26.8 Ah.

The student needs to take these three electronic devices on a school trip for one week.

Determine whether the maximum charge of the power bank is enough to recharge the batteries of the three electronic devices during the school trip.

A wrench is used to turn a nut.

(Source: https://www.shutterstock.com/image-photo/adjustable-spanner-isolated-on-white-chrome-1794553030)

The force applied to the wrench is 28 N.

Calculate the moment applied by the wrench on the nut.

Give a suitable unit.

State two changes that could be made to increase the size of the moment applied to the nut.

Diagram 2 shows the wrench as it is turned through 90°

(Source: https://www.shutterstock.com/image-photo/adjustable-spanner-isolated-on-white-chrome-1794553030)

The force is applied over a distance that is equal to a quarter of the circumference of a circle.

The circle has a radius of 15 cm.

Calculate the distance over which the force is applied. [circumference of circle = 2πradius]

Calculate the work done by the force as the wrench is turned through a quarter of the circumference of the circle.

This question is about astrophysics.

Which of these is a large collection of billions of galaxies?

Which of these is a correct unit for gravitational field strength, g ?

Which statement explains why the gravitational field strength on the Moon is less than the gravitational field strength on Earth?

Describe the differences between the orbit of the Moon and the orbit of a comet.

You may include a diagram to support your answer.

The diagram shows some apparatus that can be used to determine the specific heat capacity of water.

Describe how a student could use this apparatus to determine the specific heat capacity of water.

Include details of any additional equipment needed in your answer.

The table shows the student’s results.

Use the student’s results to calculate the specific heat capacity of water.

specific heat capacity of water =_........ J / kg °C

Give two reasons why the energy from the heater is not all retained in the thermal store of the water.

This question is about momentum and forces.

State the principle of conservation of momentum.

The diagram shows an air track that can be used to investigate motion without friction.

Air comes out through a series of small holes in the air track. The air lifts the glider slightly above the track.

A small spacecraft engine floats at rest on a cushion of air.

State the momentum of the spacecraft engine when it is at rest.

The spacecraft engine ejects large numbers of xenon ions to the left.

A mass of 2.6 × 10⁻⁸kg of xenon ions leaves the engine with a mean speed of 26 km / s.

Calculate the momentum of all the ejected xenon ions.

momentum =_........ kg m / s

State the magnitude and direction of the spacecraft engine’s momentum after these xenon ions leave the engine.

The ions exert a force of 2.6 mN on the spacecraft engine.

The spacecraft engine has a mass of 1.2 kg.

Calculate the acceleration of the engine.

Give your answer to 2 significant figures.

acceleration =_........ m / s²

The engine is designed to accelerate a spacecraft while the spacecraft is travelling through space.

The spacecraft carries a mass of 0.75 kg of xenon ions for the engine.

When the engine is used, 9.9 × 10⁻⁸kg of xenon ions leave the engine each second.

A student suggests that this small spacecraft engine would not be useful because the acceleration it produces is very small.

Evaluate the student’s suggestion.

This is a question about radioactivity.

Which of these is the unit of activity?

Which of these is the correct description of the term half-life ?

A teacher demonstrates how the activity of a radioactive sample changes with time.

The box gives the names of different pieces of equipment.

Complete the sentences using words from the box.

The teacher measures time with a_........ .

The teacher measures the count rate with a_........ and a counter.

The graph shows the teacher’s results.

Draw a circle around the anomalous result.

Use the graph to determine the half-life of the radioactive sample.

Give a reason why the teacher should not expect the data points to lie exactly on the curve of best fit.

Protactinium is an element with several different radioactive isotopes.

Protactinium‑234 has a half‑life of 6.7 hours.

A sample of protactinium‑234 has an initial activity of 800 units.

Give a suitable unit for activity.

On the axes below, sketch a graph for the decay of the sample of protactinium‑234 during its first three half‑lives.

When protactinium‑234 undergoes beta (β^–) decay it becomes uranium‑234.

The incomplete nuclear equation shows this process.

Complete the nuclear equation to show the beta decay of protactinium‑234.

Write your answers in the dashed boxes.

A student suggests an experiment to determine the type of radiation emitted by a different isotope of protactinium, protactinium‑231.

This is the suggested method.

Step 1 connect a suitable radiation detector to a radiation counter

Step 2 place a source of protactinium‑231 at a fixed distance of 3 cm from the radiation detector

Step 3 record the count of detected radiation for a time of one minute

Step 4 place a sheet of paper between the source and detector

Step 5 record the count of detected radiation for a time of one minute

Step 6 repeat Steps 4 and 5 using a sheet of aluminium and then a sheet of lead instead of the sheet of paper

The table shows the results of the investigation when it is done by a teacher.

Which of these is the dependent variable in the investigation?

The student’s method does not allow for background radiation.

Describe how the student’s method should be modified to allow for background radiation.

Describe how the student’s method could be modified to improve the reliability of the results.

Evaluate the data from the experiment to conclude the type of radiation emitted by protactinium‑231.

A dam is a structure designed to hold water in a reservoir.

The water in the reservoir has a depth of 35 m.

State the formula linking pressure difference, height, density and g.

Atmospheric pressure at the surface of the reservoir is 100 kPa.

Calculate the total pressure at the bottom of the reservoir.

[for water, density = 1000 kg / m³]

An underwater camera is used in the water reservoir.

The camera lens experiences a force of 430 N at a pressure of 260 kPa.

State the formula linking pressure, force and area.

Calculate the area of the camera lens.

Give a suitable unit.

Sea water has a density of 1030 kg / m³.

Explain how the design of the dam would need to be changed to hold the same depth of sea water safely.

The boxes show some physical quantities and their units.

Draw a straight line from each physical quantity to its correct unit.

One has been done for you.

Physical quantity
Unit

Some physical quantities are scalars and other physical quantities are vectors.

State the difference between a scalar quantity and a vector quantity.

Give an example of a scalar quantity.

A student uses the circuit shown in diagram 1 to investigate how the current changes with voltage for a filament lamp.

Give the name of component Y.

Give a reason why component Y is included in the circuit.

The graph shows some of the student’s results.

State the formula linking charge, current and time.

Determine the current in the lamp when the voltage across the lamp is 10 V.

Calculate the charge transferred through the lamp in 30 s when the voltage across the lamp is 10 V.

Give the unit.

Calculate the time for the lamp to transfer 250 J of energy when the voltage across the lamp is 10 V.

The student disconnects the cell and reconnects it with its terminals reversed.

Complete the graph to show how the current in the lamp varies with voltage across the lamp when the cell is connected with its terminals reversed.

The student replaces the filament lamp with a light emitting diode (LED) and replaces the cell with an alternating current (a.c.) power supply, as shown in diagram 2.

The student also removes the ammeter and voltmeter from the circuit.

Explain why the LED flashes on and off in this circuit.

The diagram shows an electric circuit containing component X and a lamp connected in series.

Add another component to the diagram to measure the voltage of component X.

Give the name of component X.

The graph shows how the resistance of component X changes with light intensity.

Use the graph to determine the resistance of component X when the light intensity is 4.0 arbitrary units.

The current in the circuit is 0.0018 A.

Calculate the voltage across component X at a light intensity of 4.0 arbitrary units.

Explain what happens to the brightness of the lamp when component X is covered with a dark sheet of paper.

Diagram 1 shows a gate fitted with a spring mechanism.

The spring mechanism shuts the gate automatically.

The graph shows some data from an investigation into how the extension of the spring changes with an increasing force.

Describe the relationship shown by the graph.

Diagram 2 shows the gate viewed from above.

The force the spring exerts on the gate is 480 N.

Show that the moment of the force the spring exerts on the gate is about 400 Nm.

The force, F, is the minimum force needed to start opening the gate.

Calculate the magnitude of force F.

The spring is removed for testing.

Explain what will happen to the spring if the force applied to extend the spring is too large.

Cobalt‑60 is a radioactive isotope of cobalt.

The table gives the activity of a sample of cobalt‑60 over a period of 10 years.

Give a suitable unit for activity.

The graph shows the data.

Label both axes.

Draw the curve of best fit.

Use the graph to determine the half‑life of cobalt‑60.

Estimate the time taken for the activity to decrease to of its initial value.

Cobalt‑60 decays by beta emission.

Describe what happens to the nucleus of a cobalt‑60 atom during beta decay.

Cobalt‑60 also emits gamma radiation.

Cobalt‑60 is produced in a nuclear reactor.

Discuss the hazards involved and the precautions taken when disposing of cobalt‑60.

The diagram shows a circuit that includes a battery, an ammeter, a voltmeter and three different resistors.

Give the voltmeter reading.

State the formula linking voltage, current and resistance.

Calculate the resistance of resistor X.

Give the reason why the reading on the ammeter would be 16 mA.

Calculate the resistance of resistor Y.

Resistor X and the voltmeter are removed from the circuit, leaving a break in this part of the circuit.

Explain how the current in the battery changes when these components are removed.

A student uses this apparatus to investigate moments.

This is the student’s method.

• attach elastic bands at 15 cm intervals on a one metre tall clamp stand

• attach a newton meter to the highest elastic band and measure the horizontal force required to tilt the stand

• repeat the method at each 15 cm interval

Name an instrument that the student should use to accurately measure the distances on the clamp stand.

The table shows the student’s results.

The photograph shows the reading on the newton meter when the distance is 45.0 cm.

Use the photograph to determine the force required to tilt the stand when the distance is 45.0 cm.

Give a reason why this newton meter is unsuitable for measuring the force for distances less than 15.0 cm.

Plot a graph of the student’s results on the grid.

Draw the curve of best fit.

The student concludes that the moment required to tilt the clamp stand does not change when the distance is varied.

Use data from the table or the graph to evaluate the student’s conclusion.

This question is about momentum.

Diagram 1 shows a neutron approaching a uranium-235 nucleus.

State the formula linking momentum, mass and velocity.

Calculate the momentum of the neutron.

Give a unit with your answer.

[mass of neutron = 1.67 × 10^–27kg]

State what is meant by the term conservation of momentum.

Diagram 2 shows that when the neutron collides with the uranium-235 nucleus, they combine to give a uranium-236 nucleus.

Use conservation of momentum to calculate the velocity, v, of the uranium-236 nucleus.

[mass of uranium-235 nucleus = 3.99 × 10^–25kg]

[mass of uranium-236 nucleus = 4.01 × 10^–25kg]

Give your answer to 2 significant figures.