EDEXCEL IGCSE / CERTIFICATE IN PHYSICS 4-3

Work and PowerEdexcel IGCSE Physics pages 142 to 149

June 17th 2012

All content applies for Triple & Double Science

Edexcel SpecificationSection 4: Energy resources and energy transfer c) Work and powerknow and use the relationship between work, force and distance moved in the direction of the force:work done = force × distance moved W = F × dunderstand that work done is equal to energy transferredknow and use the relationship: gravitational potential energy = mass × g × heightGPE = m × g × hknow 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 workdescribe power as the rate of transfer of energy or the rate of doing workuse the relationship between power, work done (energy transferred) and time taken:power = work done / time taken P = W / t

Work and energyWhen 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 frictionWork 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 = F x d

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

F d

W

Question 1Calculate the work done when a force of 5N moves through a distance of 3m.

W = F x d = 5N x 3m

work = 15 J

Question 2

Calculate the work done when a force of 6N moves through a distance of 40cm.

W = F x d = 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 = F x d becomes:

F = W ÷ d

= 600 J ÷ 50 m

force = 12 N

Question 4Calculate the distance moved by a force of 8N when it does 72J of work.

W = F x d becomes:

d = W ÷ F

= 72 J ÷ 8 N

distance moved = 9 m

Question 5Calculate 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 = F x d

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 6Calculate 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 = F x d the person must exert an upward force equal their weightthe person’s weight = (80kg x 10N/kg) = 800Nthe distance moved upwards equals (10 x 25cm) = 2.5mwork = 800 N x 2.5 mwork = 2000 J

Completework force distance

J 50 N 3 m

800 J N 20 m

500 J 250 N m

kJ 4000 N 2 m

2 MJ 3.03 N 5 km

150

40

2

80

400

Answers

Choose appropriate words to fill in the gaps below:

Work is done when a _______ moves through a distance.

The amount of _______ transferred is also equal to the work done. When a car brakes energy is transformed to ______.

Work done is ______ to the force _________ by the distance moved in the __________ of the force. The work done is measured in ______ if the force is measured in newtons and the _________ in metres.

multiplied distance joulesequalforceenergy direction

WORD SELECTION:

heat

multiplied

distance

joules

equal

force

energy

direction

heat

Gravitational potential energyGravitational potential energy (GPE) is the energy stored in an object when work is done in moving the object upwards.

GPE = mass x g x heightGPE = 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 1Calculate 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 2.5mGPE = 3000 J

Question 2Calculate 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 1Calculate the kinetic energy of a car of mass 1000kg moving at 5 m/s.

KE = ½ x m x v2 = ½ x 1000kg x (5m/s)2

= ½ x 1000 x 25= 500 x 25kinetic energy = 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 3Calculate 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 4Calculate 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 162 000 000 = 8 x mass2 000 000 ÷ 8 = mass mass = 250 000 kg

Question 5Calculate 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 = 25speed = 5 m/s

Question 6Calculate 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 = 100speed = 10 m/s

Completekinetic energy mass speed

J 4 kg 2 m/s

27 J kg 3 m/s

1000 J 80 kg m/s

kJ 200 kg 8 m/s

3.2 J 3.03g 4 m/s

8

6

5

6.4

400

Answers

Falling objectsIf 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

h

m

½ h

v1

v2

gpe = mgh

ke = ½ mv22

ke = 0

gpe = 0

gpe = kegpe = ½ mghke = ½ mv1

2

ke = mgh

Graphs of GPE and KE

En

erg

y

Time0

0object dropped

GPE

KE

TOTAL ENERGY = GPE + KE

object reaches lowest point

QuestionA 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 3mGPE = 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:

Gravitational ________ energy is the energy stored when an object is lifted ________. This energy is released when the object _____ back to its initial position.

Kinetic energy is the energy possessed by an object due to its _______ and mass. If the mass of an object is ________ its kinetic energy doubles. If the speed is doubled the kinetic energy will increase by ______ times.

When a __________ object is released gravitational potential energy is converted into _________ energy.

doubledkinetic raisedfalls potential upwardsfour

WORD SELECTION:

speed

doubled

kinetic

raised

falls

potential

upwards

four

speed

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 1Calculate the power of a motor that exerts a force of 40N over a distance of 2m for 10seconds.

W = F s= 40 N x 2 mwork done = 80 J

P = W / t= 80J / 10 spower = 8.0 W

Question 2Calculate the power of an electric motor that lifts a mass of 50 kg upwards by 3.0 m in 20 seconds.

g = 10 N/kg

gain in GPE = m g h= 50 kg x 10 N/kg x 3 m= 1500 J

P = E / t= 1500 J / 20 spower = 75 W

Complete:

energy transfer

work done time power

600 J 600 J 120 s 5 W

440 J 440 J 20 s 22 W

28 800 J 28 800 J 2 hours 4 W

2.5 mJ 2.5 kJ 50 s 50 W

Answers

600 J 5 W

440 J 20 s

28 800 J 28 800 J

2500 J 50 W

Measuring a person’s power1. Measure the weight, W of person using weighing scales.

2. Measure the time taken for the person to run up a flight of stairs of height, h

3. Work done= weight x height= W x h= W x n x s

4. Power of the person= work done / time taken= (W x n x s) / t

total stairs height, h

= n x sstairs of n steps

s

person of weight, W

Example calculationWeight of person, W = 800NTime taken, t = 3.0 seconds

Stairs:number of steps, n = 12height of step = 0.20mtotal stair height, h = 12 x 0.20m = 2.4m

Work done= weight x height= 800N x 2.4m = 1920J

Power = 1920J / 3.0s= 640W

total stairs height, h

= n x sstairs of n steps

s

person of weight, W

Choose appropriate words to fill in the gaps below:

Power is a measure of how ___________ a device does work. Power is equal to work done in _________divided by the time taken.

The _________ of a device is also equal to the rate at which a device transforms ___________ from one form to another.

Power is measured in _________, symbol W.

A one kilowatt motor will perform one ____________ joules of work every __________.

joules energy

thousandquickly power

watts

second

WORD SELECTION:

joules

energy

thousand

quickly

power

watts

second

Work and PowerNotes questions from pages 142 to 149

1. Give the equation for work done, state the units used and give an example calculation.

2. Give the equation for kinetic energy, state the units used and give an example calculation.

3. Give the equation for gravitational potential energy, state the units used and give an example calculation.

4. 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.

5. Give the equation for power, state the units used and give an example calculation.

6. Explain how the power of a person can be measured using a flight of stairs.

7. Answer the questions on page 149.8. Verify that you can do all of the items listed in the end of chapter

checklist on page 149.

Online SimulationsWork (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