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Tutorial 1
Work
In this section you can use the equation:
work done = force x distance
also written as
Ew = Fd
Ew
F
d
where
1.
= work done in joules (J)
= force in newtons (N)
= distance in metres (m).
Find the missing values in the following table.
Force (N)
Distance (m)
(a)
150
25
(b)
6·5 x 103
320
Work Done (J)
(c)
52
6 500
(d)
72·7 x 10-3
2
(e)
2
542
(f)
90
1·45 x 106
2.
A gardener pushes a wheelbarrow with a force of 250 N over a distance of 20 m.
Calculate how much work he does.
3.
Fiona pushes a pram with a force of 150 N. If she does 30 000 J of work calculate
how far she pushes the pram.
4.
Joseph pulls his sledge to the top of a hill. He does 1 500 joules of work and pulls
the sledge a distance of 50 metres. With what force does he pull the sledge?
5.
A horse pulls a cart 3 km along a road. The horse does 400 kJ of work. What force
does the horse exert on the cart?
6.
A car tows a caravan with a constant force of 2·5 kN over part of its journey. If the
car does 8·5 x 106 J of work calculate how far it pulls the caravan.
7.
During a race a motorcycle engine produced a steady forward force of 130 N.
Calculate the work done by the engine if the motorcycle covered a distance of
50 km.
8.
A motor boat tows a yacht out of a harbour. If the motor boat exerted a force of
110 kN and did 200 MJ of work calculate how far it towed the yacht.
9.
A locomotive exerts a force of 15 kN on a train of carriages. The locomotive pulls
the train over a distance of 5 x 103 m. Calculate the work done by the locomotive.
10. On an expedition to the North Pole, Husky dogs were used to pull the sledges
carrying supplies for the journey. One team of dogs did 650 MJ of work during the
1 500 km journey.
(a)
Calculate the average force that the team of dogs exerted on the sledge.
(b)
There are 8 dogs in a team. Calculate the average force exerted by each
dog during the journey.
11. How far can a milk float travel if the electric engine can produce a steady force of
2 kN and can do 9 500 kJ of work before the battery needs recharged?
12. Peter and John work at a supermarket. They are responsible for collecting trolleys
from the trolley parks in the car park and returning them to the store.
(a)
Peter pulls trolleys 150 m back to the store and collects 10 trolleys at a
time. If Peter pulls the 10 trolleys together with an average force of 350
N calculate how much work he does in one journey.
(b)
John does not have so far to walk so he collects 20 trolleys at a time. He
pulls his trolleys with an average force of 525 N and covers 100 m each
journey. Calculate how much work he does in one trip.
(c)
Each boy has to return 80 trolleys to the store before finishing their
shift.
(i)
Calculate how many journeys each boy has to make.
(ii)
Show by calculation who does the most work.
Helpful Hint
Special case
When work is done lifting an object the force required is equal to the weight of the
object .
13. A painter is painting the ceiling of a room. She fills her tray with paint and lifts it
up the ladder. The weight of the full paint tray is 30 newtons and she lifts it a
distance of 2 metres up the ladder. Calculate the amount of work she does.
14. Marco climbs a rope in the school gym during his P.E. lesson. He weighs 600 N
and climbs 8 m up the rope. Calculate how much work he does.
15. A chair lift carries two skiers and their equipment to the top of a ski run which is
at a height of 300 m. The chair lift weighs 500 N and the skiers with their
equipment weigh 1 800 N. Calculate the work done by the chair lift motor in
lifting the skiers to the top of the ski run.
16. A crane lifts a concrete block through a height of 40 m. The crane does 650 kJ of
work.
Calculate:
(a)
the weight of the concrete block
(b)
the mass of the concrete block.
17. A librarian is placing books on to the fiction shelf which is 2 metres from the
ground. He does 80 joules of work lifting the books from the floor to the shelf.
(a)
Calculate the weight of the books.
(b)
What is the mass of the books?
(c)
If each book has an average mass of 400 g calculate how many books
the librarian places on the shelf.
18.
A search and rescue helicopter is called to a ship in the North Sea to airlift an
injured sailor to hospital. The helicopter lifts the sailor 150 m at a constant
speed of 4 m/s . The sailor has a mass of 75 kg. Calculate:
(a)
the weight of the sailor
(b)
the work done by the helicopter during this lifting operation.
19. Brian is learning to rock climb. After two weeks of practice he can climb 10 m up
the practice wall without help. Brian has a mass of 82 kg.
(a)
Calculate Brian’s weight.
(b)
Calculate the amount of work Brian does climbing the wall.
20. In a supermarket shop assistants are asked to stack the shelves with tins of beans.
Each tin of beans has a mass of 450 g. Jane lifts 150 cans of beans from the box on
the floor to the middle shelf. The shelf is 140 cm from the floor.
(a)
Calculate the weight of 150 cans of beans.
(b)
Calculate how much work Jane does.
(c)
Martin has been asked to stack the top shelf. The top shelf is 200 cm
from the floor. He lifts 150 cans of beans from the box on the floor onto
the shelf.
Calculate how much more work he does than Jane.
Tutorial 2
Power, Energy and Time
In this section you can use the equation:
power = energy
time
also written as
P=E
t
P = power in watts (W)
E = energy in joules (J)
t = time in seconds (s).
where
1.
Find the missing values in the following table.
Power (W)
Energy (J)
Time (s)
(a)
1 500
30
(b)
180 000
36 000
(c)
100
600
(d)
1 200
2
(e)
3 000
120 000
(f)
2·5
25
2.
How long will it take for a 60 W bulb to use 720 J of electrical energy?
3.
A bulb uses 45 000 J of energy in 300 seconds.
What is its power rating?
4.
A 50 W immersion heater is switched on for 80 seconds. How much electrical
energy passes through it in this time?
5.
Calculate the power rating of an electric sewing
machine which uses 4 560 J of energy in 8 minutes.
6.
A 1 200 W hairdryer is switched on for 20 minutes. How much electrical energy
does it use?
7.
For how many minutes must a 600 W shaver be switched on in order to use 540
000 J of electrical energy?
8.
An electric fire uses 5·22 MJ of electrical energy in half an hour. Calculate the
power rating of the fire.(1 MJ = 1 x 10 6 J = 1 000 000 J )
9.
How long will it take a 1·4 kW paint stripper to use 1·68 MJ of electrical energy?
10.
A microwave oven is on for twenty minutes
each day. If it uses 7·98 MJ of electrical energy
in one week, what is its power rating?
This formula can also be used for mechanical power.
11. A firework rocket gains 135 joules of energy in 4 seconds. Calculate the power of
the rocket motor.
12.
How long would it take a 500 W engine to do 6 500 J of work?
13. If a toy motor boat gains 350 J of energy in 30 seconds calculate the power of its
electric motor.
14. How long would it take for a 40 W model railway engine to convert 2 800 J of
energy?
Tutorial 3
Potential Energy
In this section you can use the equation:
potential energy = mass x gravitational field strength x height
also written as
Ep = mgh
where
Ep
m
g
h
1.
2.
=
=
=
=
potential energy in Joules (J)
mass in kilograms (kg)
gravitational field strength in newtons per kilogram (N/kg)
height in metres (m).
Find the missing values in the following table.
Mass (kg)
Gravitational Field
Strength (N/kg)
Height (m)
Potential Energy (J)
(a)
25
10
15
(b)
30
10
45
(c)
35
10
450
(d)
2
10
70
(e)
10
5
120
(f)
10
57
6000
Calculate the gravitational potential energy gained when:
(a)a crate of mass 20 kg is lifted up 12 m
(b)an injured climber of mass 75 kg is raised through a height of 200 m
(c) a pile of bricks of mass 15 kg is hoisted up 25 m.
3.
Calculate the mass of a loaded crate which:
(a)gains 200 J of gravitational potential energy when lifted up 15 m
(b)loses 2 000 J of gravitational potential energy when dropped 26 m
(c) loses 1 500 J of gravitational potential energy when dropped 8 m.
4.
Calculate the height reached by a 60 kg window cleaner on:
(a)level 1, if he gains 600 J of gravitational potential energy climbing up
(b)level 2, if he gains 1 200 J of gravitational potential energy climbing up
(c) level 3, if he gains 1 800 J of gravitational potential energy climbing up
(d)level 4, if he gains 2 400 J of gravitational potential energy climbing up.
5.
A pot holer of weight 70 kg climbs 60 m. How much potential energy does he
gain?
6.
A car containing 4 passengers has a total mass of 1 200 kg. How much potential
energy does it lose if it accelerates down a 40 m high slope?
7. Calculate the mass of a skier if he loses 78 000 J of
potential energy when skiing down a slope of 120 m.
8.
Calculate the potential energy gained by a ping pong ball lifted to a height of 2m if
it has a mass of 30 g.
9.
Water in the reservoir of a hydroelectric power station ‘holds’ 120 MJ of potential
energy. The mass of water is 120 tonnes (1 tonne = 1 000 kg). Calculate the height
of the stored water.
10. A mountain rescuer is trying to rescue a group of climbers stranded on a ledge 250
m above ground level. The only way to reach the climbers is to climb down to
them from another ledge 440 m above ground level. If the mountain rescuer has a
mass of 85 kg calculate:
(a)the potential energy gained initially by climbing to the higher ledge
(b)the amount of potential energy he loses as he climbs to the lower ledge.
Helpful Hint
If a question gives you the weight of an object and asks you to calculate the potential
energy, you can use
Ep = (mg) x height
Ep = weight x height ( Since weight = mg)
11. Calculate the potential energy lost by a person of weight 500 N who jumps from a
wall 2 m high.
12. Calculate the potential energy lost by a lift which descends through 50 metres. The
total weight of lift plus passengers is 10 800 N.
13. During a sponsored ‘stretcher lift’ to raise money for charity a group of students
lift a stretcher plus patient 120 metres up a hill. If the total weight of the patient
and the stretcher is 1 000 N, calculate the amount of potential energy they gain.
14. Calculate the maximum height of a fun ride in which the passengers lose 8 500 J
of energy as their carriage drops through the maximum height. The passengers and
the carriage have a combined weight of 400 N
15. Calculate the weight of a pile of bricks if they gain 2 000 J of energy as they are
lifted up 20 metres.
Tutorial 4
1. During the Tour de France cycle race one of the competitors
maintains a steady speed of 14 m/s over a 5 km stretch of the
route. The cyclist produces a steady power of 2 kW over this part
of the race course which he covers in 6 minutes.
(a)
Calculate how much work the cyclist does during these 6 minutes.
(b)
Calculate the average forward force that the cyclist provides over the 5 km.
2.
At a horse show there are many different
competitions such as show jumping and dressage.
Often there are horse and carriage races.
During such a race one horse pulled its carriage with an average force of 130 N over
the 1 km race course.
(a)
Calculate the work done by the horse during the race.
(b)
The horse took 3 minutes to complete the course. Calculate the power of this
animal.
3.
A helicopter rises vertically from the ground to a height of 400 m in 2 minutes.
The helicopter engine has a power of 155 kW.
(a)
Calculate the work done by the helicopter engine and therefore the potential
energy gained by the helicopter in these 2 minutes.
(b)
Calculate the mass of the helicopter
Tutorial 5
Kinetic Energy
In this section you can use the equation:
kinetic energy =
1
2
x mass x velocity2
also written as
Ek
m
v
where
1.
Ek = 1 mv2
2
= kinetic energy in joules (J)
= mass in kilograms (kg)
= speed in metres per second (m/s).
Find the missing values in the following table.
Mass (kg)
Velocity (m/s)
(a)
2·0
3·0
(b)
0·5
15·0
(c)
4·5
4·0
(d)
4·0
5·0
(e)
0·24
10·0
(f)
20·0
200·0
Kinetic energy (J)
2.
Calculate the kinetic energy of a car travelling at 15 m/s if the car has a mass of
1 200 kg.
3.
A ball, which has a mass of 0·5 kg, rolls down a hill. What is its kinetic energy at
the foot of the hill if its speed is 3 m/s?
4.
A mass of 2 kg falls from a table and has a speed of 4·4 m/s just before it hits the
ground. How much kinetic energy does it have at this point?
5.
A bus, travelling at a constant speed of 10 m/s, accelerated to a new speed of 24
m/s. If the bus had a mass of 5 000 kg, calculate :
(a)
the kinetic energy of the bus before it accelerated
(b)
the kinetic energy of the bus at its new speed
6.
A long distance runner has a mass of 70 kg. If he crosses the finishing line with a
speed of 5·4 m/s, how much kinetic energy does he have at the finishing line?
7.
The mass of an electron is 9·11 x 10-31 kg. What is the kinetic energy of an electron
which is travelling with a speed of 2 x 10 7 m/s?
8.
9.
A 50 000 kg train is travelling at 72 km/h.
(a)
What is its speed in m/s?
(b)
How much kinetic energy does the train have?
A tortoise is moving along the ground with a speed of 5 cm/s. If its mass is 3 kg,
how much kinetic energy does it have?
5 cm/s
10. The graph below shows how the speed of a space capsule decreased as the capsule
re-entered the Earth’s atmosphere.
If the space capsule had a mass of 4 500 kg, how much kinetic energy did it lose as it
re-entered the Earth’s atmosphere?
11.What is the speed of a ball which has 114 J of kinetic energy and a mass of 2·28
kg?
12.Find the mass of an apple given that the apple is rolling
along a table at 0·8 m/s and has 0·04 J of kinetic energy.
13. Calculate the speed of a taxi which has a mass of 1500 kg and 363 kJ of kinetic
energy.
14.
A space capsule travelling at 5 km/s has 6 x 1010J
of kinetic energy.
(a)
What is the speed of the capsule in m/s?
(b)
What is the mass of the capsule?
15. A motor cycle and a 5 000 kg bus have equal amounts of kinetic energy . The
motor cycle is travelling at 35 m/s and has a mass, including rider, of 370 kg.
(a)
How much kinetic energy does the motorcycle have?
(b)
Calculate the speed of the bus.
16. A trolley rolls down a ramp which is 80 cm long. It passes through a light gate
near the bottom of the ramp and the timer records a time of 0·19 s for the trolley to
cut the light beam.
The mass of the trolley is 800 g and it has a length of 10 cm.
(a)
What is the speed of the trolley as it passes through the light gate?
(b)
How much kinetic energy does it have as it passes through the light
gate?
17. A hospital lift has a mass of 800 kg when empty. On one occasion the lift, carrying
passengers, rises with a speed of 1·5 m/s and has 1 215 J of kinetic energy.
How many people were in the lift on this occasion? (Assume that each person has
a mass of 70 kg)
18. A minibus of mass 2 800 kg was travelling with a speed of 10 m/s. It then
accelerated at a rate of 0·8 m/s2 for 10 seconds.
(a)
What was the kinetic energy of the minibus while it was travelling at 10
m/s?
(b)
What was the speed of the minibus after 10 seconds of acceleration?
(c)
How much kinetic energy did the minibus gain during the acceleration
period?
19. A helicopter has a mass of 8 000 kg and rises from the ground with a speed of 5
m/s. In a later flight the helicopter carries an extra load of 800 kg. Find the new
speed of the rising helicopter, assuming that it maintains the kinetic energy it had
when it had no cargo.
20. A tennis ball has a mass of 50 g. During a game a player lobs the ball over the net
giving it a speed of 10 m/s as it leaves the racket. If the ball loses 0·475 J of
kinetic energy during its flight what is its speed on reaching the other player?
Tutorial 6
Efficiency
In this section you can use the following two equations:
efficiency =
useful energy out
useful energy in
efficiency =
useful power out
useful power in
Helpful Hint
Efficiency is usually expressed as a percentage and you should change percentages
to decimals before using this equation.
Example 1
A generator in a thermal power station converts 1 000 J of kinetic energy into 800
J of electrical energy. What is the efficiency of the generator?
efficiency
= useful energy out = 800 = 0·8 = 80%
useful energy in 1000
Example 2
A motor is 65 % efficient. What power can this motor deliver when it receives
2 000 W?
65 %= 0·65 = useful power out
2 000
useful power out = 0·65 x 2 000 = 1 300 W
1.
Find the missing values in the following table.
Efficiency (%)
Useful energy in(J)
Useful energy out(J)
(a)
1 400
700
(b)
675
135
(c)
80
(d)
45
(e)
60
(f)
25
1 200
1 500
300
6 000
2.
A coal fired power station has a power output of 200 MW. The power produced by
the boiler is 340 MW. Calculate the efficiency of the power station.
3.
A turbine converts 65 000 J of heat energy into 13 000 J of kinetic energy. What is
the efficiency of the turbine?
4.
A generator converts 3 156 MJ of kinetic energy into 450 MJ of electrical energy.
What is the efficiency of the generator?
5.
A thermal power station converts 420 MJ of chemical energy into 124 MJ of
electrical energy. What is the efficiency of this power station?
6.
An electrical pump used in a pumped storage hydroelectric power station is 80 %
efficient. How much work can the pump do if it is supplied with 25 kJ of energy
each second?
7.
An oil fired power station which is 40% efficient produces an output of 300 MW.
How much power must be supplied to the station to produce this output?
8.
The output from an oil-fired power station is
250 MW and it is 32 % efficient. How much
power must be provided by the oil to
produce this output?
9.
The Glenlee hydroelectric power station produces 24 000 kW of electricity. How
much power is provided by water falling from the reservoir if the station is 25 %
efficient?
10. The boiler of a thermal power station releases 2·8 x 108 J of heat energy for each
kilogram of coal burned. The generator of the power station produces 1·26 x 108 J
of electrical energy for each kilogram of coal burned. What is the efficiency of this
power station?
11. The tidal power station at the Rance in Brittany, France opened in 1966. Each of
the 24 turbines can generate an output of up to 10 MW from the tidal currents
funnelled into the river estuary. Assuming that each turbine is 45 % efficient
calculate the power of the tide required to generate 10 MW at one turbine.
12. Water flowing into the turbines of a hydroelectric power station loses 4·5 x 106 J
of potential energy each second. How much electrical energy could this power
station produce if it is 35 % efficient?
13. A house has solar panels covering an area of 10 m2 to provide domestic hot water.
The solar power received by each square metre is 180 W on a summer day and the
panels are 20 % efficient. What would be the heat produced by the panels on such
a day?
14. The average power in waves washing the north Atlantic coast of Europe is 50 kW
per metre of wave front. What length of wave front would be required to generate
10 MW of electricity from these waves using a 45 % efficient wave - power
device?
15. The 3 MW wind turbine at Burger Hill in Orkney provides energy for the national
grid. If this turbine is 25 % efficient calculate how much energy is wasted each
second in this system.
Tutorial 7
Conservation of Energy
Helpful Hint
When an object falls all of its potential energy is converted to kinetic
energy. (assuming air resistance is negligible)
i.e.
Ep
Ek
We can use this principle of conservation of energy to solve many
problems.e.g. ball (mass m kg) falling through a height, h.
Ep = mgh
h
Finding the velocity
of the falling object.
Ep = Ek
= 1 mv2
2
Ek = 1 mv2
2 So, rearranging this:
Finding the height
through which an
object falls.
Ek = Ep
= mgh
So, rearranging this:
Ö
2Ep
v = m
h = Ek
mg
1.
3m
A 2 kg ball falls through 3 m to land on Earth.
(a)
How much potential energy does it lose during its fall?
(b)
How much kinetic energy does it gain during its fall, assuming that there is no
air resistance?
(c)
Calculate the maximum speed of the ball as it hits the ground.
2.
3.
A spanner falls from a desk which is 0·8 m high. If the spanner has a mass of 0.5
kg, calculate :
(a)
the potential energy lost by the spanner as it falls
(b)
the kinetic energy gained by the spanner as it falls
(c)
the speed of the spanner just as it hits the ground.
A pencil case has a mass of 200 g and is dropped from a height of 0·45 m.
4.
(a)
How much potential energy does the pencil case lose as it falls to the
ground?
(b)
What is the kinetic energy of the pencil case as it hits the ground?
(c)
With what speed does the pencil case hit the ground?
A trolley rolls towards a ramp with a speed of 2 m/s. The trolley has a mass of
0·3 kg.
h
5.
2 m/s
(a)
Calculate the kinetic energy of the trolley before it goes up the ramp.
(b)
If there are no energy losses due to friction how much potential energy
does the trolley gain as it goes up the ramp?
(c)
What height does the trolley reach on the ramp?
A skateboarder, of mass 65 kg travels towards a hill with a speed of 5 m/s.
5 m/s
6.
(a)
What is the kinetic energy of the skateboarder as he travels towards the
hill?
(b)
If there are no energy losses due to friction, how much potential energy
will the skateboarder gain on the hill?
(c)
What height will the skateboarder reach on the hill?
An 8 kg boulder rolls down a hill as shown below.
8 kg
20 m
(a)
How much potential energy does the boulder lose as it rolls, assuming
that no energy is lost due to friction?
(b)
Calculate the speed of the boulder at the bottom of the hill.
7.
A diver, who has a mass of 70 kg, dives from a cliff top into the sea. The cliff top
is 11·25 m above the water surface. At what speed does the diver enter the water?
8.
A box is released from a helicopter which is hovering 10 m above the ground.
Calculate the speed of the box as it strikes the ground, assuming that frictional
effects are negligible.
9.
A twenty pence piece falls from the top of a skyscraper and lands, on the street
below, with a speed of 80 m/s. How tall is the skyscraper? (Assume that there is
no air resistance.)
10.
A crate is released from a crane while it is hanging 20 cm above the ground.
With what speed does the crate land on the ground?
11. An advertising company produces a stunt where a girl on horseback jumps across
a gap between two buildings. The combined mass of horse and rider is 420 kg and
they are galloping with a speed of 28 m/s as they leave the first building.
The roof of the second building is 1 m below the roof of the first one.
(a)
Calculate the kinetic energy of the horse and rider as they leave the first
building.
(b)
How much gravitational potential energy do the horse and rider lose
during the stunt?
(c)
Assuming that there are no energy losses due to air resistance, what is
the total amount of kinetic energy of the horse and rider as they land on
the second building?
(d)
With what speed do the horse and rider land on the second building?
12. If a bullet is fired vertically upwards, with a speed of 150 m/s, what is the
maximum height it could reach? (Assume that frictional effects are negligible.)
13. A skateboarder moves towards a slope with a constant speed of 8 m/s. Her mass,
including her skateboard, is 60 kg and she reaches a height of 2·5 m on the slope
which has a rough surface.
(a)
How much kinetic energy did she have at the foot of the slope?
(b)
What happened to her kinetic energy as she moved up the slope?
(c)
How much potential energy did she gain on the slope?
(d)
How much energy was ‘lost’ due to friction on the slope?
14. A car, of mass 1 500 kg, is parked on a hill at a height of 20 m. The brakes fail and
the car begins to roll towards a busy junction at the foot of the hill. The car reaches
the junction with a speed of 18 m/s.
15.
(a)
Calculate the amount of potential energy lost by the car as it rolled
down the hill.
(b)
How much kinetic energy did the car have at the junction?
(c)
How much energy was ‘lost’ due to friction as the car rolled down the
hill?
A typical loop-the-loop rollercoaster in a fun park is shown below :
A
C
15 m
h
B
During one ride the total mass of carriage and passengers was 3 000 kg. When all
passengers were locked in place the carriage was pulled up the track to the start
point A. This was at a height of 15 m. The carriage was then released and it sped
down the track past point B and round the loop. By the time it had reached the top
of the loop, point C, it had lost 6 000 J of energy due to friction and was travelling
at 8 m/s.
(a)
How much potential energy did the carriage lose in going from A to B?
(b)
How much kinetic energy did the carriage have at the top of the loop?
(c)
How much potential energy did the carriage regain between B and C?
(d)
Calculate the height of the loop.
Tutorial 8
Series Circuits
Helpful Hint
The rules for series circuits are:
1.
2.
1.
the current is the same at all points in the circuit
the voltage of the source is shared amongst the components in the
circuit.
Two identical 2·5 V bulbs are connected to a supply as shown. What is the voltage
of the supply?
2·5 V
2.
2·5 V
Four identical resistors are connected across a 12 V supply as shown in the
diagram. What is the voltage across each of the resistors?
12 V
A
3.
B
C
D
A simple circuit with a bulb and resistor in series is shown below.
36 V
(a)
12 V, 36 W
R
If the bulb is operating at its correct voltage and power rating what is
the voltage across the resistor R?
(b)
The current in the bulb is 3 A. What current flows in the resistor?
4.
Two resistors are connected in series to a supply as shown in the diagram.
15 V
200 W
5.
100 W
(a)
The current in the 200 W resistor is 0·05 A. What is the current in the
other resistor?
(b)
The voltage across the 100 W resistor is 5 V. What is the voltage across
the 200 W resistor?
A variable resistor is used as a dimmer switch in a simple series circuit as shown.
14 V
The rheostat is adjusted until the bulb is shining brightly. The voltage across the
bulb is 13·8 V and the current through the rheostat at this setting is 1·7 A.
(a)
Calculate the voltage across the rheostat.
(b)
What is the current flowing in the bulb?
Tutorial 9
Parallel Circuits
Helpful Hint
The rules for parallel circuits are:
1.
2.
1.
the voltage is the same across all the components in parallel.
the current from the supply is shared amongst the different branches
of the circuit.
Two resistors are connected in parallel to a 12 V battery.
(a)
What is the voltage across R1?
(b)
What is the voltage across R2?
(c)
What size of current is drawn from
the battery?
6V
4A
2.
3.
L1
Two identical bulbs and a resistor are connected
in parallel to a 6 V supply.
(a)
What is the voltage across L2 ?
(b)
A current of 1·8 A flows through each of the bulbs.
What is the current flowing through the resistor?
L2
R1
An electric fire has three elements which can be switched on and off
independently. The elements are connected in parallel to the mains supply. Each
element draws a current of 0·3 A when switched on.
230 V
(a)
What is the voltage across the middle
element?
(b)
What is the total current flowing from the
supply when two of the elements
are switched on?
(c)
What is the maximum current drawn
from the mains by the fire?
4.
Look at the four circuits below labelled A, B, C and D.
B
A
2A
A3
A2
3A
A1
1A
C
9A
A4
D
A6
3A
5A
3A
A7
A5
(a)
Which of the four circuits are parallel circuits and which are series?
(b)
State the current which would be shown on ammeters A1 to A7.
5.
A
The following circuits are used to measure the voltage across light bulbs.
V1
B
5V
9V
V3
3V
V2
6V
C
S1
V1
S2
bulb 1
2V
bulb 2
S3
V2
bulb 3
(a)
State the voltage which would be shown on voltmeters V1 to V5 (all
switches in circuit C are closed).
(b)
Look at circuit C above. Which bulb or bulbs would light if
(i)
switch S1 and S3 closed
(ii)
switch S1 and S2 were closed
(iii)
switch S2 and S3 were closed?
Tutorial 10
Current, Charge and Time
In this section you can use the equation:
charge = current x time
also written as
Q = It
where Q = charge in coulombs (C)
I = current in amperes (A)
t = time in seconds (s).
1.
Find the missing values in the following table.
Charge (C)
Current (A)
Time (s)
(a)
5
30
(b)
0·005
3 600
(c)
3
1·5
(d)
27·6
2·3
(e)
1 800
60
(f)
94
10
2.
A bulb draws a current of 1 A. How much charge flows through it in 60
seconds?
12V
3.
756 C of charge flow though an electric heater in 180 seconds. What is the current
in the heater?
4.
A hairdryer operates with a current of 5 A. How much time would it take for 6 000
C to pass through the hairdryer?
5.
A current of 2·1 A flows through an electric
shaver for 5 minutes. How much charge flows
in this time?
6.
A 60 W bulb is switched on for 30 minutes. If 450 C pass through it in this time,
what is the current flowing in the bulb?
7.
A ‘surround sound’ speaker system on a TV draws a current of 0·6 A. In an
average day 6 480 C of charge flows through the speaker system. For how long is
the TV switched on each day?
8.
An electric kettle has a label on it as shown below.
MODEL No. 5510 - 01
capacity 1·7 litres
9·2 A /220 - 240V
2·2 kW
After the kettle is switched on it automatically switches off when the water in it
has boiled. On one occasion 1 656 C passed through the kettle before it switched
off. Use the information given to work out how long the water took to boil?
9.
An electric fire is rated at 2·875 kW, 230 V, 12·5 A. How much charge will flow
through this fire in a period of 2 hours 20 minutes?
10. One day an electric iron was switched on from 1·45 p.m. until 3·15 p.m. What
current was drawn by the iron if 2·484 x 10 4 C passed through it in this time?
Tutorial 11
Potential Dividers
1.
The transistor is often controlled by a potential divider acting as the input.
Look at the three voltage dividers below. State whether each has a high or low
signal at point X.
(a)
(b)
(c)
+5V
+5V
20 Ω
10 kΩ
X
2.
+5V
X
500 Ω
200 Ω
0V
0V
X
0V
Find the voltage at point Y in each of the following divider circuits.
(a)
(b)
+5V
Y
10 Ω
0V
(c)
+6V
+ 12 V
5500 Ω
10 Ω
10 Ω
Y
Y
500 Ω
20 Ω
0V
3.
A potentiometer is used as an input to a
transistor as shown opposite.
(a)
What will be the signal (High or Low)
entering B if the sliding contact of the
C
potentiometer is moved to
(i)
the top of the potentiometer
(ii)
the bottom of the potentiometer? sliding
contact
The sliding contact is placed exactly ¼
of the way up the potentiometer from A.
(i)
What will be the resistance
between points A and B?
A
(ii)
What will be the voltage between
points A and B?
(b)
10 kΩ
potentiometer
0V
+ 10 V
1000 Ω
potentiometer
B
0V
4.
A transistor is used in a switching circuit shown below. The circuit is used as
part of a
temperature alarm in a greenhouse.
+5V
buzzer
thermistor
variable resistor
0V
(a)
A thermistor is used as the input device in this electronic circuit. What happens
to the thermistor’s resistance as its surrounding temperature changes?
(b)
The arrangement above causes the buzzer to sound when the temperature gets
too warm. How would the operation of the alarm be altered if the position of
the thermistor and variable resistor were exchanged?
(c)
The alarm is found to switch on when the temperature in the greenhouse
reaches 30°C. How could the alarm be modified to alter the temperature at
which it switches on?
5.
A car-park is lit by floodlights which come on automatically when it gets dark.
The circuit that controls their operation is shown below.
+5V
variable resistor
relay
mains 230 V
floodlight
light dependant
resistor
0V
(a)
Explain how the transistor circuit is able to operate the relay to switch
on the floodlight.
(b)
Why is a relay necessary in the circuit?
(c)
The variable resistor can be adjusted to control how dark it has to be to
make the light come on. What effect will increasing the resistance of the
variable resistor have on the operation of the light?
Tutorial 12
Voltage, Current and Resistance
In this section you can use the equation:
voltage = current x resistance
also written as:
V = IR
where V = voltage in volts (V)
I = current in amps (A)
R = resistance in ohms (W).
Helpful Hint.
Many appliances run from mains voltage which is 230 V ac.
Useful units for electricity are:
1 mA = 0·000 001 A = 1 x 10-6 A
1 mA = 0·001 A = 1 x 10-3 A
1.
Find the missing values in the following table.
Voltage (V)
2.
Current (A)
Resistance (W)
(a)
15
35
(b)
0·2
1 000
(c)
230
125
(d)
24
550
(e)
120
12
(f)
6
6·25 x 10-3
Look at the following circuits and calculate the supply voltage in each case:
(a)
Vs
b)
Vs
10 A
5W
(c)
Vs
2·56 A
250 W
50 mA
480 W
3.
Look at the following circuits and calculate the current in each case:
(a) 24 V
(b)
12 V
I
I
12 W
4.
I
50 W
550 W
Look at the following circuits and calculate the unknown resistance in each case:
(a)
24 V
(b)
12 V
R
(c)
48 V
30 mA
25 mA
5.
48 V
(c)
R
660 mA
R
Calculate the resistance of a lamp if the current through it is 10 mA when operated
by a 24 V supply.
6. A power drill is operated at mains voltage and
has a resistance of 1·5 kW. Calculate the current
through the drill.
7.
The maximum current an electric motor can safely handle is 10 mA and it has a
resistance of 360 W. Calculate its safe operating voltage.
8.
A cooker draws a maximum current of 28·75 A and has a resistance of 8 W. At
what voltage should it operate?
9.
Hairdryers work from the mains voltage and can have currents of up to 15 mA
flowing through them. Calculate the resistance of the hairdryer.
10. Overhead cables have resistance of 25 kW. If the voltage across the cables is 4 000
V calculate the current through them.
Tutorial 13
Resistance in Series
In this section you can use the equation:
Rs = R1 + R2 + R3 +......
where Rs = total resistance of a series circuit or series section of a circuit (W).
1.
Three resistors R1, R2 and R3 are arranged in series as shown in the diagram below.
R2
R1
R3
Find the missing values in the table.
R1 (W)
R2 (W)
R3 (W)
(a)
5 000
490
85
(b)
80
300
25
(c)
800
2 000
200
(d)
700
300
(e)
(f)
2.
1 400
140
225
100
550
85
390
Calculate the total resistance of the following circuit.
800 W
3.
Rs (W)
5 kW
3·2
The resistance of the following circuit is 8·8 kW. Calculate the resistance of R.
950 W
R
6·3
Tutorial 14
Resistance in Parallel
In this section you can use the equation
1
1
1
1
Rp =R1 +R2 +R3
+ ....
where Rp = total resistance of a parallel circuit or parallel section of a circuit (W).
1.
Calculate the total resistance of each of the following circuits:
(a)
(b)
(c)
80 W
20 W
120 W
80 W
20 W
120 W
(d)
(e)
(f)
80 W
100 W
400 W
120 W
150 W
1 600 W
(g)
(h)
(i)
300 W
150 W
800 W
600 W
300 W
2 400 W
2.
Calculate the total resistance of each of the following circuits:
(a)
(b)
600 W
3 kW
1·2
kW
600 W
3 kW
600 W
600 W
3 kW
600 W
(d)
3.
(c)
(e)
(f)
280 kW
300 W
3 kW
560 kW
600 W
900 W
560 kW
200 W
600 W
The total resistance of the circuit below is 80 W. Calculate the resistance of R.
R
220 W
1 232 W
4.
The total resistance of the following circuit is 112·5 W. Calculate the resistance of
resistor A.
300 W
A
900 W
5.
The total resistance of the following circuit is 240 W. Calculate the resistance of
resistor X
1 200 W
X
1 800 W
Combination Circuits
Helpful Hint
Rs
=
=
1
Rp
1.
R1 + R2 + R3 +......
( for a series section of a circuit)
1 + 1 + 1 +......
R1 R2 R3
(for a parallel section of a circuit)
Calculate the total resistance in each of the following networks:
(a)
(b)
20 W
10 W
60 W
40 W
60 W
20 W
(d)
(c)
10 W
10 W
10 W
10 W
15 W
15 W
30 W
30 W
2.
The following circuit shows part of a car lighting system.
250 W
560 W
X
Z
Y
250 W
560 W
Calculate the resistance between points:
3.
(a)
X and Y
(b)
Y and Z
(c)
X and Z.
Calculate the resistance of the network of resistors shown below.
40 W
80 W
80 W
120 W
60 W
4.
Which network of resistors has the lowest total resistance?
Network A
Network B
90 W
90 W
90 W
15 W
15 W
90 W
5.
A school technician has different resistors to use in building house wiring models.
10 W
10 W
50 W
50 W
100 W
100 W
He has two 10 W resistors, two 50 W resistors and two 100 W resistors.
How can these resistors be combined to produce a total resistance of:
(a) 260 W
(b) 300 W
(c) 30 W
(d) 35 W?
Tutorial 15
Diodes
1. The graph below shows how the current varies with applied voltage for a diode.
a. What is the voltage at which the diode could be said to start to “turn
on”?
b. Calculate (using V/I) the effective resistance of the diode when the
voltage applied is:
i. 1V
ii. 0.6V
c. Does the diode obey Ohm’s Law?
I - V For Diode
Current (mA)
600
500
400
300
200
100
0
0
0.2
0.4
0.6
0.8
Voltage (V)
1
Helpful Hint
When working with LED circuits you can use the equation:
V = IR
When applying this equation remember that the supply voltage is shared between the
LED and the resistor.
Example
A certain LED takes a current of 10 mA and the voltage across it is 2 V. What should
be the value of the series resistor when a supply voltage of 5 V is used?
1st. Sketch the circuit
R.
5V
2nd. Calculate the voltage across resistor
VR
=
Vsupply - Vled
=
5
- 2
=
3V
3rd. Apply V = IR to find the value of R
I = 10 mA
= 0·010
A
R
VR = 3 V
I = 0·01 A
R = ?
¬2V®
2.
VR =
3 =
R =
R =
IR
0·01 x R
3 / 0·01
300 W
Use the stages outlined above to find the missing values in the following table.
Vsupply
I
¬Vled®
Vsupply
R
¬VR®
Voltage across
LED (V)
Current (A)
(V)
(a)
6
2·0
0·010
(b)
12
2·0
0·010
(c)
8
1·8
0·016
(d)
20
1·6
0·008
(e)
4
1·5
0·020
(f)
11
2·0
0·012
Voltage across
R (V)
Resistance of R
(W)
3.
For each of the following circuits calculate the value of the series resistor which
will enable the LED to operate at its ideal voltage and current.
9V
4V
(a)
(b)
R
R
1·8 V,
12 mA
2·1 V,
10 mA
12 V
(c)
(d)
6V
R
R
2·2 V,
10 mA
(e)
1·6 V,
11 mA
(f)
14 V
9·8 V
12mA
15mA
R
R
¬2 V®
¬2·3 V®
(g)
(h)
9·5 V
5V
10mA
20mA
R
¬3 V®
R
¬4 V®
4.
Consider the following circuit.
5·1 V
8mA
400 W
5.
(a)
Calculate the voltage across the 400 W resistor.
(b)
Calculate the voltage across the LED.
For the circuit shown below work out the value of the supply voltage which will
enable the LED to operate at it’s stated rating.
800 W
2·2 V,
11 mA
6.
7.
The voltage and current specifications for a certain LED are 1·75 V and 10 mA
respectively. What should be the value of the series resistor if the LED is powered
by a 6 V supply?
Calculate the ammeter reading in the following circuit.
12 V
A
¬1·8 V®
2 040 W
Tutorial 16.
Components
In this section you can use the equation:
V = IR
V = voltage in volts (V)
I = current in amps (A)
R = resistance in ohms (W ).
where
Helpful Hint
When choosing components for an electronic system, think about the types of
energies involved.
1.
Some students are given the electronic components shown below to use in their
school design projects.
A
B
D
E
C
M
F
(a)Name each of the components.
(b)Which of the components would be most suitable to use as the input device for
a gardeners frost alarm?
Capacitor
motor
thermistor
photovoltaic cell
light dependent resistor (LDR)
loudspeaker thermocouple
2.
Select from the list above a suitable component for use in each of the
following:
(a)
Public address system in a railway station
(b)
Digital thermometer
(c)
Photographers light meter
(d)
Time delay circuit for courtesy lights in a car
(e)
Remotely operated Garage door
(f)
Sunlight hours recorder at a weather station.
3.
The circuits below show two identical LDR’s each connected to a 6 V supply.
One LDR is placed in a cupboard and the other is placed beside a window.
The current in each circuit is also shown.
0·03 A
6V
0·002 4 A
6V
Circuit (i)
4.
(a)
Calculate the resistance of each LDR.
(b)
Which circuit shows the LDR in the cupboard?
Circuit (ii)
The following circuit shows a thermistor connected to a 5 V supply and placed in
a school laboratory.
A
5V
In the morning the ammeter gave a reading of 1·25 mA. Later in the same day the
reading had risen to 2·5 mA.
(a)
Calculate the resistance of the thermistor in the morning.
(b)
What happened to the temperature in the room during the day?
Explain your answer.
5.
The following information for an LDR was found in a components catalogue.
Light Source
Illumination (lux)
Resistance (kW)
moonlight
0·1
10 000
60 W bulb at 1m
50
2·4
fluorescent light
500
0·2
bright sunlight
30 000
0·02
This LDR is connected to a 12 V supply with an ammeter in series with it as
shown in the diagram.
12 V
A
(a) What is the resistance in ohms of the LDR when exposed to fluorescent
light?
(b)What would the ammeter read when a lamp with a 60 W bulb in it is placed 1
m away from the LDR?
(c) When the ammeter gives a reading of 0·6 A which light source is being used?
6.
A pupil uses a thermistor as a simple electronic thermometer. She connects the
thermistor to an ammeter and places the thermistor into a beaker of hot water. The
ammeter gives a reading of 8 mA.
Temperature (oC)
Resistance (W)
20
3 750
40
198
60
750
80
350
100
200
6V
A
(a)
What is the temperature of the water in the beaker?
(b)
The pupil adds some more water to the beaker and the ammeter gives a
new reading of 1·6 mA. Did the pupil add hot or cold water to the
beaker?
(c)
What is the new temperature of the water?
(d)
What will the ammeter read when the water is boiling?
7. In the circuit below a switch provides the option of point A being connected to
either point B (as shown) or point C.
a. Which position of the switch allows the capacitor to charge?
b. What happens to the voltage across the capacitor as it is charging?
c. What happens the voltage across the resistor as the capacitor is
charging?
d. The value of the resistor R, has an effect on how long it takes to charge
the capacitor. Explain this effect.
Once the capacitor is fully charged, the switch is moved to connect points AC
together.
e. Describe the effect this has on the lamp.
B
A
C
R
Tutorial 17
Power, Current and Voltage
In this section you can use the equation:
power = current x voltage
also written as
P = IV
P = power in watts (W)
I = current in amps (A)
V = voltage in volts (V).
where:
Helpful Hint
The voltage of the mains is 230 V ac.
1.
Find the missing values in the following table.
Power (W)
2.
3.
Current (A)
Voltage (V)
(a)
2·5
12
(b)
0·6
9
(c)
1·5 x 103
230
(d)
36
12
(e)
0·624
2·6 x 10-3
(f)
1·5
0·25
A car battery supplies a voltage of 12 V. One headlamp bulb draws a current of 3
A. What is the power rating of this bulb?
An electric shower has a power rating of
12 W and draws a current of 0·11 A. What
voltage is required to operate the shower?
4.
What current flows through a 230 V, 60 W household lamp when it is operating at
the correct voltage?
5.
Calculate the power rating of an electric drill which draws a current of 3 A when
connected to the mains.
6.
What would be the reading on the ammeter in the circuit shown?
12 V
24 W
A
7.
The following information was found on the rating plate of a food processor:
BL300
360 W
230 V 50/60 Hz
made in the U.K
Calculate the current flowing in the food processor.
8.
A fridge has a power rating of 160 W. When it is plugged into the mains what
current will it draw?
9.
A radio has a power rating of 6 W and draws a current of 0·5 A when operating
normally.
10.
(a)
What voltage does this radio need?
(b)
How many 1·5 V batteries would be needed to operate the radio?
The circuit shows a heating element (resistor) operating correctly.
I = 4·2 A
1 kW
What is the voltage of the supply?
11. A torch bulb draws a current of 500 mA. It has a power rating of 1·75 W. What
voltage is required to light the bulb to its correct brightness?
12. An electric locomotive on the East Coast line gets its electricity from the overhead
cables which supply 25 kV a.c. The locomotive has a top speed of 140 mph and it
operates at 4·7 MW. Calculate the current flowing to the locomotive.
13. A helium - neon laser emits red light and has many uses in medicine. The laser
uses the 230 V mains supply and has a power rating of 5 mW. What current flows
in the laser?
14. The current flowing in an electric keyboard is measured as 800 mA. What voltage
is required to operate the keyboard if it has a power rating of 7·2 W?
15. An electric fire has three heating elements which can be switched on and off
independently. Each element has a power of 1·3 kW and is controlled by a switch
on the side of the fire.
(a)
Calculate the current drawn from the socket when one heating element
is switched on.
(b)
What is the maximum current that the fire could draw?
Tutorial 18
Power and Resistance
Helpful Hint
By combining the formulae:
P = I V and V = I R
we have alternative forms of the formula for power.
i.e.
P = I (IR)
P = I2 R
and
P = (V/R) V
P = V2/R
Use these alternative forms of ‘power formulae’ in the following questions.
1.
Calculate the power rating of a lawn mower
which has a resistance of 70·5 W and draws a
current of 2·5 amps.
2.
What power is dissipated in the element of a toaster if it has a resistance of 64 W
and draws a current of 3·75 amps?
3.
Find the power rating of a television given that it operates at mains voltage and
has a resistance of 480 W.
4.
What would be the power rating of an iron if it operates at mains voltage and has a
resistance of 45 W?
5.
Calculate the power rating of a hedge trimmer given that it draws a current of 1·67
A and has a resistance of 144 W.
6.
Calculate the power rating of a Karaoke machine if it has a resistance of 5 760 W
and operates at mains voltage.
7.
How much power is dissipated in curling tongs if they draw a current of 1·05 A
and have a resistance of 230 W while operating from the mains?
8.
A microwave oven has a resistance of 68 W and works properly from a mains
supply. What is the power rating for such an oven?
9.
Find the power rating of a Hoover
designed with a resistance of 110 W
when operating at mains voltage.
10. What current is drawn from the supply by a transistor radio if it has a power rating
of 3 W and a resistance of 12 W?
11. Find the resistance of a table lamp which has a power rating of 115 W and draws a
current of 0·5 A.
12. An alarm clock is driven by a domestic supply voltage of 230 V. What is its
resistance if it has a power rating of 2 W?
13. Calculate the total resistance of an electric fire if it operates safely at 230 V and
uses electrical energy at a rate of 750 W.
14. Calculate the voltage of a car alarm which has a power rating of 3 W and
resistance of 50 W.
15. Find the power rating of an electric food
mixer if it operates at mains voltage and
has a resistance of 400 W.
Tutorial 19
Specific Heat Capacity
In this section you can use the equation:
heat energy = specific heat capacity x mass x temperature change
also written as
Where Eh
c
(J/kgoC)
m
DT
Eh = cmDT
= heat energy in joules (J)
= specific heat capacity in joules per kilogram per degree Celsius
= mass in kilograms (kg)
= change in temperature (oC).
Helpful Hint
You will need to look up values for the specific heat capacity of different materials
These values can be found on the data sheet on page 31.
1.
Find the missing values in the following table.
Heat energy
(J)
Specific heat capacity
(J/kgoC)
Mass (kg)
Temperature change
(oC)
(a)
4 200
2
65
(b)
902
5·5
15
386
1·6
(c)
2·4 x 10 3
(d)
4 250
17
0·5
(e)
1·6 x 103
1·5
2
50 x 10-3
30
(f)
128
2.
How much heat is required to raise the temperature of 3 kg of aluminium by 10
o
C?
3.
3 kJ of heat is supplied to a 4 kg block of lead. What would be the rise in
temperature of the block?
4.
In an experiment on specific heat capacity an electric heater supplied 14 475 J of
heat energy to a block of copper and raised its temperature by 15 oC. What mass of
copper was used in the experiment?
5.
6·9 kJ of heat is supplied to 500 g of methylated spirit in a plastic beaker and
raises its temperature by 1.5 oC. What is the specific heat capacity of methylated
spirit?
6.
How much heat energy would be required to raise the temperature of 2 kg of
alcohol from 20 oC to 65 oC?
7.
A 250 g block of copper is allowed to cool down from 80 oC to 42 oC. How much
heat energy will it give out?
8.
254×4 kJ of energy are required to heat 2 kg of glycerol from 12 oC to 65 oC. What
is the specific heat capacity of glycerol?
9.
Which of the following would give out more heat:
A - a 2 kg block of aluminium as it cools from 54 oC to 20 oC
or
B - a 4 kg block of copper as it cools from 83 oC to 40 oC?
10. 2·5 kJ of heat is supplied to a quantity of alcohol and raises its temperature from
22 oC to 45 oC. What mass of alcohol was being heated?
11. Each concrete block in a storage heater has a mass of 1·4 kg. The blocks are
heated to 85 oC at night when the electricity is cheaper and cool down during the
day to 20 oC. If each block releases 77 kJ of energy during the day calculate the
specific heat capacity of the concrete.
12. An immersion heater is used to heat 30 kg of water at 12 oC. The immersion heater
supplies 8·6 M J of heat. Ignoring heat losses to the surroundings calculate the
final temperature of the water.
13. A kettle supplies 262 k J of energy to 800 g of water in
order to heat it to 90 oC. What was the temperature of the
water before the kettle was switched on?
14.
A cup containing 140 g of water is heated in a microwave
oven. The microwave supplies 4·9 x 104 J of heat to the water
which was originally at 10 oC.
What is the final temperature of the water?
15. A 400 g block of lead is heated to 45 oC by an electric heater which supplies 1·2 kJ
of heat. What was the initial temperature of the lead block?
Tutorial 20
Conservation of Energy
Helpful Hint
The energy required to heat materials is often produced by an electrical heater.
Two useful equations are:
E = Pt and
E = ItV
where
E = energy on joules (J)
P = power in watts (W)
t = time in seconds (s)
I = current in amps (A)
You can use the principle of conservation of energy to solve problems where an
electrical heater is used:
Eh = Pt = cmDT
Eh = ItV = cmDT
Use the principle of conservation of energy to solve the following:
1.
How long would it take a 50 W immersion heater to heat 2 kg of water from
10 oC to 80 oC?
2.
How long would it take for a 2 kW kettle to heat 800 g of water from 40 oC to 100
o
C?
3.
A 100 W heater is used to heat a 4 kg block of lead. If the heater is left on for
10 minutes calculate the rise in temperature of the block of lead.
4.
Calculate the power of an immersion heater which takes 20 minutes to heat 4 kg of
water by 60 oC.
5.
600 g of water was supplied with 163 020 J of heat. Energy losses were negligible.
(a)What was the change in temperature of the water?
(b)If heat was supplied to the water at a rate of 543·4 joules per second, how long
did it take to heat the water?
6.
The temperature of 2 kg of steel is raised by 10 0C. It takes 3 minutes for an
electric heater connected to the mains (230 V) to do this.
(a)What is the minimum energy supplied to the steel?
(b)Assuming no energy losses, what is the power rating of the heater?
(c) What current is drawn by the heater?
7.
A 500 g mass of copper is heated by a 40 W immersion heater while a 500 g mass
of steel is heated by a 50 W heater. The initial temperature of each block is 20 0C.
Which block is the first to reach a temperature of 80 oC? You can assume that
there are no energy losses.
8.
80 g of alcohol at 20 0C is heated by an electric heater for 6 minutes until it
reaches its boiling point of 65 oC. The heater operates at 230 V and draws a current
of 125 mA.
(a)How much electrical energy is used by the heater?
(b)How much heat energy is absorbed by the alcohol?
(c) How much energy was ‘lost’ to the environment?
Tutorial 21
Pressure, Force and Area
2
-4
2
1.
Show that 1 cm = 1x10 m .
2.
Convert the following from volumes from cm to m :
2
2
2
(a) 10 cm
2
(b) 75 cm
2
(c) 200 cm
3. Copy and complete the table by calculating the missing values.
4. The standard unit of pressure is the pascal, Pa. State an alternative unit for pressure
from the formula P= F / A
.
4
5. An aircraft cruises at an altitude where the air pressure is 4x10 Pa. The inside of
5
the aircraft however is maintained at normal atmospheric pressure, 1x10 Pa.
2
Calculate the outward force produced on the external cabin door of area 2 m .
6. A rectangular block of mass 10 kg is lying on a flat surface on a planet where the
-1
gravitational field strength is 4 N kg . The base of the box measures 4m by 2m.
Which of the following statements is/are true?
I The weight of the box is 100 N.
II The weight of the box is 40 N.
III The pressure the box exerts on the flat surface is 5 Pa.
Tutorial 22
Pressure and volume (constant temperature)
1.
Copy and complete the table by calculating the missing values.
2.
100 cm3 of air is contained in a syringe at atmospheric pressure (1 x 105 Pa).
If the volume is reduced to a) 50 cm3 or b) 20 cm3 without a change in
temperature, what will be the new pressures?
3.
If the piston in a cylinder containing 300 cm3 of gas at a pressure of 1 x 105 Pa
is moved outwards so that the pressure of the gas falls to 8 × 104 Pa, find the
new volume of the gas.
4.
A weather balloon contains 80 m3 of helium at normal atmospheric pressure of
1 x 105 Pa.
What will be the volume of the balloon at an altitude where air pressure is
8 × 10 4 Pa?
5.
The cork in a pop-gun is fired when the pressure reaches 3 atmospheres. If the
plunger is 60 cm from the cork when the air in the barrel is at atmospheric
pressure, how far will the plunger have to move before the cork pops out?
6.
A swimmer underwater uses a cylinder of compressed air which holds 15 litres
of air at a pressure of 12000 kPa.
(a) Calculate the volume this air would occupy at a depth where the pressure is
200 kPa.
(b) If the swimmer breathes 25 litres of air each minute at this pressure,
calculate how long the swimmer could remain at this depth (assume all the air
from the cylinder is available).
Tutorial 23
Pressure and temperature (constant volume)
1.
Convert the following celsius temperatures to kelvin.
a) -273 °C
2.
b) -150 °C
c) 0 °C
d) 27 °C
e) 150 °C
Convert the following kelvin temperatures to celsius.
a) 10 K
b) 23 K
c) 100 K
d) 350 K
e) 373 K
3.
Copy and complete the table by calculating the missing values.
4.
A cylinder of oxygen at 27 °C has a pressure of 3 × 106 Pa. What will be the
new pressure if the gas is cooled to 0 °C?
5.
An electric light bulb is designed so that the pressure of the inert gas inside it is
100 kPa (normal air pressure) when the temperature of the bulb is 350 °C. At
what pressure must the bulb be filled if this is done at 15 °C?
6.
The pressure in a car tyre is 2.5 × 105 Pa at 27 °C. After a long journey the
pressure has risen to 3.0 × 105 Pa. Assuming the volume has not changed, what
is the new temperature of the tyre?
7.
A compressed air tank which at room temperature of 27 °C normally contains
air at 4 atmospheres is fitted with a safety valve which operates at 10
atmospheres.
During a fire the safety valve was released. Estimate the average temperature of
the air in the tank when this happened.
8.
(a) Describe an experiment to find the relationship between the pressure and
temperature of a fixed mass of gas at constant volume. Your answer should
include:
(i) a labelled diagram of the apparatus
(ii) a description of how you would use the apparatus
(iii) the measurements you would take.
(b) Use the following results to plot a graph of pressure against temperature
in °C using axes as shown below.
(i)Explain why the graph you have drawn shows that pressure does not
vary directly as celsius temperature.
(ii) Explain how the graph can be used to show direct variation between
temperature and pressure if a new temperature scale is introduced.
(iii) Use the graph to estimate the value in °C of the zero on this new
temperature scale.
(c) Use the particle model of a gas to explain the following:
(i)why the pressure of a fixed volume of gas decreases as its
temperature decreases
(ii) why the pressure of a gas at a fixed temperature decreases if its
volume increases
(iii) what happens to the molecules of a gas when Absolute Zero is
reached.
Tutorial 24
Volume and temperature (constant pressure)
1.
Describe an experiment to find the relationship between the volume and
temperature of a fixed mass of gas at constant pressure. Your description
should include:
(a) a diagram of the apparatus used
(b) a note of the results taken
(c) an appropriate method to find the relationship using the results.
2.
Copy and complete the table by calculating the missing values.
3.
100 cm3 of a fixed mass of air is at a temperature of 0 °C. At what temperature
will the volume be 110 cm3 if its pressure remains constant?
4.
Air is trapped in a glass capillary tube by a bead of mercury. The volume of air
is found to be 0.10 cm3 at a temperature of 27 °C. Calculate the volume of air at
a temperature of 87 °C.
5.
The volume of a fixed mass of gas at constant temperature is found to be
50 cm3.
The pressure remains constant and the temperature doubles from 20 °C to
40 °C.
Explain why the new volume of gas is not 100 cm3. You must show
calculations.
Tutorial 25
General gas equation
1.
Given, for a fixed mass of gas, P α T and P α 1/V, derive the general gas
equation.
2.
Find the unknown quantity from the readings shown below for a fixed mass of
gas.
(a)
P1 = 2 × 105 Pa
P2 = 3 × 105 Pa
V1 = 50 cm3
V2 = ?
T1 = 20 °C
T2 = 80 °C
(b)
P1 = 1 × 105 Pa
P2 = 2.5 × 105 Pa
V1 = 75 cm3
V2 = 100 cm3
T1= 20 °C
T2 = ?
(c)
P1 = 2 × 105 Pa
P2 = ?
V1 = 60 cm3
V2 = 80 cm3
T1 = 20 °C
T2= 150 °C
d)
P1 = 1 × 105 Pa
P2 = 2.5 × 105 Pa
V1 = 75 cm3
V2 = 50 cm3
T1 = ?
T2 = 40 °C
3.
A sealed syringe contains 100 cm3 of air at atmospheric pressure (1 x 10 5 Pa)
and a temperature of 27 °C. When the piston is depressed the volume of air is
reduced to 20 cm3 and this produces a temperature rise of 4 °C. Calculate the
new pressure of the gas.
4.
Calculate the effect the following changes have on the pressure of a fixed mass
of gas.
(a) Its temperature (in K) doubles and volume halves.
(b) Its temperature (in K) halves and volume halves.
(c) Its temperature (in K) trebles and volume quarters.
5.
Calculate the effect the following changes have on the volume of a fixed mass
of gas.
(a) Its temperature (in K) doubles and pressure halves.
(b) Its temperature (in K) halves and pressure halves.
(c) Its temperature (in K) trebles and pressure quarters.
6.
Explain the pressure-volume, pressure-temperature and volume-temperature
laws qualitatively in terms of the kinetic model.
7.
After a car has been parked in the sun for some time, it is found that the
pressure in the tyres has increased.
This is because
A the volume occupied by the air molecules in the tyres has increased
B the force produced by the air molecules in the tyres acts over a smaller area
C the average spacing between the air molecules in the tyres has increased
D the increased temperature has made the air molecules in the tyres expand
E the air molecules in the tyres are moving with greater kinetic energy.
8.
A girl wrote the following statements in her physics notebook.
I
The pressure of a fixed mass of gas varies inversely as its volume,
provided the temperature of the gas remains constant.
II
The pressure of a fixed mass of gas varies directly as its kelvin
temperature, provided the volume of the gas remains constant.
III
A temperature change of 20 °C in a gas is the same as a temperature
change of 293 K.
Which of the above statements is/are true?
A I only
B II only
C III only
D I and II only
E I, II and III
9. The end of a bicycle pump is sealed with a small rubber stopper. The air in
chamber C is now trapped.
The plunger is then pushed in slowly, causing the air in chamber C to be
compressed. As a result of this, the pressure of the air increases.
Which of the following explain(s) why the pressure increases, assuming that the
temperature remains constant?
I
The air molecules increase their average speed.
II
The air molecules are colliding more often with
the walls of the chamber.
III
Each air molecule is striking the walls of the chamber with greater
force.