gcseprep.com€¦ · web viewtopic 2 – mechanics. q1. the diagram shows the carriage of a...

Topic 2 – Mechanics

Q1.

The diagram shows the carriage of a rollercoaster about to enter a vertical loop of diameter 17.0 m. The carriage is initially at rest at a height Δh above the bottom of the loop.

(i) So that a passenger remains in contact with their seat at the top of the ride, show that the minimum speed of the car at the top of the loop is 9.1 m s−1.

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(ii) Calculate the minimum value of Δh that will enable the passenger to remain in contact with their seat at the top of the loop.

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Δh = ...........................................................

(Total for question = 4 marks)

Q2.

A physics class made a toy rocket. A drinks bottle was partially filled with water and inverted over a valve. An air pump delivered air to the bottle until the pressure forced the bottle from the valve and the water was ejected from the bottle at high speed.

A velocity-time graph for the bottle for the first 4 s after take-off is shown.

Sketch the corresponding acceleration-time graph on the axes below.

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Q3.

Motors usually have a rotating component which can do work W.

(a) A motor lifts a load in a time t. The axle of the motor has a radius r and exerts a force F.

The power produced by a motor can be calculated by using the following word equation.

Power = moment of the force exerted by the rotating axle × angular velocity

Derive this equation, starting with power (4)

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(b) An electrostatic motor was first demonstrated by Benjamin Franklin in 1750.

The diagram shows a simplified version of part of this motor.This consists of a rod, with an oppositely charged sphere at either end, which rotates around a fixed pivot. Two stationary charged spheres apply a force on the spheres at either end of the rod.

(i) In the diagram below, electric field lines have been drawn around one pair of these spheres.Add to the diagram to show

· the directions of the field lines· the lines of equipotential.

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(ii) The distance between the centres of each charged sphere in this pair is 5.0 cm.Show that the force between this pair of charged spheres is about 0.04 N.charge on each sphere = 0.10 μC

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(c) The table shows the typical power and the corresponding angular velocity required for three different appliances.

Deduce which of these appliances, in principle, could use the electrostatic motor in (b).You should use the word equation in (a) and assume that the length of the rod in the electrostatic motor is 8.0 cm.Assume that the electrostatic motor would deliver a constant force throughout one complete rotation.

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Q4.

A student is investigating a 'Cartesian diver'.

The diver is made from a plastic pipette. When placed in a plastic bottle full of water the diver rises to the top and touches the lid.

(a) Show that the downward force of the lid on the diver is about 0.02 N.

volume of diver = 8.0 × 10–6 m3

mass of diver = 0.0059 kgdensity of water = 1.0 × 103 kg m–3

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(b) When the pressure is increased by squeezing the bottle, water is forced into the diver increasing its weight. The diver sinks, then remains at rest in the position shown.

The volume of air in the empty pipette in part (a) was 8.0 × 10–6 m3.Show that the volume now occupied by the air is about 6 × 10–6 m3.

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(c) The pressure of the air in the empty pipette in part (a) was 1.01 × 105 Pa.

Calculate the pressure of the air in part (b).(2)

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Pressure = ...........................................................


Q5.

A school dynamics trolley has a plunger attached to a spring. When the plunger is pushed in, the spring is compressed. When the plunger is released, it is pushed back out by the spring.

(a) A student investigated the spring to determine whether it obeys Hooke's law in compression.

The trolley was placed vertically in front of a scale and weights were added in turn to the top of the plunger, as shown. The position of the end of the plunger was recorded each time.

The recorded results are shown in the table.

(i) Use the results to plot a graph of weight against compression. You may use the additional column for your processed data.

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(ii) The student concluded that the spring obeys Hooke's law with a spring constant of about 600 N m–

1.Determine whether the student's conclusion is justified.

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(b) Another trolley was adapted by placing a tube around the plunger so that it could be used to launch marbles. A marble was placed in the tube while the plunger was depressed. When the plunger was released it launched the marble.

Determine the maximum possible launch velocity of the marble when the spring is compressed by 5.4 cm.spring constant = 610 N m–1

mass of marble = 4.1 gmass of plunger = 35.4 g

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Maximum launch velocity = ...........................................................

(c) The launch velocity was measured using a light gate and data logger. This produced a smaller value for the launch velocity than that calculated in (b).

Give a reason why this method produced a smaller value for the launch velocity.(1)

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Q6.

A student investigates the motion of a friction-free trolley down a ramp. On the top of the trolley there is a metal loop which makes contact with a length of thin resistance wire, AB, fixed above the ramp. The resistance wire has a uniform diameter.

The trolley accelerates down the ramp and the metal loop stays in contact with the wire along the full length of the ramp.

The student uses a protractor to measure the angle θ between the ramp and the horizontal and records a value of 4° with an uncertainty of ±1°.

(a) The two ends of the wire are connected to a 1.5 V cell. A data logger, set to measure potential difference, is connected to the metal loop and to the negative terminal of the cell.

Explain how the potential difference recorded by the data logger will vary as the loop moves along the length of the wire AB.

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(b) The graph shows the data obtained from the data logger.

Determine the velocity of the trolley at 1.5 s.

1.5 V represents a distance of 2.00 m.

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Velocity = ...........................................................

(c) The student calculated the velocity of the trolley at 2.0 s to be 1.5 m s–1.

By considering the acceleration of the trolley, determine whether the student's measurement of θ was

within the uncertainty quoted.

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Q7.

Mass spectrometry is a technique used to separate ions based on their charge to mass ratio.

The atoms in a sample are ionised and then accelerated and formed into a fine beam. This beam is passed into a region of uniform magnetic field and the ions are deflected by different amounts according to their mass.

Analysis of mass spectrometer data shows that chlorine exists in nature as two isotopes, chlorine-35 and chlorine-37.

In a mass spectrometer, chlorine-35 ions are accelerated through a potential difference of 8.50 kV to produce an ion beam.

Show that the speed of singly ionised chlorine-35 atoms is about 2.2 × 105 m s−1.

mass of an ion of chlorine-35 = 34.97 u

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Q8.

A fairground game requires the player to catapult a ball towards a target to score points.

The ball is required to reach a target a horizontal distance of 50 m away, at the same vertical height, as shown.

The time taken for the ball to reach the target is 2.0 s.

Calculate the angle to the horizontal at which the ball is launched.

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Angle to the horizontal = ...........................................................


Q9.

A student uses a lamp and a light sensor as a light gate connected to a data logger and computer to determine the speed of a falling object. He drops a small cylinder through a clear plastic tube. The light gate and data logger measure the time of fall of the cylinder and the speed is calculated.

The student repeats the experiment five times and records the results in a table.

The student incorrectly includes all the values when calculating the mean speed. A second student thinks that the true value of the mean speed is different.

Explain whether the second student is correct.

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Q10.

The Shanghai Maglev Train is the first commercially operated high-speed magnetic levitation train in the world, connecting the airport and central Shanghai.

The total distance travelled is 29.9 km and the total journey time is 440 s. The train starts from rest and reaches a speed of 97 m s−1 in 120 s.

(i) Calculate the average acceleration of the train during the first 120 s.

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Average acceleration of train = ...........................................................

(ii) Calculate the average speed of the train for the period following the 120 s acceleration.

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Average speed of train = ...........................................................


Q11.

A gardener used a trolley to move a paving stone.

A force meter was attached to the handle of the trolley.

The gardener recorded the following measurements when the trolley was at rest in the position shown in the diagram.

mass of trolley and paving stone = 18.5 kg

length of trolley = 97 cm

force on handle = 50 N

The gardener then pulled the trolley and measured the applied force while the trolley was moving.

The direction of the applied force is 25° to the vertical, as shown by the arrow.

(i) Calculate the magnitude of the applied force.

Assume the magnitude of the vertical component of the force remains at 50 N.(2)

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Magnitude of applied force = ...........................................................

(ii) The gardener continues to walk and pulls the trolley a distance of 15 m in a time of 4.2 s.

Calculate the power developed while pulling the trolley.(3)

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Power = ...........................................................


Q12.

Extinct animals can be studied by using their fossils. 70-million-year-old fossils from the Tyrannosaurus rex and Triceratops dinosaurs show that a Triceratops was sometimes eaten by a Tyrannosaurus rex.

The diagram shows a Tyrannosaurus rex skull.

On the diagram, the position of the main biting muscle is indicated by the line labelled 'muscle force'. The muscle is connected to the jaw at point J. This produces a moment about point P where the jaw is hinged. Teeth marks found in fossilised Triceratops bones show that the force exerted by a tooth at the front of the jaw X could reach 6500 N.

The skull is drawn to a scale of 1 to 10. The force arrows are not drawn to scale.

Take measurements from the diagram to determine the size of the muscle force when the force exerted by the tooth at X is 6500 N.

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Muscle force = ...........................................................


Q13.

Newton's laws relate the changes in motion of an object to the forces acting on the object.

A hot-air balloon is made of an envelope, containing hot air, with a wicker basket suspended from it. The balloon rises upwards because the heated air in the envelope is less dense than the surrounding air.

The total volume of the hot-air balloon is 2880 m3. The total mass of the hot-air balloon, including the envelope, is 3400 kg. The density of the surrounding air is 1.20 kg m−3.

Calculate the initial upward acceleration of the balloon.

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Initial acceleration = ...........................................................


Q14.

A tennis player uses a racket to hit a ball over a net.

The player stands 12 m from the net. He throws the ball vertically upwards and hits the ball at a height of 2.5 m above the ground. The ball leaves the racket horizontally with a velocity of 25 m s−1. The ball has a mass of 0.06 kg.

The ball is in contact with the racket for 0.04 s.

Calculate the average force on the ball.

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Average force = ...........................................................


Q15.

A length of string is threaded through a drinking straw. The string is fixed at one end and held at the other so that it is at 30° to the horizontal. A balloon is inflated and attached to the straw. When the balloon is released, the air escapes from the balloon and the balloon and straw start to move up the string.

Calculate the minimum force on the balloon due to the escaping air if the balloon is to move in this way.

mass of straw and balloon = 11 g

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Minimum force = ...........................................................

Q16.

A website about the physics of baseball states, "The bat hits the ball with a force equivalent to 2 tonnes."

In a baseball game, a ball travelling at 40 ms−1 is in contact with a bat for 0.70 ms and has a speed after impact of 49 ms−1.

1 tonne = 1000 kg mass of ball = 0.15kg

Evaluate the statement from the website.

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Q17.

The photograph shows a praying mantis hanging from a thin twig. Four of the praying mantis's six legs are in contact with the twig. The tension in the legs balances the weight to keep the praying mantis stationary.

(a) The diagrams show a simplified model of the situation. For each leg in contact with the twig, the upper section is horizontal and the lower section is at an angle of 30° to the vertical.

(i) Calculate the tension in the lower section of each leg in contact with the twig assuming that these tensions are all equal.

mass of praying mantis = 5.4 × 10−4 kg(4)

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Tension = ...........................................................

(ii) A student suggests that the tension in each leg in contact with the twig is 25% of the weight of the praying mantis. State why this is not correct.

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(b) The praying mantis moves around the twig so that it is now standing upright and on top of the twig.

State the difference between the stress in the legs when the praying mantis is beneath the twig and when it is on top of the twig.

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Q18.

The diagram shows a diver of weight 680 N on a diving board.

The diving board has a length L of 3.6 m and is fixed at the end labelled X. It is supported at position Y which is 0.9 m from X. The diving board is uniform and has a weight of 390 N.

By taking moments about X, determine the upward force exerted by the support at Y on the diving board.

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Force = ...........................................................


Q19.

A stationary ball is released from a height of 2.0 m onto a hard surface.

The simplified velocity-time graph shows the motion of the ball as it falls and bounces back to its maximum height.

(a) Calculate the maximum height reached by the ball after bouncing.

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Maximum height = ...........................................................

(b) Calculate the decrease in kinetic energy of the ball as it bounces.

mass of ball = 60 g(2)

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Decrease in kinetic energy = ...........................................................

(c) Calculate the resultant force on the ball when it is in contact with the ground.

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Resultant force = ...........................................................

(d) The ball is replaced with one that is softer. It is released from a height of 2.0 m onto the same surface as before. A velocity-time graph is drawn to show the motion of the new ball.

Describe the similarities and differences between the two graphs.(3)

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Q20.

Read the passage and answer the question below.

The Solar Impulse 2 is a solar-powered plane that completed a round the world trip in 2016 without using fossil fuels. The wings are covered in thin solar panels, keeping the total mass of the plane and pilot at 1600 kg. The need to reduce the weight limits the efficiency of the solar panels to 23%. However, in daylight, these panels generate enough energy to run the four 7.5 kW electric motors that keep the plane airborne and to fully charge the batteries that power the plane during the night. The batteries take about 6 hours to fully charge.

In daylight the plane flies at a height of 8500 m to harness the most sunlight, and at night descends to 1500 m. This descent makes use of the gravitational potential energy gained during the day to help the plane get through the night. (Source: www.solarimpulse.com)

The plane flies at the greater height during the day. At night it glides down to the lower height over a period of 4 hours, with the motors switched off.

Calculate the change in gravitational potential energy as the plane glides down.

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Change in gravitational potential energy = ...........................................................


Q21.

A teacher uses a linear air track to provide a frictionless surface for two gliders, each of mass m. She uses this, with a pair of light gates connected to a computer, to investigate a collision between the gliders.

The gliders are each given a small push and travel towards the centre of the track. The gliders collide and move off together.

The teacher asked a student to justify the change in velocity of glider 1 using Newton's laws of motion.

The student began his explanation with the statement:

Complete the explanation to justify the change in velocity of glider 1, making reference to Newton's laws of motion where appropriate.

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Q22.

An exhibit in a science museum requires the observer to use a pump to create air bubbles in a column of liquid. The bubbles then rise through the liquid.

(i) Complete the free-body force diagram for a bubble as it rises through the liquid.

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*(ii) It is observed that larger bubbles reach the top of the column of liquid in less time than smaller bubbles.

By considering the forces acting on a bubble as it rises, explain this observation.(3)

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Q23.

* The photograph shows a probe moving in space.

Whilst moving, empty fuel tanks can be ejected by means of an explosion. This has the effect of increasing the speed of the probe.

Discuss whether conservation of momentum and conservation of energy apply in this situation and why the speed of the probe increases.

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Q24.

A child in a bumper car travelling at velocity of 7.0ms−1 collides with a stationary bumper car directly ahead of him. The diagram shows the bumper cars before the collision.

(a) (i) Assume that the bumper cars move off together after the collision. Calculate the velocity of the bumper cars after the collision.

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Velocity = ...........................................................

(ii) After travelling 1.3m the cars come to rest.Calculate the magnitude of the frictional force between the cars and the floor.

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Frictional force = ...........................................................

(b) State one assumption made in order to carry out the calculation in (a)(i).

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Q25.

A motorist received a speeding penalty notice, from the police, for a short journey along 120 m of road.

(a) The car's specification states that the minimum time for the car to accelerate from 0 to 60 miles per hour is 9.5 seconds.

Show that the maximum value for the average acceleration of the car over 9.5 s is about 3 m s–2.1 mile = 1600 m

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(b) The police recorded a maximum speed for the car of 20 m s–1.

The motorist knows that the speed at the start and at the end of the 120 m journey was zero.Assume that the car had:

· constant positive acceleration, equal to the value in part (a), for the first 60 m of the journey· constant negative acceleration of the same magnitude for the final 60 m of the journey.

Determine whether the motorist should challenge the penalty notice.(3)

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(c) Explain why the assumptions about the acceleration in (b) may not be correct in practice.

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Q26.

The diagram shows a battery-powered clock on a wall. It has a minute hand and an hour hand.

(a) Calculate the average angular velocity of the minute hand.

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Angular velocity = ...........................................................

(b) The diagram shows the position of the minute hand when the time is 1 : 44 and when the time is 1 : 46.

Show that the work done against the force of gravity to move the minute hand from 1 : 44 to 1 : 46 is about 1 mJ.mass of minute hand = 14 glength of minute hand = 8.0 cm

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(c) The clock uses a 1.5 V cell and draws a maximum current of 8.0 μA.

After a time, the maximum power of the cell has reduced to 65% of its initial value making the clock run slowly.Calculate the time taken for the minute hand to move from the 1 : 44 position to the 1 : 46 position.

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Time taken = ...........................................................


Q27.

Cathode ray tubes are used in oscilloscopes.

The diagram shows a simplified cathode ray tube that can be used to determine the magnitude and polarity of a potential difference (p.d.).

The cathode ray tube consists of an electron gun, a pair of deflecting plates and a fluorescent screen.

(a) The electron gun includes a filament. When this filament is heated, electrons are released and are accelerated by a p.d. of 1.5 kV to form an electron beam.

(i) Name the process by which electrons are released from the heated filament.(1)

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(ii) Show that the maximum velocity of the electrons is about 2 × 107 m s−1.(2)

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(b) The electron beam then enters a uniform electric field between the two parallel horizontal deflecting plates. The magnitude and direction of the deflection is determined by the p.d. V that is applied across the plates.

The diagram shows one possible path of the electron beam as it passes between the plates.

(i) Show that the acceleration of an electron, of mass m and charge Q, is given by

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(ii) Calculate the magnitude of the vertical deflection y of the beam as it leaves the plates.V = 50 V d = 0.01 m

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y = ...........................................................

(c) A laboratory oscilloscope with the time base turned off operates in the same way as this simplified cathode ray tube. A student uses an oscilloscope in this way to monitor an alternating p.d. of 53 Vrms

On the grid, draw the trace that would be seen on the screen.(4)

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Q28.

* The following extract comes from a section on forces, on a website written for children.

Criticise this extract.

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Q29.

The photograph shows a type of drink known as stout.

When the drink is poured, it contains many spherical bubbles of gas which rise and form the foamy 'head' at the top of the drink. The manufacturers of the drink state "It takes 120 seconds for the head to form".

For the smallest bubbles, the uniform upward velocity can be calculated using the equation

(i) Derive this equation by considering the forces acting on a bubble.(3)

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(ii) State an assumption you have made.(1)

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(iii) Evaluate the statement from the manufacturers that it takes 120 seconds for the head to form.You should consider the time for a bubble to travel from the bottom of the glass to the top.height of glass = 11.5 cm density of gas = 1.22 kg m−3

density of stout = 1.01 × 103 kg m−3

viscosity of stout = 2.06 × 10−3 Pa s diameter of bubble = 122 μm

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Q30.

Physical quantities can be vectors or scalars.

Describe what is wrong with each of the following statements.

(3)A car has a mass of 10 000 N acting vertically downwards.

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The velocity of light from the Sun is 3 × 108 m s−1.

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The car slowed down with an acceleration of 2.5 m s−2.

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Q31.

The graph shows the variation of the gravitational field strength with distance from the centre of the Earth. R0 is the radius of the Earth.

Describe how gravitational field strength varies with distance from the centre of the Earth

· for distances between 0 and R0

· for distances greater than R0

(3) .............................................................................................................................................

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Q32.


A student wishes to determine the total drag force acting on a bubble.

(i) Explain why it might not be possible to use Stokes' law to calculate the drag force acting on a bubble.

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*(ii) Describe an additional measurement that would need to be taken from the photograph and how it could be used to determine the drag force, assuming that the bubble has reached its terminal velocity.

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Q33.

A gardener used a trolley to move a paving stone.

A force meter was attached to the handle of the trolley.

The gardener recorded the following measurements when the trolley was at rest in the position shown in the diagram.

mass of trolley and paving stone = 18.5 kg

length of trolley = 97 cm

force on handle = 50 N

Determine the distance of the centre of gravity of the loaded trolley from the wheels.

(3) .............................................................................................................................................

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Distance = ...........................................................


Q34.

A physics class made a toy rocket. A drinks bottle was partially filled with water and inverted over a valve. An air pump delivered air to the bottle until the pressure forced the bottle from the valve and the water was ejected from the bottle at high speed.

A velocity-time graph for the bottle for the first 4 s after take-off is shown.

Determine the height to which the rocket travelled.

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Height = ...........................................................


Q35.

The world land speed record of 341 m s–1 was set in October 1997. In an attempt to break this record, a new supersonic car has been developed called the Bloodhound.

The developers of the Bloodhound have used computer modelling to produce a velocity-time graph for the predicted motion of the car, on a straight track, during the record attempt.

A track of length 23 km is available for the record attempt.

Determine whether this track is long enough.

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Q36.

A fairground game requires the player to catapult a ball towards a target to score points.

The ball is required to reach a target a horizontal distance of 50 m away, at the same vertical height, as shown.

During another launch, the catapult exerts a force on the ball of 9.0 N at 40° to the horizontal at the time of release.

Draw a labelled vector diagram to determine the resultant force acting on the ball at the time of release.

(4)weight of ball = 2.0 N

Magnitude of resultant force = ...........................................................

Angle of resultant force to the horizontal = ...........................................................


Q37.

A sports class is studying cycling. They produce a video of a cyclist on a horizontal lawn. The cyclist starts from rest. They produce a sketch graph of the velocity v of the cyclist against time t.

Explain the shape of this graph and include a consideration of force as part of your answer.

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Q38.

A teacher uses a linear air track to provide a frictionless surface for two gliders, each of mass m. She uses this, with a pair of light gates connected to a computer, to investigate a collision between the gliders.

The gliders are each given a small push and travel towards the centre of the track. The gliders collide and move off together.

The computer displays the velocity of the gliders as they pass through the light gates.

Calculate the velocity of the gliders after the collision, using the principle of conservation of linear momentum.

(3)initial velocity of glider 1 = 0.30 m s–1 to the right initial velocity of glider 2 = 0.70 m s–1 to the left

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Magnitude of velocity = ...........................................................

Direction of velocity = ...........................................................


Q39.

In 2015 the Messenger spacecraft crashed into the surface of the planet Mercury after four years in orbit observing the surface of Mercury.

Messenger's orbit was highly elliptical, varying between 200 km and 15 000 km above the surface of Mercury. Messenger completed one full orbit every 12 hours.

mass of Messenger spacecraft = 565 kg mass of planet Mercury = 3.30 × 1023 kg radius of planet Mercury = 2430 km

Calculate the velocity an object would have as it reached the surface of Mercury if it was released from Messenger's maximum orbital height. Assume the object is released from rest and that Mercury has no atmosphere.

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Velocity = ...........................................................


Q40.

The photograph shows a toy that fires rubber bands.

A student investigates the properties of one of the rubber bands and obtains the following graph.

(a) The student wants to determine the mass of one of the rubber bands. He places five rubber bands on a balance and obtains a reading of 2 g. He divides the reading on the balance by five to determine the mass of one rubber band.

Explain how he could improve his result.(3)

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(b) The rubber band is stretched by 17.4 cm when it is placed on the toy.

Show that the work done on the rubber band is about 1 J.(3)

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(c) Calculate the maximum possible value for the initial velocity of the rubber band as it is fired from the toy. Assume the mass of a rubber band is 0.4 g.

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Maximum initial velocity = ...........................................................

(d) The student thinks the calculated value of maximum velocity is too high because the band does not travel as far as expected.

Explain how the student could determine the initial velocity with the use of a video camera and why light gates would not be suitable.

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Q41.

The shot put is an Olympic field event. The distance for the women's world record shot put is in excess of twenty two metres.

The shot is a metal ball, which is thrown from a standing position so that it lands on the ground a horizontal distance R away from the thrower.

A shot is thrown from a height h above the ground with an initial velocity of 14.2 m s–1 at an angle of 37.0° to the horizontal. The time it takes for the shot to reach the ground is 1.98 s.

(a) Show that the vertical component of the initial velocity is about 8.6 m s–1.

(2) .............................................................................................................................................

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(b) Calculate the height h above the ground from which the shot was thrown.

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h = ...........................................................

(c) Calculate the horizontal distance R for this throw.

(3) .............................................................................................................................................

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R = ...........................................................


Q42.

A centrifuge is a machine which rotates.

A particle in a centrifuge moves in a circle of radius r, centre O, with a constant speed v.

The diagram represents two positions of the particle.

Derive the equation for centripetal acceleration by considering the velocity at these two positions.

Your answer should include a vector diagram.

(5)

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Q43.

A small helium balloon is released into the air. The balloon initially accelerates upwards.

The resultant force F on the balloon is given by

F = upthrust − weight − viscous drag

Eventually the balloon reaches a constant upwards speed.

Calculate a value for the viscous drag force acting on the balloon at this speed. The balloon may be considered as a sphere with radius 12 cm.

(4)density of air = 1.2 kg m−3

mass of unfilled balloon = 4.0 g mass of helium in balloon = 1.2 g

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Viscous drag force = ...........................................................


Q44.

* The graph shows the velocity of a skydiver from the moment that she begins her freefall jump, until she lands on the ground.

Explain, in terms of the force acting, the shape of the graph from the point when the parachute opens until point D.

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Q45.

A passenger is standing in a train.

(a) The train accelerates and he falls backwards.

Use Newton's first law of motion to explain why he falls backwards.(3)

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*(b) As the train leaves the station the passenger holds on to a vertical support as the train accelerates. This prevents the passenger falling backwards.

With reference to Newton's laws of motion, explain why holding on to a vertical support prevents the passenger falling backwards.

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Q46.

(a) State what is meant by work done.

(1).............................................................................................................................................

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(b) A car of mass 1.5 × 103 kg is travelling on a country road towards a village at 55 miles per hour. The speed limit in the village is 30 miles per hour.

When the brakes are applied, there is a constant braking force of 3750 N.Calculate the minimum distance before reaching the village that the driver should apply the brakes to avoid exceeding the speed limit.55 miles per hour = 24.6 m s−1

30 miles per hour = 13.4 m s−1

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Minimum distance = ...........................................................


Q47.

A small, gas-filled balloon was dropped from a height. The displacement-time graph for the balloon is shown.

As the displacement of the balloon from its point of release increased, gravitational potential energy was transferred to kinetic energy and thermal energy.

(a) State why the rate of energy transfer was greatest at 1.20 s.

(1).............................................................................................................................................

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(b) By calculating the change in gravitational potential energy of the balloon between 1.05 s and 1.20 s, show that the average rate at which the gravitational potential energy was transferred during this time interval was about 0.2 W.

mass of balloon and air = 0.004 kg(3)

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Q48.

A tennis player uses a racket to hit a ball over a net.

The player stands 12 m from the net. He throws the ball vertically upwards and hits the ball at a height of 2.5 m above the ground. The ball leaves the racket horizontally with a velocity of 25 m s−1. The ball has a mass of 0.06 kg.

The ball must land within 6.1 m of the other side of the net.

Determine whether the ball hits the ground within this distance. Support your answer with a calculation. Ignore the height of the net.

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Q49.

Physical quantities can be vectors or scalars.

A car travels 45 km due north and then 30 km due east.

(i) Calculate the total distance travelled by the car.

(1).............................................................................................................................................

Total distance travelled = ...........................................................

(ii) Calculate the displacement of the car.

(3).............................................................................................................................................

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Magnitude of displacement = ...........................................................

Direction = ...........................................................

Q50.

A teacher is demonstrating the principle of conservation of momentum using a flat glass surface and air

pucks. Lightweight tubing supplies compressed air to the pucks which is forced out from the bottom of the pucks. This means that the pucks move with very little friction across the glass surface.

(a) Explain, using ideas about molecular movement, how the puck is able to hover a small distance above the glass surface.

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*(b) Applying Newton's 2nd and 3rd laws of motion to the collision between two pucks leads to the conclusion that momentum is conserved.

Justify this statement.(6)

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(c) The teacher uses two identical pucks to investigate collisions. In one collision, one puck moves with a velocity of 4.0 m s−1 and collides with a second puck that is stationary. After the collision, the first puck has a velocity v at an angle of 30° to its original direction, and the second puck moves off with a velocity of 2.0 m s−1 at an angle of 60° to the original direction.

(i) Show that the magnitude of the velocity v of the first puck after the collision is about 3.5 m s−1.(3)

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(ii) Use the data to determine if the collision is elastic or inelastic.(3)

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Q51.

A thin wire of negligible mass is used to hang a picture on a wall. The wire is hung over a nail and can be attached to the picture using arrangement 1 or arrangement 2, as shown.

Deduce which wire arrangement should be used to keep the tension in the wire as small as possible.

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Q52.

A beam bridge is a rigid structure that consists of one horizontal beam supported at each end.

The diagram shows a bridge with a uniform beam of mass 8 500 kg.

A small truck is crossing the beam bridge. The position of the truck and the forces of the truck on the bridge are shown, but are not drawn to scale.

(a) (i) State the conditions necessary for the bridge to be in equilibrium.

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(ii) Calculate the vertical forces at each of the bridge supports.(5)

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Force at A = ...........................................................

Force at B = ...........................................................

The Volgograd Bridge is a concrete beam bridge across the River Volga in Russia.

In 2010 the bridge was closed to traffic due to windy conditions leading to resonance of the structure.(i) Explain what is meant by resonance in this context.

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(ii) To suppress the oscillations of the bridge, dampers were installed.Explain how damping resulted in the suppression of the oscillations of the bridge.

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(iii) Each damper contains an enclosure filled with a fluid. When this fluid is subjected to a magnetic field, the viscosity of the fluid greatly increases.

Describe how the behaviour of the fluid would change in a magnetic field and how this would be useful for the operation of the dampers.

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Q53.

The diagram shows a rock climber of mass 55 kg. She is hanging on a rope with one foot in contact with a rock face. She uses this foot to push herself horizontally away from the rock face. The rope is inclined at 20° to the vertical.

(a) Complete the free-body force diagram below to represent the forces acting on the climber.

(3)

(b) (i) Show that the tension in the rope is about 600 N.

(3) .............................................................................................................................................

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(ii) The rope extends by 2.5 cm when used as shown.

Calculate the energy stored within the rope.(2)

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Energy stored = ...........................................................

(iii) State one assumption made in this calculation.(1)

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Q54.

The diagram shows an optical fibre. A small force F is applied to the end of the optical fibre causing it to bend through an angle α.

Explain why the stress parallel to the surface of the fibre increases as the fibre bends.(4)

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Q55.

A 'Gauss gun' can be made from five ball bearings of equal mass and two magnets, as shown.

Pairs of ball bearings are placed to the right of two strong magnets. A single ball bearing is released from the left, as shown. The ball bearing is attracted to, and collides with, the first magnet. This and all subsequent collisions can be assumed to be elastic.

A student set up the apparatus shown to measure the speed of the last ball bearing. The 'Gauss gun' was placed at the end of a bench, so that the ball bearing left the gun and broke two strips of metal foil which formed part of an electric circuit.

As the ball bearing left the gun, it broke the first foil strip at its centre so that the capacitor started to discharge. When the ball bearing broke the second foil strip the capacitor discharge stopped.

(i) Calculate the energy stored in the capacitor when it was fully charged.

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Energy stored = ...........................................................

(ii) The voltmeter reading halved in the time taken for the ball bearing to travel between the two foil strips.

Show that the time taken for the ball bearing to travel between the two foil strips was about 0.1 s.(2)

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(iii) The two foil strips were 0.50 m apart.

Calculate the horizontal velocity of the ball bearing.(2)

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Horizontal velocity = ...........................................................

(iv) The student positioned the second foil strip with its centre 8.0 cm lower than the centre of the first foil strip.

Deduce whether the ball bearing broke the second foil strip at its centre.Assume the ball bearing was travelling horizontally as it broke the first foil strip.

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Q56.

As a baseball bat hits a ball, kinetic energy of the ball is transferred to the bat and a standing wave is set up along the length of the bat.

The diagram shows the standing wave that is set up.

The graph shows how the velocity of the ball after impact varies with the distance of impact from the free end of the bat for two bats made of different materials. Both bats have a length of 0.85m.

A baseball player states, "It is better to use a hollow aluminium bat, hitting the ball at a distance of about a quarter of the length from the free end of the bat."

Evaluate the baseball player's statement.

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Q57.


The following photographs were taken at 0.33 s intervals.

(i) Sketch on the axes below two labelled lines to show how the displacements of the smaller bubble A and the larger bubble B vary with time over the four images.

(2)

(ii) The photographs are at a scale of 1 to 12. By using measurements from the photographs, calculate the speed of bubble B between photographs 2 and 3.

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Speed of bubble B = ...........................................................

Q58.

The International Space Station (ISS) is in a low Earth orbit. Astronauts in ISS have an apparent weight of zero. In order to determine their mass, the astronauts must secure themselves to a platform which is set into oscillation and moves with simple harmonic motion.

State what is meant by simple harmonic motion.

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Q59.

The graph shows the variation of the gravitational field strength with distance from the centre of the Earth. R0 is the radius of the Earth.

A scientist suggests the following:

"If a tunnel were made through the centre of the Earth, an object dropped at one end would accelerate downwards until it reached the centre. It would then decrease in speed until it reached the other end of the tunnel with a speed of zero. The object would then return the other way, undergoing simple harmonic motion."

Using the graph between 0 and R0, determine whether simple harmonic motion would occur.

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Q60.

An aeroplane is flying at a constant height and speed towards an airport.

At one instant, the airport is 600km from the aeroplane, in a direction 60° east of north.

A wind of speed 30 ms−1 acts on the aeroplane in the direction west to east.

The aeroplane must reach its destination in 50 minutes.

Using calculation and a scaled vector diagram, determine the speed and direction of the aeroplane relative to the air.

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Speed = ...........................................................

Direction = ...........................................................


Q61.

The photographs show successive frames of a pellet being fired at a falling droplet of water.

(a) By taking measurements from the photographs, show that the horizontal speed of the pellet is about 300 ms−1.

Assume the photograph is shown actual size.frame rate = 9600 frames per second

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(b) The droplet fell 33cm from rest before colliding with the pellet.

Calculate the time taken for the droplet to fall this distance.(2)

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Time taken = ...........................................................

(c) Before the photographs were taken, the release of the droplet started a timer. After a short delay, the pellet was automatically fired and it took 1.43 × 10−3 s to reach the droplet.

If the pellet is to hit the droplet, the resolution of the timer must be sufficiently small.Explain one factor that affects the size of the resolution required.

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Q62.

A student investigated the physics of football.

(a) She used the equations of motion to model the behaviour of a ball when kicked at different angles to the horizontal. She predicted the height of the ball when it reached the goal, presuming it was kicked from the same place, with the same initial speed, each time. The results are shown in the table below.

(i) State the significance of the negative value of height for an angle of 10°.(1)

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(ii) On the diagram below, sketch and label the predicted path of the ball for angles of 20° and 40°.(2)

(b) (i) During a football match the ball is kicked towards the goal, at an angle of 15° to the horizontal, from a distance of 11 m as shown.

The ball has a diameter of 0.22 m and an initial speed of 26 m s−1.By means of a calculation, determine whether or not the ball will pass into the goal. You may ignore the effects of air resistance.

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(ii) Air resistance would cause an additional force on the ball.Explain the effect this would have on the ball's motion.

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Q63.

The world land speed record of 341 m s–1 was set in October 1997. In an attempt to break this record, a new supersonic car has been developed called the Bloodhound.

The developers of the Bloodhound have used computer modelling to produce a velocity-time graph for the predicted motion of the car, on a straight track, during the record attempt.

* Discuss, with reference to the graph, the factors that would have been used to predict the motion of the car over the 120 s.

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Q64.

A student is carrying out an experiment to determine a value for the acceleration due to gravity g. He drops a ball from various heights, which he measured with a metre rule. The ball has a built in timer which starts when the ball is released and stops when the ball hits the ground.

The student starts by releasing the ball from a height of 1.00 m and measures the time taken for the ball to fall. He repeats this twice.

(a) Use the student's data to calculate a value for g.

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g = ...........................................................

(b) Estimate the percentage uncertainty in your value for g.

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Percentage uncertainty = ...........................................................

(c) The student then measured the time interval for the ball to fall from a 3.00 m height. Explain how this would improve the value obtained for g.

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Q65.

A lift moves upwards from the ground to the tenth floor of a building. The velocity-time graph for the lift is shown.

The power developed by the lift when travelling upwards with different loads is shown in the table.

(i) By considering the forces acting on the lift as it rises, discuss the difference in values for the power developed by the lift.

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(ii) Lifts use a significant proportion of all total energy consumption of a building.When designing the lift systems, engineers compare the predicted daily energy consumption of different lift motors by

· estimating the time for typical lift journey based on the number of floors in the building and the speed of the lift· estimating the number of lift journeys per day· using daily energy consumption = maximum power output of motor × number of journeys × time per journeyDiscuss the advantages and disadvantages of using this method to compare the predicted energy consumption of different lift motors.

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Q66.

A liquid-crystal display uses a series of segments to form letters and numbers on a screen.

The construction of a display segment is shown.

· Unpolarised white light passes through the lower polarising filter and becomes plane polarised.· When there is no potential difference (p.d.) across the liquid crystal, the molecules in the liquid crystal rotate the plane of polarisation by 90°.· Light then passes through the upper polarising filter and appears on the screen.· When a p.d. is applied across the liquid crystal, the molecules no longer rotate the plane of polarisation. The light will not pass through the upper polarising filter and the screen appears dark.

(i) The intensity of the emitted light at the surface of a display segment is 7.8 W m–2.

The segment has an exposed area of 1.8 × 10–3 m2.Calculate the power of the emitted light at the surface of the display segment.

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Power of emitted light = ...........................................................

(ii) A light-emitting diode (LED) is used to provide the unpolarised white light for the liquid-crystal display.

Calculate the efficiency of the liquid-crystal display segment.(3)

current in LED = 20 mA p.d. across LED = 3.6 V

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Efficiency of liquid-crystal display segment = ...........................................................


Q67.

(a) Solar sails are a form of propulsion for spacecraft. The sail is made of a thin sheet of reflective material. When photons of light from the Sun reflect from the material a force is exerted on the sail. The photons reflect with a momentum equal to their initial momentum but in the opposite direction.

(i) Show that a single photon of frequency 1.5 × 1015 Hz has a momentum of about 3 × 10–27 N s.(2)

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(ii) Hence determine the momentum transferred to the solar sail by this photon.(1)

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Momentum transferred = ...........................................................

(b) An alternative method of producing a momentum change is being investigated. Researchers have suggested that 'larger changes in momentum could be produced by directing laser light at graphene oxide'. Electrons are emitted from the graphene oxide surface, resulting in a force being exerted on the graphene oxide in the opposite direction.

A researcher has suggested that one possible mechanism for the emission of the electrons is the photoelectric effect.(i) Show that the maximum velocity for a photoelectron emitted after absorption of a photon of light of frequency 1.5 × 1015 Hz is about 8 × 105 m s–1.

work function of graphene oxide = 6.7 × 10–19 J(3)

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(ii) Hence calculate the momentum of the photoelectron.(2)

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Momentum of photoelectron = ...........................................................

(c) Explain whether the suggestion in (b) that 'larger changes in momentum could be produced by directing laser light at graphene oxide' is true.

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Q68.

The diagram shows a diver of weight 680 N on a diving board.

The free-body force diagram for the diver standing on the board is shown.

The two forces shown do not form a Newton third law pair.

Give two reasons why.

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Q69.

The photograph shows a small plastic container, its lid and some pellets of frozen carbon dioxide, known as dry ice. When at room temperature the dry ice gradually changes state directly from solid to gas.

Dry ice is placed in the container and the lid is put on. The container is turned upside down and placed on the floor. After a few minutes the pressure of the gas causes the container to fly into the air, leaving the lid and some dry ice behind.

A student investigated the motion of the container.

(a) The student obtained measurements of the maximum height reached by the container for a particular initial mass of dry ice. The student determined that the maximum height was 2.5 m.

Calculate the initial speed of the container.(2)

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Initial speed = ...........................................................

(b) The student investigated how the maximum horizontal distance travelled by the container varies with launch angle.

Calculate the maximum horizontal distance the container would travel if launched at an initial speed of 6.5 m s−1 at an angle of 20° to the horizontal.

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Maximum horizontal distance = ...........................................................

(c) The student added dry ice to the container again and placed it on its side on the floor. When the lid was forced off, the container moved forward at a speed of 5.5 m s−1 and the lid moved backwards. The pellets of dry ice remained in their original position.

mass of container = 4.3 g mass of lid = 1.6 g

(i) Calculate the initial speed of the lid.(3)

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Initial speed of lid = ...........................................................

(ii) Explain why the dry ice remained at the original position.(2)

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Q70.

A lift moves upwards from the ground to the tenth floor of a building. The velocity-time graph for the lift is shown.

(i) Calculate the magnitude of the maximum acceleration of the lift.

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Maximum acceleration = ...........................................................

(ii) Sketch the corresponding acceleration-time graph on the axes below.

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Q71.

In a game of tug-of-war two teams of children pull on opposite ends of a rope. The team that pulls the other team over a marker wins the game.

(a) Initially Team A and Team B are stationary.

Add labels to the free-body force diagram for the child at the end of the rope for Team A at this instant.(3)

*(b) Team B wins by pulling Team A over the marker.

By considering the forces on the children and on the rope explain, in terms of Newton's laws, the process by which Team A loses the game.

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Q72.

The photograph shows a person on a ladder which is propped up against a wall at an angle θ to the horizontal.

The ladder and the person form a system. The diagram shows four of the forces acting on the system, friction between the wall and the ladder can be neglected. One of the forces has been labelled.

· = centre of gravity of the system

(a) Complete the diagram by labelling the other three forces acting on the system.

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*(b) Use the principle of moments to explain why the system is stable in the position shown, but will topple over if θ becomes too large.

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Q73.

A thin wire of negligible mass is used to hang a picture on a wall. The wire is hung over a nail and can be attached to the picture using arrangement 1 or arrangement 2, as shown.

It was observed that if the wire was not hung with its midpoint over the nail, as in Diagram 1, the picture moved and then remained in the position shown in Diagram 2.

Use the idea of moments to explain why.

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Q74.

Read the passage and answer the question below.

The Solar Impulse 2 is a solar-powered plane that completed a round the world trip in 2016 without using fossil fuels. The wings are covered in thin solar panels, keeping the total mass of the plane and pilot at 1600 kg. The need to reduce the weight limits the efficiency of the solar panels to 23%. However, in daylight, these panels generate enough energy to run the four 7.5 kW electric motors that keep the plane airborne and to fully charge the batteries that power the plane during the night. The batteries take about 6 hours to fully charge. In daylight the plane flies at a height of 8500 m to harness the most sunlight, and at night descends to 1500 m. This descent makes use of the gravitational potential energy gained during the day to help the plane get through the night. (Source: www.solarimpulse.com)

After four hours the engines are switched on again.

Explain whether the plane should fly at a slower horizontal speed at its lower height.

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