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EDEXCEL IGCSE / CERTIFICATE IN PHYSICS 4-3
Work and Power
Edexcel IGCSE Physics pages 142 to 149
June 17th 2012
All content applies for Triple & Double Science
Edexcel Specification
Section 4: Energy resources and energy transfer
c) Work and power
know and use the relationship between work, force and distance moved in the
direction of the force:
work done = force × distance moved W = F × d
understand that work done is equal to energy transferred
know and use the relationship:
gravitational potential energy = mass × g × height
GPE = m × g × h
know and use the relationship:
kinetic energy = ½ × mass × speed2 KE = ½ × m × v2
understand how conservation of energy produces a link between gravitational
potential energy, kinetic energy and work
describe power as the rate of transfer of energy or the rate of doing work
use the relationship between power, work done (energy transferred) and time
taken:
power = work done / time taken P = W / t
Work and energy
When a force causes a body to move through a distance,
energy is transferred and work is done.
work done = energy transferred.
Both work and energy are measured in joules (J).
Work and friction
Work done against frictional
forces is mainly transformed into
heat.
Rubbing hands together causes
them to become warm.
Brakes pads become hot if they
are applied for too long. In this
case some of the car’s energy
may also be transferred to sound
in the form of a ‘squeal’
The work equation
work done = force applied × distance moved in
the direction of
the force
W=Fxd
work, W is measured in joules (J)
force, F is measured in newtons (N)
distance, d is measured in metres (m)
also:
force = work done ÷ distance moved
and:
distance = work done ÷ force
W
F
d
Question 1
Calculate the work done when a force of 5N
moves through a distance of 3m.
W=Fxd
= 5N x 3m
work = 15 J
Question 2
Calculate the work done when a force of
6N moves through a distance of 40cm.
W=Fxd
= 6 N x 40 cm
= 6 N x 0.40 m
work = 2.4 J
Question 3
Calculate the value of the force required to
do 600J of work over a distance of 50m.
W=Fxd
becomes:
F=W÷d
= 600 J ÷ 50 m
force = 12 N
Question 4
Calculate the distance moved by a force of
8N when it does 72J of work.
W=Fxd
becomes:
d=W÷F
= 72 J ÷ 8 N
distance moved = 9 m
Question 5
Calculate the work done by
a child of weight 300N who
climbs up a set of stairs
consisting of 12 steps each
of height 20cm.
W=Fxd
The child must exert an
upward force equal to its
own weight.
Therefore: force = 300N
This force is exerted
upwards and so the
distance must also be
measured upwards.
= (12 x 20cm)
= 2.4m
therefore:
work = 300 N x 2.4 m
work = 720 J
Question 6
Calculate the work done by a person of mass 80kg who
climbs up a set of stairs consisting of 25 steps each of
height 10cm.
W=Fxd
the person must exert an upward force equal their weight
the person’s weight = (80kg x 10N/kg) = 800N
the distance moved upwards equals (10 x 25cm) = 2.5m
work = 800 N x 2.5 m
work = 2000 J
Complete
Answers
work
force
distance
150 J
50 N
3m
800 J
40 N
20 m
500 J
250 N
2m
80 kJ
4000 N
2m
2 MJ
3.03
400 N
5 km
Choose appropriate words to fill in the gaps below:
force
Work is done when a _______
moves through a distance.
energy transferred is also equal to the work
The amount of _______
heat
done. When a car brakes energy is transformed to ______.
equal to the force _________
multiplied by the distance
Work done is ______
moved in the __________
of the force. The work done is
direction
measured in ______
joules if the force is measured in newtons and
distance in metres.
the _________
WORD SELECTION:
energy direction force equal multiplied distance heat joules
Gravitational potential energy
Gravitational potential energy (GPE) is the energy stored
in an object when work is done in moving the object
upwards.
GPE = mass x g x height
GPE = m x g x h
GPE is measured in joules (J)
mass, m is measured in kilograms (kg)
gravitational field strength, g is measured
in newtons per kilogram (N/kg)
height, h is measured in metres (m)
Question 1
Calculate GPE gained when
a weightlifter lifts a mass of
120kg up by 2.5m.
(g = 10N/kg)
GPE = m x g x h
= 120kg x 10N/kg x 2.5m
GPE = 3000 J
Question 2
Calculate the gravitational potential energy
gained by a student of mass 70kg climbing a
flight of stairs of height 4m.
GPE = m x g x h
= 70kg x 10N/kg x 4m
GPE = 2 800 J
Kinetic energy
Kinetic energy is the energy possessed by a body
because of its speed and mass.
kinetic energy = ½ x mass x (speed)2
KE = ½ x m x v2
kinetic energy, KE is measured in joules (J)
mass, m is measured in kilograms (kg)
speed, v is measured in metres per second (m/s)
Question 1
Calculate the kinetic energy of a car of mass
1000kg moving at 5 m/s.
KE = ½ x m
= ½ x 1000kg
= ½ x 1000 x
= 500 x 25
kinetic energy
x v2
x (5m/s)2
25
= 12 500 J
Question 2
Calculate the kinetic energy of a child of mass
60kg moving at 3 m/s.
KE = ½ x m x v2
= ½ x 60kg x (3m/s)2
= ½ x 60 x 9
= 30 x 9
kinetic energy = 270 J
Question 3
Calculate the kinetic energy of a apple of mass
200g moving at 12m/s.
KE = ½ x m x v2
= ½ x 200g x (12m/s)2
= ½ x 0.200kg x 144
= 0.100 x 144
kinetic energy = 14.4 J
Question 4
Calculate the mass of a train if its kinetic
energy is 2MJ when it is travelling at 4m/s.
KE = ½ x m x v2
2MJ = ½ x mass x (4m/s)2
2 000 000J = ½ x mass x 16
2 000 000 = 8 x mass
2 000 000 ÷ 8 = mass
mass = 250 000 kg
Question 5
Calculate the speed of a car of mass 1200kg if its
kinetic energy is 15 000J.
KE = ½ x m x v2
15 000J = ½ x 1200kg x (speed)2
15 000 = 600 x (speed)2
15 000 ÷ 600 = (speed)2
25 = (speed)2
speed = 25
speed = 5 m/s
Question 6
Calculate the speed of a ball of mass 400g if its
kinetic energy is 20J.
KE = ½ x m x v2
20J = ½ x 400g x (speed)2
20 = ½ x 0.400kg x (speed)2
20 = 0.200 x (speed)2
20 ÷ 0.200 = (speed)2
100 = (speed)2
speed = 100
speed = 10 m/s
Complete
Answers
kinetic energy
mass
speed
8J
4 kg
2 m/s
27 J
6 kg
3 m/s
1000 J
80 kg
5 m/s
6.4 kJ
200 kg
8 m/s
3.2 J
3.03g
400
4 m/s
Falling objects
If there is no significant air
resistance then conservation
of energy results in
gravitational potential energy
being converted into kinetic
energy as an object falls.
gain in KE = loss of GPE
m
gpe = mgh
ke = 0
h
v1
gpe = ke
gpe = ½ mgh
ke = ½ mv12
v2
gpe = 0
ke = ½ mv22
ke = mgh
½h
Graphs of GPE and KE
TOTAL ENERGY
= GPE + KE
GPE
Energy
KE
0
object
dropped
0
Time
object reaches
lowest point
Question
A child of mass 40kg climbs a
wall of height 3m and then
steps off. Calculate the speed
at which the child reaches the
bottom of the wall.
Child’s initial gravitational
potential energy:
GPE = m x g x h
= 40kg x 10N/kg x 3m
GPE = 1 200 J
If air resistance is insignificant
then all of this GPE is converted
into kinetic energy
KE = ½ x m x v2
1200 J = ½ x 40kg x (speed)2
1 200 = 20 x (speed)2
1 200 ÷ 20 = (speed)2
60 = (speed)2
speed = 60
speed = 7.75 m/s
Choose appropriate words to fill in the gaps below:
potential energy is the energy stored when an
Gravitational ________
upwards This energy is released when the
object is lifted ________.
falls back to its initial position.
object _____
Kinetic energy is the energy possessed by an object due to its
speed and mass. If the mass of an object is ________
doubled its
_______
kinetic energy doubles. If the speed is doubled the kinetic
four
energy will increase by ______
times.
raised
When a __________
object is released gravitational potential
kinetic
energy is converted into _________
energy.
WORD SELECTION:
falls
speed four kinetic potential upwards
doubled raised
Power (P)
Power is a measurement of how quickly work is done.
power = work done
time taken
P= W
t
power, P is measured in watts (W)
work done, W is measured in joules (J)
time, t is measured in seconds (s)
One watt is the same as one joule per second.
Power is also equal to how quickly
energy is transformed from one form to
another.
power = energy change
time
P=E
t
Question 1
Calculate the power of a motor that exerts a force
of 40N over a distance of 2m for 10seconds.
W=Fs
= 40 N x 2 m
work done = 80 J
P=W/t
= 80J / 10 s
power = 8.0 W
Question 2
Calculate the power of an
electric motor that lifts a
mass of 50 kg upwards by
3.0 m in 20 seconds.
gain in GPE = m g h
= 50 kg x 10 N/kg x 3 m
= 1500 J
g = 10 N/kg
P=E/t
= 1500 J / 20 s
power = 75 W
Answers
Complete:
energy
transfer
600 J
work done
time
power
600 JJ
600
120 s
55 W
440 J
440 JJ
440
20 ss
22 W
28 800
28
800JJ
28 800
800 JJ
28
2 hours
4W
2.5 mJJ
2500
2.5 kJ
50 s
50 W
W
50
Measuring a person’s power
1. Measure the weight, W of
person using weighing scales.
s
total stairs
height, h
stairs
of n
steps
person of
weight, W
=nxs
2. Measure the time taken for
the person to run up a flight of
stairs of height, h
3. Work done
= weight x height
=Wxh
=Wxnxs
4. Power of the person
= work done / time taken
= (W x n x s) / t
Example calculation
Weight of person, W = 800N
Time taken, t = 3.0 seconds
s
total stairs
height, h
stairs
of n
steps
person of
weight, W
=nxs
Stairs:
number of steps, n = 12
height of step = 0.20m
total stair height, h
= 12 x 0.20m = 2.4m
Work done
= weight x height
= 800N x 2.4m = 1920J
Power = 1920J / 3.0s
= 640W
Choose appropriate words to fill in the gaps below:
quickly
Power is a measure of how ___________
a device does work.
Power is equal to work done in _________divided
by the
joules
time taken.
power
The _________
of a device is also equal to the rate at which a
device transforms ___________
from one form to another.
energy
watts
Power is measured in _________,
symbol W.
thousand
A one kilowatt motor will perform one ____________
joules
second
of work every __________.
WORD SELECTION:
second
quickly
watts
power
joules
thousand
energy
Work and Power
Notes questions from pages 142 to 149
1.
2.
3.
4.
5.
6.
7.
8.
Give the equation for work done, state the units used and give an
example calculation.
Give the equation for kinetic energy, state the units used and give an
example calculation.
Give the equation for gravitational potential energy, state the units
used and give an example calculation.
Explain how gravitational potential and kinetic energy vary as an
object falls. You should copy all the diagrams on page 146 as part of
your answer.
Give the equation for power, state the units used and give an example
calculation.
Explain how the power of a person can be measured using a flight of
stairs.
Answer the questions on page 149.
Verify that you can do all of the items listed in the end of chapter
checklist on page 149.
Online Simulations
Work (GCSE) - Powerpoint presentation by KT
Kinetic Energy (GCSE) - Powerpoint presentation by KT
Gravitational Potential Energy (GCSE) - Powerpoint presentation by KT
Bouncing ball with different surfaces showing KE & PE - Freezeway.com
Energy Skate Park - Colorado - Learn about conservation of energy with a skater dude!
Build tracks, ramps and jumps for the skater and view the kinetic energy, potential
energy and friction as he moves. You can also take the skater to different planets or
even space!
Rollercoaster Demo - Funderstanding
Energy conservation with falling particles - NTNU
Ball rolling up a slope - NTNU
Pulley System - Fendt
Bicycle gear distance multiplier demonstration - Freezeway.com
BBC AQA GCSE Bitesize Revision:
Work, force and distance
Potential and kinetic energy
Kinetic energy equation