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Worksheet 18 Combine

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AS and A Level Physics Original material © Cambridge University Press 2010 1 18 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet. 1 Convert the following angles into radians. a 30° [1] b 210° [1] c 0.05° [1] 2 Convert the following angles from radians into degrees. a 1.0 rad [1] b 4.0 rad [1] c 0.15 rad [1] 3 The planet Mercury takes 88 days to orbit once round the Sun. Calculate its angular displacement in radians during a time interval of: a 44 days [1] b 1 day. [1] 4 In each case below, state what provides the centripetal force on the object. a A car travels at a high speed round a sharp corner. [1] b A planet orbits the Sun. [1] c An electron orbits the positive nucleus of an atom. [1] d Clothes spin round in the drum of a washing machine. [1] 5 An aeroplane is circling in the sky at a speed of 150 m s 1 . The aeroplane describes a circle of radius 20 km. For a passenger of mass 80 kg inside this aeroplane, calculate: a her angular velocity [2] b her centripetal acceleration [3] c the centripetal force acting on her. [2] 6 The diagram shows a stone tied to the end of a length of string. It is whirled round in a horizontal circle of radius 80 cm. The stone has a mass of 90 g and it completes 10 revolutions in a time of 8.2 s. a Calculate: i the time taken for one revolution [1] ii the distance travelled by the stone during one revolution (this distance is equal to the circumference of the circle) [1] iii the speed of the stone as it travels in the circle [2] iv the centripetal acceleration of the stone [3] v the centripetal force on the stone. [2] b What provides the centripetal force on the stone? [1] c What is the angle between the acceleration of the stone and its velocity? [1]
Transcript

AS and A Level Physics Original material © Cambridge University Press 2010 1

18 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet.

1 Convert the following angles into radians. a 30° [1] b 210° [1] c 0.05° [1]

2 Convert the following angles from radians into degrees. a 1.0 rad [1] b 4.0 rad [1] c 0.15 rad [1]

3 The planet Mercury takes 88 days to orbit once round the Sun. Calculate its angular displacement in radians during a time interval of: a 44 days [1] b 1 day. [1]

4 In each case below, state what provides the centripetal force on the object. a A car travels at a high speed round a sharp corner. [1] b A planet orbits the Sun. [1] c An electron orbits the positive nucleus of an atom. [1] d Clothes spin round in the drum of a washing machine. [1]

5 An aeroplane is circling in the sky at a speed of 150 m s−1. The aeroplane describes a circle of radius 20 km. For a passenger of mass 80 kg inside this aeroplane, calculate: a her angular velocity [2] b her centripetal acceleration [3] c the centripetal force acting on her. [2]

6 The diagram shows a stone tied to the end of a length of string. It is whirled round in a horizontal circle of radius 80 cm.

The stone has a mass of 90 g and it completes 10 revolutions in a time of 8.2 s. a Calculate:

i the time taken for one revolution [1] ii the distance travelled by the stone during one revolution (this distance is equal to the

circumference of the circle) [1] iii the speed of the stone as it travels in the circle [2] iv the centripetal acceleration of the stone [3] v the centripetal force on the stone. [2]

b What provides the centripetal force on the stone? [1] c What is the angle between the acceleration of the stone and its velocity? [1]

18 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

7 A lump of clay of mass 300 g is placed close to the edge of a spinning turntable. The centre of mass of the lump of clay travels in a circle of radius 12 cm.

a The lump of clay takes 1.6 s to complete one revolution.

i Calculate the rotational speed of the clay. [2] ii Calculate the frictional force between the clay and the turntable. [3]

b The maximum magnitude of the frictional force F between the clay and the turntable is 70% of the weight of the clay. The speed of rotation of clay is slowly increased. Determine the speed of the clay when it just starts to slip off the turntable. [4]

8 The diagram shows a skateboarder of mass 70 kg who drops through a vertical height of 5.2 m.

The dip has a radius of curvature of 16 m. a Assuming no energy losses due to air resistance or friction, calculate the speed of the

skateboarder at the bottom of the dip at point B. You may assume that the speed of the skateboarder at point A is zero. [2]

b i Calculate the centripetal acceleration of the skateboarder at point B. [3] ii Calculate the contact force R acting on the skateboarder at point B. [3]

9 A car of mass 820 kg travels at a constant speed of 32 m s−1 along a banked track. The track is banked at an angle of 20° to the horizontal.

a The net vertical force on the car is zero. Use this to show that the contact force R on the car is 8.56 kN. [2]

b Use the answer from a to calculate the radius of the circle described by the car. [4]

18 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 3

10 A stone of mass 120 g is fixed to one end of a light rigid rod.

The stone is whirled at a constant speed of 4.0 m s−1 in a vertical circle of radius 80 cm.

Calculate the ratio: BA

at rodin thetension at rod in thetension [6]

Total: 59

Score: %

AS and A Level Physics Original material © Cambridge University Press 2010 1

19 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet.

1 Define gravitational field strength at a point in space. [1]

2 Show that the gravitational constant G has the unit N m2 kg−2. [2]

3 The gravitational field strength on the surface of the Moon is 1.6 N kg−1. What is the weight of an astronaut of mass 80 kg standing on the surface of the Moon? [2]

4 Calculate the magnitude of the gravitational force between the objects described below. You may assume that the objects are ‘point masses’. a two protons separated by a distance of 5.0 × 10−14 m (mass of a proton = 1.7 × 10−27 kg) [3] b two binary stars, each of mass 5.0 × 1028 kg,

with a separation of 8.0 × 1012 m [2] c two 1500 kg elephants separated by a distance of 5.0 m [2]

5 The diagram shows the Moon and an artificial satellite orbiting round the Earth. The radius of the Earth is R.

a Write an equation for the gravitational field strength g at a distance r from the centre of an isolated object of mass M. [1]

b By what factor would the gravitational field decrease if the distance from the centre of the mass were doubled? [2]

c The satellite orbits at a distance of 5R from the Earth’s centre and the Moon is at a distance of 59R. Calculate the ratio:

Moon ofposition at strength field nalgravitatiosatellite ofposition at strength field nalgravitatio [3]

6 The planet Neptune has a mass of 1.0 × 1026 kg and a radius of 2.2 × 107 m. Calculate the surface gravitational field strength of Neptune. [3]

19 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

7 Calculate the radius of Pluto, given its mass is 5.0 × 1023 kg and its surface gravitational field strength has been estimated to be 4.0 N kg−1. [3]

8 A space probe of mass 1800 kg is travelling from Earth to the planet Mars. The space probe is midway between the planets. Use the data given to calculate: a the gravitational force on the space probe due to the Earth [3] b the gravitational force on the space probe due to Mars [2] c the acceleration of the probe due to the gravitational force acting on it. [3]

Data

separation between Earth and Mars = 7.8 × 1010 m

mass of Earth = 6.0 × 1024 kg mass of Mars = 6.4 × 1023 kg

9 An artificial satellite orbits the Earth at a height of 400 km above its surface. The satellite has a mass 5000 kg, the radius of the Earth is 6400 km and the mass of the Earth is 6.0 × 1024 kg. For this satellite, calculate: a the gravitational force experienced [3] b its centripetal acceleration [2] c its orbital speed. [3]

10 a Explain what is meant by the term gravitational potential at a point. [2] b Write down the gravitational potential energy of a body of mass 1 kg when it is at

an infinite distance from another body. [1] c The radius of the Earth is 6.4 × 106 m and the mass of the Earth = 6.0 × 1024 kg.

Calculate the potential energy of the 1 kg mass at the Earth’s surface. [3] d Write down the minimum energy required to remove the body totally from the Earth’s

gravitational field. [1]

11 The planets in our solar system orbit the Sun in almost circular orbits. a Show that the orbital speed v of a planet at a distance r from the centre of the Sun is

given by:

v = r

GM [4]

b The mean distance between the Sun and the Earth is 1.5 × 1011 m and the mass of the Sun is 2.0 × 1030 kg. Calculate the orbital speed of the Earth as it travels round the Sun. [2]

12 There is a point between the Earth and the Moon where the net gravitational field strength is zero. At this point the Earth’s gravitational field strength is equal in magnitude but opposite in direction to the gravitational field strength of the Moon. Given that:

Moon of massEarth of mass = 81

calculate how far this point is from the centre of the Moon in terms of R, where R is the separation between the centres of the Earth and the Moon. [4]

Total: 57

Score: %

AS and A Level Physics Original material © Cambridge University Press 2010 1

20 Worksheet (A2) 1 For an oscillating mass, define:

a the period [1] b the frequency. [1]

2 The graph of displacement x against time t for an object executing simple harmonic motion (s.h.m.) is shown here.

a State a time at which the object has maximum speed. Explain your answer. [2] b State a time at which the magnitude of the object’s acceleration is a maximum.

Explain your answer. [2]

3 An apple is hung vertically from a length of string to form a simple pendulum. The apple is pulled to one side and then released. It executes 12 oscillations in a time of 13.2 s. a Calculate the period of the oscillations. [2] b Calculate the frequency of the oscillations. [2]

4 This is the graph of displacement x against time t for an oscillating object.

Use the graph to determine the following: a the amplitude of the oscillation [1] b the period [1] c the frequency in hertz (Hz) [2] d the angular frequency in radians per second (rad s−1). [2] e the maximum speed of the oscillating mass. [2]

20 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

5 Two objects A and B have the same period of oscillation. In each case a and b below, determine the phase difference between the motions of the objects A and B. a [2]

b [2]

6 A mass at the end of a spring oscillates with a period of 2.8 s. The maximum displacement of the mass from its equilibrium position is 16 cm. a What is the amplitude of the oscillations? [1] b Calculate the angular frequency of the oscillations. [2] c Determine the maximum acceleration of the mass. [3] d Determine the maximum speed of the mass. [2]

7 A small toy boat is floating on the water’s surface. It is gently pushed down and then released. The toy executes simple harmonic motion. Its displacement–time graph is shown here.

For this oscillating toy boat, calculate: a its angular frequency [2] b its maximum acceleration [3] c its displacement after a time of 6.7 s, assuming that the effect of damping on the boat is

negligible. [3]

20 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 3

8 The diagram shows the displacement–time graph for a particle executing simple harmonic motion.

Sketch the following graphs for the oscillating particle: a velocity–time graph [2] b acceleration–time graph [2] c kinetic energy–time graph [2] d potential energy–time graph. [2]

9 A piston in a car engine executes simple harmonic motion. The acceleration a of the piston is related to its displacement x by the equation:

a = −6.4 × 105x a Calculate the frequency of the motion. [3] b The piston has a mass of 700 g and a maximum displacement of 8.0 cm.

Calculate the maximum force on the piston. [2]

10 The diagram shows a trolley of mass m attached to a spring of force constant k. When the trolley is displaced to one side and then released, the trolley executes simple harmonic motion.

a Show that the acceleration a of the trolley is given by the expression:

a = xmk⎟⎠⎞

⎜⎝⎛−

where x is the displacement of the trolley from its equilibrium position. [3] b Use the expression in a to show that the frequency f of the motion is given by:

f = mk

π21 [2]

c The springs in a car’s suspension act in a similar way to the springs on the trolley. For a car of mass 850 kg, the natural frequency of oscillation is 0.40 s. Determine the force constant k of the car’s suspension. [3]

Total: 59

Score: %

AS and A Level Physics Original material © Cambridge University Press 2010 1

21 Worksheet (A2) Specific heat capacity of water = 4200 J kg−1 K−1 Specific latent heat of fusion of water = 3.4 × 105 J kg−1

1 Describe the arrangement of atoms, the forces between the atoms and the motion of the atoms in: a a solid [3] b a liquid [3] c a gas. [3]

2 A small amount of gas is trapped inside a container. Describe the motion of the gas atoms as the temperature of the gas within the container is increased. [3]

3 a Define the internal energy of a substance. [1] b The temperature of an aluminium block increases when it is placed in the flame of a

Bunsen burner. Explain why this causes an increase in its internal energy. [3]

c A lump of metal is melting in a hot oven at a temperature of 600 °C. Explain whether its internal energy is increasing or decreasing as it melts. [4]

4 Write a word equation for the change in the thermal energy of a substance in terms of its mass, the specific heat capacity of the substance and its change of temperature. [1]

5 The specific heat capacity of a substance is measured in the units J kg−1 K−1, whereas its specific latent heat of fusion is measured in J kg−1. Explain why the units are different. [2]

6 During a hot summer’s day, the temperature of 6.0 × 105 kg of water in a swimming pool increases from 21 °C to 24 °C. Calculate the change in the internal energy of the water. [3]

7 A 300 g block of iron cools from 300 °C to room temperature at 20 °C. The specific heat capacity of iron is 490 J kg−1 K−1. Calculate the heat released by the block of iron. [3]

8 Calculate the energy that must be removed from 200 g of water at 0 °C to convert it all into ice at 0 °C. [2]

21 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

9 a Change the following temperatures from degrees Celsius into kelvin. i 0 °C ii 80 °C iii −120 °C [3]

b Change the following temperatures from kelvin into degrees Celsius. i 400 K ii 272 K iii 3 K [3]

10 An electrical heater is used to heat 100 g of water in a well-insulated container at a steady rate. The temperature of the water increases by 15 °C when the heater is operated for a period of 5.0 minutes. Determine the change of temperature of the water when the same heater and container are individually used to heat: a 300 g of water for the same period of time [3] b 100 g of water for a time of 2.5 minutes. [3]

11 The graph below shows the variation of the temperature of 200 g of lead as it is heated at a steady rate.

a Use the graph to state the melting point of lead. [1] b Explain why the graph is a straight line at the start. [1] c Explain what happens to the energy supplied to the lead as it melts at a constant

temperature. [1] d The initial temperature of the lead is 0 °C. Use the graph to determine the total

energy supplied to the lead before it starts to melt. [3] (The specific heat capacity of lead is 130 J kg−1 K−1.) e Use your answer to d to determine the rate of heating of the lead. [2] f Assuming that energy continues to be supplied at the same rate, calculate the

specific latent heat of fusion of lead. [3]

21 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 3

12 The diagram shows piped water being heated by an electrical heater.

The water flows through the heater at a rate of 0.015 kg s−1. The heater warms the water from 15 °C to 42 °C. Assuming that all the energy from the heater is transferred to heating the water, calculate the power of the heater. [5]

13 A gas is held in a cylinder by a friction-free piston. When the force holding the piston in place is removed, the gas expands and pushes the piston outwards. Explain why the temperature of the gas falls. [2]

14 Hot water of mass 300 g and at a temperature of 90 °C is added to 200 g of cold water at 10 °C. What is the final temperature of the mixture? You may assume there are no losses to the environment and all heat transfer takes place between the hot water and the cold water. [5]

15 A metal cube of mass 75 g is heated in a naked flame until it is red hot. The metal block is quickly transferred to 200 g of cold water. The water is well stirred. The graph shows the variation of the temperature of the water recorded by a datalogger during the experiment.

The metal has a specific heat capacity of 500 J kg−1 K−1. Use the additional information provided in the graph to determine the initial temperature of the metal cube. You may assume there are no losses to the environment and all heat transfer takes place between the metal block and the water. [5]

Total: 71

Score: %

AS and A Level Physics Original material © Cambridge University Press 2010 1

22 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet.

1 Determine the number of atoms or molecules in each of the following. a 1.0 mole of carbon [1] b 3.6 moles of water [1] c 0.26 moles of helium [1]

2 The molar mass of helium is 4.0 g. Determine the mass of a single atom of helium in kilograms. [2]

3 The molar mass of uranium is 238 g. a Calculate the mass of one atom of uranium. [2] b A small rock contains 0.12 g of uranium. For this rock, calculate the number of:

i moles of uranium [2] ii atoms of uranium. [1]

4 Explain what is meant by the absolute zero of temperature. [3]

5 a Write the ideal gas equation in words. [1] b One mole of an ideal gas is trapped inside a rigid container of volume 0.020 m3.

Calculate the pressure exerted by the gas when the temperature within the container is 293 K. [3]

6 A fixed amount of an ideal gas is trapped in a container of volume V. The pressure exerted by the gas is P and its absolute temperature is T. a Using a sketch of PV against T, explain how you can determine the number of moles

of gas within the container. [4] b Sketch a graph of PV against P when the gas is kept at a constant temperature.

Explain the shape of the graph. [3]

7 A rigid cylinder of volume 0.030 m3 holds 4.0 g of air. The molar mass of air is about 29 g. a Calculate the pressure exerted by the air when its temperature is 34 °C. [4] b What is the temperature of the gas in degrees Celsius when the pressure is twice

your value from part a? [4]

22 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

8 The diagram shows two insulated containers holding gas. The containers are connected together by tubes of negligible volume.

The internal volume of each container is 2.0 × 10−2 m3. The temperature within each container is −13 °C. The gas in container A exerts a pressure of 180 kPa and the gas in container B exerts a pressure of 300 kPa. a Show that the amount of gas within the two containers is about 4.4 moles. [3] b The valve connecting the containers is slowly opened and the gases are allowed to mix.

The temperature within the containers remains the same. Calculate the new pressure exerted by the gas within the containers. [3]

9 The diagram shows a cylinder containing air at a temperature of 5.0 °C. The piston has a cross-sectional area 1.6 × 10−3 m2

It is held stationary by applying a force of 400 N applied normally to the piston. The volume occupied by the compressed air is 2.4 × 10−4 m3. The molar mass of air is about 29 g. a Calculate the pressure exerted by the compressed air. [2] b Determine the number of moles of air inside the cylinder. [3] c Use your answer to b to determine:

i the mass of air inside the cylinder [1] ii the density of the air inside the cylinder. [2]

10 The mean speed of a helium atom at a temperature of 0 °C is 1.3 km s–1. Estimate the mean speed of helium atoms on the surface of a star where the temperature is 10 000 K. [6]

11 The surface temperature of the Sun is about 5400 K. On its surface, particles behave like the atoms of an ideal gas. The atmosphere of the Sun mainly consists of hydrogen nuclei. These nuclei move in random motion. a Explain what is meant by random motion. [1] b i Calculate the mean translational kinetic energy of a hydrogen nucleus

on the surface of the Sun. [2] ii Estimate the mean speed of such a hydrogen nucleus.

(The mass of hydrogen nucleus is 1.7 × 10−27 kg.) [3]

12 a Calculate the mean translational kinetic energy of gas atoms at 0 °C. [2] b Estimate the mean speed of carbon dioxide molecules at 0 °C.

(The molar mass of carbon dioxide is 44 g.) [5] c Calculate the change in the internal energy of one mole of carbon dioxide gas when its

temperature changes from 0 °C to 100 °C. [3]

22 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 3

13 The diagram below shows three different types of arrangements of gas particles.

A gas whose particles consist of single atoms is referred to as monatomic – for example helium (He). A gas with two atoms to a molecule is called diatomic – for example oxygen (O2). A gas with more than two atoms to a molecule is said to be polyatomic – for example water vapour (H2O).

A single atom can travel independently in the x, y and z directions: it is said to have three degrees of freedom. From the equation for the mean translational kinetic energy of the atom,

we can generalise that a gas particle has mean energy of kT21 per degree of freedom.

Molecules can also have additional degrees of freedom due to their rotational energy. a Use the diagram above to explain why:

i the mean energy of a diatomic molecule is kT25 [2]

ii the mean energy of a polyatomic molecule is 3kT. [2] b Calculate the internal energy of one mole of water vapour (steam) per unit kelvin. [3]

Total: 75

Score: %

AS and A Level Physics Original material © Cambridge University Press 2010 1

23 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet.

1 a Explain what is meant by the electric field strength at a point. [1] b Explain what is meant by the electric potential at a point. [1]

2 A pair of parallel metal plates has a potential difference of 5000 V across them. The electric field strength between them is 400 kN C−1. Calculate: a the separation between the plates [2] b the force on a dust particle between the plates which carries a charge of 1.6 × 10−19 C. [2]

3 The electric field strength E at a distance r from a point charge Q may be written as:

E = k 2rQ

What is the value for k? [1]

4 The diagram shows a point charge +q placed in the electric field of a charge +Q.

The force experienced by the charge +q at point A is F. Calculate the magnitude of the force experienced by this charge when it is placed at points B, C, D and E. In each case, explain your answer. [9]

5 A spherical metal dome of radius 15 cm is electrically charged. It has a positive charge of +2.5 µC distributed uniformly on its surface. a Calculate the electric field strength on the surface of the dome. [3] b Explain how your answer to a would change at a distance of 30 cm from the surface of

the dome. [2]

23 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

6 The diagram shows two point charges. The point X is midway between the charges.

a Calculate the electric field strength at point X due to:

i the +20 µC charge [3] ii the +40 µC charge. [2]

b Calculate the resultant electric field strength at point X. [2]

7 The dome of a van de Graaff generator has a diameter of 30 cm and is at a potential of +20 000 V. Calculate: a the charge on the dome [2] b the electric field strength at the surface of the dome [2] c the force on a proton near the surface of the dome. [1]

8 a An isolated charged sphere of diameter 10 cm carries a charge of −2000 nC. Calculate the potential at its surface. [3]

b Calculate the work that must be done to bring an electron from infinity to the surface of the dome. [2]

9 Describe some of the similarities and differences between the electrical force due to a point charge and the gravitational force due to a point mass. [6]

10 The diagram shows two point charges. Calculate the distance x of point P from charge +Q where the net electric field strength is zero. [6]

11 Show that the ratio:

protons obetween tw force nalgravitatioprotons obetween tw force electrical

is about 1036 and is independent of the actual separation between the protons. [6]

12 A helium nucleus consists of two protons and two neutrons. Its diameter is about 10−15 m. a Calculate the force of electrostatic repulsion between two protons at this separation. [2] b Calculate the potential at a distance of 10–15 m from the centre of a proton. [2] c How much work would need to be done to bring two protons this close to each other? [2] d If one proton were stationary, at what speed would the second proton need to be fired

at it to get this close? (Ignore any relativistic effects.) [3]

Total: 66

Score: %

AS and A Level Physics Original material © Cambridge University Press 2010 1

24 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet.

1 A 30 µF capacitor is connected to a 9.0 V battery. a Calculate the charge on the capacitor. [2] b How many excess electrons are there on the negative plate of the capacitor? [2]

2 The p.d. across a capacitor is 3.0 V and the charge on the capacitor is 150 nC. a Determine the charge on the capacitor when the p.d. is:

i 6.0 V [2] ii 9.0 V. [2]

b Calculate the capacitance of the capacitor. [2]

3 A 1000 µF capacitor is charged to a potential difference of 9.0 V. a Calculate the energy stored by the capacitor. [2] b Determine the energy stored by the capacitor when the p.d. across it is doubled. [2]

4 For each circuit below, determine the total capacitance of the circuit. [13]

5 The diagram shows an electrical circuit.

a Calculate the total capacitance of the two capacitors in parallel. [2] b What is the potential difference across each capacitor? [1] c Calculate the total charge stored by the circuit. [2] d Calculate the total energy stored by the capacitors. [2]

24 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

6 A 10 000 µF capacitor is charged to its maximum operating voltage of 32 V. The charged capacitor is discharged through a filament lamp. The flash of light from the lamp lasts for 300 ms. a Calculate the energy stored by the capacitor. [2] b Determine the average power dissipated in the filament lamp. [2]

7 The diagram shows a 1000 µF capacitor charged to a p.d. of 12 V. a Calculate the charge on the 1000 µF capacitor. [2]

b The 1000 µF capacitor is connected across an uncharged 500 µF capacitor by closing the switch S. The charge initially stored by the 1000 µF capacitor is now shared with the 500 µF capacitor. i Calculate the total capacitance of the capacitors in parallel. [2] ii Show that the p.d. across each capacitor is 8.0 V. [2]

8 The diagram shows a circuit used to measure the capacitance of a capacitor.

The reed switch vibrates between the two contacts with a frequency of 50 Hz. On each oscillation the capacitor is fully charged and totally discharged. The current through the milliammeter is 225 mA. a Calculate the charge that flows off the capacitor each time it is discharged. [1] b Calculate the capacitance of the capacitor. [2] c Calculate the current through the milliammeter when a second identical capacitor

is connected: i in parallel with the original capacitor [1] ii in series with the original capacitor. [1]

reed switch mA 9.0 V

24 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 3

9 A capacitor of capacitance 200 µF is connected across a 200 V supply. a Calculate the charge stored on the plates. [1] b Calculate the energy stored on the capacitor. [1] The capacitor is now disconnected from the power supply and is connected across a 100 µF capacitor. c Calculate the potential difference across the capacitors. [3] d Calculate the total energy stored on the capacitors. [2] e Suggest where the energy has been lost. [1]

10 The diagram below shows a charged capacitor of capacitance C. When the switch S is closed, this capacitor is connected across the uncharged capacitor of capacitance 2C. Calculate the percentage of energy lost as heat in the resistor and explain why the actual resistance of the resistor is irrelevant. [7]

Total: 64

Score: %

AS and A Level Physics Original material © Cambridge University Press 2010 1

25 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet.

1 The diagram shows the magnetic field pattern for a current-carrying straight wire drawn by a student in her notes. List two errors made by the student. [2]

2 A current-carrying conductor is placed in an external magnetic field. In each case below, use Fleming’s left-hand rule to predict the direction of the force on the conductor.

a b c

[3]

3 The unit of magnetic flux density is the tesla. Show that: 1 T = 1 N A−1 m−1 [2]

4 Calculate the force per centimetre length of a straight wire placed at right angles to a uniform magnetic field of magnetic flux density 0.12 T and carrying a current of 3.5 A. [3]

5 A 4.0 cm long conductor carrying a current of 3.0 A is placed in a uniform magnetic field of flux density 50 mT. In each of a, b and c below, determine the size of the force acting on the conductor. [6]

a b c

current into paper

25 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 2

6 The diagram shows the rectangular loop PQRS of a simple electric motor placed in a uniform magnetic field of flux density B.

The current in the loop is I. The lengths PQ and RS are both L and lengths QR and SP are both x. Show that the torque of the couple acting on the loop for a given current and magnetic flux density is directly proportional to the area of the loop. [5]

7 The diagram shows a rigid wire AB pivoted at the point A so that it is free to move in a vertical plane. The lower end of the wire dips into mercury. A uniform magnetic field of 6.0 × 10−3 T acts into the paper throughout the diagram. a When the current is switched on, the wire

continuously moves up out of the mercury and then falls back again. Explain this motion. [4]

b The force on the wire due to the current may be taken to act at the midpoint of the wire. When the current is first switched on, the moment of this force about A is 3.5 × 10−5 N m.

Calculate: i the force acting on the wire [2] ii the current in the wire. [2]

8 The coil in the d.c. motor shown in question 6 has a length L = 7.0 × 10−2 m and width x = 3.0 × 10−2 m. There are 25 turns on the coil and it is placed in a uniform magnetic field of 0.19 T. The coil carries a current of 2.8 A. The coil is free to rotate about an axis midway between PQ and RS. a Calculate the force on the longest side of the coil. [2] b Calculate the maximum torque (moment) exerted on the coil. [2] c Explain why the force acting on the long side of the coil does not change as the coil rotates

but the torque exerted on the coil varies. [2]

axis

25 Worksheet (A2)

AS and A Level Physics Original material © Cambridge University Press 2010 3

9 The diagram shows an arrangement that is used to determine the magnetic flux density between the poles of a magnet.

The magnet is placed on a sensitive top pan balance. A current-carrying wire is placed at right angles to the magnetic field between the poles of the magnet. The force experienced by the current-carrying wire is equal but opposite to the force experienced by the magnet. The magnet is pushed downward when the wire experiences an upward force.

The length of the wire in the magnetic field is 5.0 cm. The balance reading is 102.00 g when there is no current in the wire. The balance reading increases to 103.14 g when the current in the wire is 8.2 A. a Show that the force experienced by the wire is equal to 1.1 × 10−2 N. [1] b Calculate the magnetic flux density of the magnetic field between the poles of the magnet. [3]

Total: 39

Score: %


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