Gravity & weight

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.

An athlete jumps vertically from the ground.

The athlete has a mass of 85 kg, and leaves the ground with an upwards velocity of 4.5 m/s.

State the formula linking kinetic energy, mass and speed.

Calculate the athlete’s kinetic energy at a speed of 4.5 m/s.

At the maximum height of the jump, the athlete has a speed of 0 m/s.

State the increase in the amount of energy in the athlete’s gravitational potential energy store from the ground to the maximum height of the jump.

State the formula linking gravitational potential energy, mass, gravitational field strength and height.

Calculate the maximum height of the athlete’s jump.

Sketch a velocity‑time graph for the athlete’s jump from the ground to the maximum height of the jump. No numbers are required.

Assume there is no air resistance.

What feature of the velocity‑time graph gives the acceleration due to gravity?

Explain why the gravitational field strength on the Moon is different from the gravitational field strength on the Earth.

The diagram shows a submarine at rest underwater.

There are two vertical forces acting on the submarine.

One of the forces is called upthrust.

Give the name of the other force.

Draw two arrows on the diagram to represent the vertical forces acting on the submarine.

State the formula linking pressure, density, gravitational field strength and height.

Calculate the pressure from the water at a point 38 m below the surface of the water.

[density of sea water = 1030 kg/m³]

To rise back to the surface, air is pumped into a storage tank inside the submarine.

Explain how the air exerts pressure on the walls of the storage tank.

The air in the storage tank starts at a pressure of 410 kPa.

As the submarine rises, the air in the storage tank increases in temperature from 2.5C to 18C. The volume of the storage tank remains constant.

Calculate the pressure of the air in the storage tank at 18C.

Diagram 1 shows the apparatus a student uses to investigate the bending of a wooden strip.

Part of the wooden strip is clamped to a table.

A load is fixed to the free end of the wooden strip, causing it to bend.

The free end of the wooden strip is positioned a length, L, beyond the edge of the table, as shown in diagram 1.

The weight of the load causes the end of the wooden strip to move down through a height, h.

A student investigates how the length, L, affects the height, h.

The load has a mass of 250 g.

Calculate the weight of the load.

Use the formula

weight = mass × gravitational field strength, g

This is the student’s method for the investigation.

• clamp the wooden strip so that L = 20 cm

• fix the load to the end of the wooden strip, as shown in diagram 1

• measure the height, h

The student repeats this method for different values of L.

Give the independent and dependent variables in the investigation.

independent variable

dependent variable

Give two control variables in the investigation.

Suggest how the student could accurately measure the height, h.

The table shows the results of the investigation.

Diagram 2 shows the wooden strip when L = 80 cm.

Using diagram 2, determine the height, h, in the laboratory. [1 cm on the diagram = 10 cm in the laboratory]

Plot a graph of the student’s results.

Draw the curve of best fit.

The student concludes that h is directly proportional to L.

Evaluate the student’s conclusion.

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.

This question is about moments.

Diagram 1 shows the raised lower leg of a person.

The moment of the weight of the lower leg about the pivot is 19 N m.

A vertical force, F, is applied to the person’s foot to keep the lower leg raised.

The lower leg does not move.

Calculate the magnitude of force F, using the formula

moment = force × perpendicular distance from pivot

Which distance is used to calculate the moment of the weight of the lower leg about the pivot?

Diagram 2 shows the person resting their lower leg on two supports.

The centre of gravity of the lower leg is 0.25 m away from support A and 0.35 m away from support B.

Explain whether force X or force Y is larger.

Ignore the weight of the upper leg.

A bag of ice is placed on the lower leg, vertically above the centre of gravity.

This causes force X and force Y to increase.

The bag is then moved towards the person’s foot.

Describe how force X and force Y change as the bag is moved towards the person’s foot.

A model electric motor is used to lift a load through a vertical height.

The load has a mass of 400 g and gains 3.2 J of energy in its gravitational store when lifted.

State the formula linking gravitational potential energy, mass, gravitational field strength (g) and height.

Calculate the height the load is lifted.

State the amount of useful work done on the load by the motor when the load is lifted through this height.

The load is lifted at a constant speed.

Diagram 1 shows the lifting force acting on the load as it is lifted.

Draw a labelled arrow on diagram 1 to show the other force acting on the load.

Ignore the effects of air resistance.

Diagram 1

A joulemeter measures the amount of energy transferred electrically to the motor as the motor lifts the load.

The joulemeter displays a reading of 11.0 J when the load has gained 3.2 J of energy in its gravitational store.

Calculate the efficiency of the motor.

Justify why 7.8 J of energy must be dissipated into the thermal store of the surroundings as the load is lifted.

Diagram 2 is an incomplete Sankey diagram.

Complete the Sankey diagram to show the energy transferred by the motor.

The drawing shows a camel and a person in a desert.

Describe a method you could use to find the pressure a person exerts on the ground when standing on two feet.

The total area of contact of the camel’s feet with the ground is 1300 cm².

The mass of the camel is 660 kg.

Calculate the pressure this camel exerts on the ground.

pressure =_........ N / cm²

The gravitational field strength of a planet decreases with increasing distance from the planet.

The table shows the value of the gravitational field strength of Mars at different distances from the centre of Mars.

A student finds this formula in a textbook, which links distance from the centre of a planet to its gravitational field strength

gravitational field strength×distance² = constant

Use data from the table to justify this formula.

Olympus Mons is the tallest mountain on Mars.

The distance between the centre of Mars and the peak of Olympus Mons is 3410 km.

Calculate the gravitational field strength at the peak of Olympus Mons.

gravitational field strength =_........ N / kg

A pencil has a weight of 0.16 N.

What is the mass of the pencil?

The diagram shows the pencil with one end resting on a small block.

A finger provides an upwards force, F, to keep the pencil horizontal.

The weight of the pencil is 0.16 N.

Calculate the moment of the weight of the pencil about the pivot.

Use the formula

moment = force × perpendicular distance from the pivot

moment =_........ N cm

State the moment of the force F.

Show that force F is 0.080 N.

This question is about electromagnetism.

Diagram 1 shows the magnetic field around a straight section of copper wire.

Explain why the copper wire has the magnetic field shown in the diagram.

A student investigates how the strength of an electromagnet varies with the current in the electromagnet.

The diagram shows their apparatus.

This is the student’s method.

• switch on the electromagnet at its maximum current

• place a load of 100 g so that it is held above the floor by the electromagnet

• slowly reduce the current in the electromagnet until the load falls from the electromagnet

• record the current at which the load falls

• record the current at which the same load falls two more times

Repeat the method for loads of different masses.

Suggest a suitable safety precaution for the student’s investigation.

The table shows the student’s results.

Calculate the mean current when the mass of the load was 600 g.

Give your answer to a suitable number of significant figures.

On the grid, plot a graph of the mean current against the mass of the load.

The scale for the mass axis has been done for you.

Draw the line of best fit.

The student predicts that a load of 1.0 kg will fall when the current in the electromagnet is 3.0 A.

Comment on the student’s prediction.

Diagram 1 shows a wooden plank balanced horizontally on two supports, A and B.

A block is suspended from the plank between the supports by a cable of negligible weight.

The weight of the block is 260 N.

State the formula linking moment, force and perpendicular distance from the pivot.

By taking moments about support A, calculate force F.

Assume the weight of the plank is negligible.

Explain what will happen to the magnitude of force F if the block is moved towards support B.

The centre of gravity of the block is located at point X.

Draw an arrow on diagram 2 to show the weight of the block.

The block also experiences a force due to the tension in the cable.

Explain why the block remains stationary when it is supported by this tension force.

Explain why the forces acting on the block are not an example of Newton’s third law of motion.

This question is about astrophysics.

Which of these do planets orbit?

Which of these has the largest diameter?

Which of these has the smallest diameter?

At the surface of the Earth, the gravitational field strength is 10 N/kg.

At the surface of the Moon, the gravitational field strength is 1.7 N/kg.

Give a reason for the difference in gravitational field strength.

The table gives data for some of the planets in the solar system.

Plot a bar chart of the gravitational field strength for each planet.

Suggest why planets have different gravitational field strengths at their surface.

Give the relationship shown by the data in the table between the orbital radius and the orbital speed for the planets in the solar system.

Calculate the time period of Mercury’s orbit around the Sun.

The diagram shows a child on a zip-line ride.

During the ride the child slides along a metal wire with the velocity in the direction shown in the diagram.

The diagram also shows the tension force acting on the safety harness the child is wearing.

Force and velocity are examples of vector quantities.

State what is meant by the term vector quantity.

Draw labelled arrows on the diagram to show two other forces that act on the child.

The photograph shows Callisto, a moon of the planet Jupiter.

In the space below, draw a labelled diagram to show how Callisto orbits Jupiter.

Callisto orbits Jupiter at an orbital radius of 1 880 000 km and with an orbital period of 400 hours.

Calculate the orbital speed of Callisto in km/s.

Give your answer to 3 significant figures.

Callisto has a gravitational field strength of 1.2 N/kg at its surface.

The Earth’s moon has a gravitational field strength of 1.6 N/kg at its surface.

Callisto has a larger mass than the Earth’s moon.

Suggest why Callisto has a lower gravitational field strength than the Earth’s moon.

An object has a weight of 59 N on the surface of the Earth’s moon.

Calculate the weight of the same object if it were on the surface of Callisto.

Very strong magnets can be made using the element neodymium.

Diagram 1 shows parts of two neodymium magnets, X and Y, when they are held close together.

Diagram 1

A uniform magnetic field is produced in the space between the magnets.

Diagram 1 shows the south pole of magnet X.

Complete diagram 1 by drawing the uniform magnetic field and labelling the pole on magnet Y.

Diagram 2 shows another neodymium magnet being used to lift an iron ball from a table.

The iron ball is shown at the instant it leaves the surface of the table.

Diagram 2

Explain why the iron ball experiences an upward magnetic force.

The iron ball experiences an upward resultant force at the instant shown in diagram 2.

Draw a labelled arrow on diagram 2 to show the weight of the iron ball.

State the formula linking weight, mass and gravitational field strength.

At the instant shown in diagram 2, the resultant force acting on the iron ball is 124 mN and the magnetic force is 165 mN.

Calculate the mass of the iron ball.

Explain why the resultant force acting on the iron ball increases as the iron ball moves towards the magnet.

The diagram shows a metal block on top of a wooden block.

The metal block is held stationary by force F.

The weight of the metal block acts through point G.

Give the name of point G.

Name a piece of apparatus that could be used to measure the weight of the metal block.

State the formula linking moment, force and perpendicular distance from the pivot.

The weight of the metal block is 0.68 N.

Show that the moment of the weight of the metal block about point P is approximately 2.9 N cm.

Force F is applied to the metal block to stop it from moving.

Calculate the magnitude of force F.

This is a question about Io, a moon of Jupiter.

The diagram shows two jets of gas from volcanoes on Io.

One jet of gas is from the volcano Prometheus and the other is from the volcano Tvashtar.

Gas particles in the Prometheus jet leave the surface of Io and move vertically upwards.

The particles reach their maximum height when their speed is zero.

Some particles in the Prometheus jet reach a maximum height of 92 km.

Calculate the initial speed of these particles as they leave the surface of Io.

[acceleration due to gravity on Io 1.8 m/s²]

Before the gas particles leave the surface of Io, they are trapped in a chamber.

Explain how the gas particles exert a pressure on the walls of the chamber.

The Tvashtar chamber has the same volume as the Prometheus chamber and contains the same number of molecules of the same type of gas.

The temperature of the gas in the Prometheus chamber is 1200 K.

The temperature of the gas in the Tvashtar chamber is 1600 K.

The pressure of the gas in the Prometheus chamber is 8.2 kPa.

Calculate the pressure of the gas in the Tvashtar chamber.

Explain why the pressure inside the chambers increases when the temperature increases.

Use ideas about particles in your answer.

Explain why the particles from the Tvashtar chamber reach a greater maximum height than the particles from the Prometheus chamber.

The diagram shows some of the forces acting on a large rubbish bin on wheels.

The weight of the bin acts through point G.

Give the name of point G.

The mass of the bin is 23 kg.

What is the weight of the bin?

State the principle of moments.

A person applies force F to the bin to keep it stationary.

Calculate the magnitude of force F.

State the magnitude and direction of the force applied to the person by the bin.

A builder needs to lift a large stone block.

Diagram 1 shows the stone block.

Draw an X on diagram 1 at the centre of gravity of the stone block.

State the formula linking weight, mass and gravitational field strength.

The mass of the stone block is 130 kg.

Calculate the weight of the stone block.

The builder uses a wooden plank to lift the large stone block.

The plank is uniform and pivoted at its centre.

The builder pushes down on one end of the plank to lift the stone block.

Diagram 2 shows the plank when it is horizontal and stationary.

State the principle of moments.

The builder is pushing down with a force of 520 N to keep the plank horizontal.

Calculate distance X.

Calculate the length of the plank.

A ship floats on the sea.

The ship floats because of the forces acting on it.

The upward force acting on the ship is called upthrust.

This force is shown on the diagram.

Draw another labelled arrow on the diagram to show the other vertical force acting on the ship.

Forces are vector quantities.

State what is meant by the term vector quantity.

Give another example of a vector quantity.

The upthrust force acting on the ship is proportional to the pressure difference between the bottom of the ship and the surface of the sea.

The pressure acting on the ship at the surface of the sea is 100 kPa.

State the formula linking pressure difference, height, density and gravitational field strength (g).

The bottom of the ship is 15.8 m below the surface of the sea.

Show that the pressure acting on the bottom of the ship is approximately 260 kPa.

[density of seawater = 1030 kg/m³]

Explain why the bottom of the ship is deeper below the surface of the sea when the ship is fully loaded with cargo.

A student investigates how much pressure she exerts on the ground when she is standing up.

The weight of the student is 520 N.

State the formula linking weight, mass and gravitational field strength (g).

Calculate the mass of the student.

The student measures the area of one of her feet when it is in contact with the ground.

She draws around her foot on a piece of squared paper.

The squares on the paper have a side length of 2 cm.

Estimate the area of the student’s foot in contact with the ground.

area =_........ ²

State the formula linking pressure, force and area.

The weight of the student is 520 N.

Calculate the pressure the student exerts on the ground when she is standing on both feet.

Give the unit.

This question is about a folding table.

The diagram shows some of the forces acting on the table.

The weight of the table acts through point G.

State the name of point G.

State the formula linking moment, force and perpendicular distance from the pivot.

The moment of the weight force of the table about the hinge is 92 N m.

By using the principle of moments, calculate the force S that a person applies to keep the table in equilibrium.

State Newton’s third law.

State the magnitude and the direction of the force that the table applies to the person holding the table.

The diagram shows a bottle supported by a finger.

State the name of point Z.

State the formula linking moment, force and perpendicular distance from the pivot.

The bottle does not move.

Calculate the weight of the bottle.

This is a question about a melting ice cube.

The diagram shows an ice cube placed on the ground.

The mass of the ice cube is 3.7 g and its area of contact with the ground is 2.610^–4 m².

Calculate the pressure the ice cube exerts on the ground.

The ice cube melts and becomes a puddle with a larger cross‑sectional area.

Explain how the pressure of the ice cube on the ground changes when it melts.

Ice melts at a temperature of 0C.

On the axes, sketch how the temperature of the ice cube changes as it rises from a temperature of –10C to a temperature of 20C.

Explain the changes that occur when a solid melts.

Refer to particles in your answer.