physics matters for gce ‘o’ level unit 6: energy, work and power

PHYSICS Matters for GCE ‘O’ Level

Unit 6: Energy, Work and Power

Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.

6.1 Energy

In this section, you’ll be able to:

• identify different forms of energy – kinetic energy, elastic potential energy, gravitational potential energy, chemical potential energy and thermal energy

• state the Principle of Conservation of Energy

• solve problems using the Principle of Conversation of Energy


6.1 Energy

What is Energy?

• Energy is the capacity to do work.

• The SI unit of energy is the joule (J).


6.1 Energy

Different forms of energy and energy conversions

There are many forms of energy. Examples include:

• Kinetic energy

• Potential energy

• Sound energy

• Electrical energy

• Thermal energy

• Light energy


6.1 Energy

Kinetic Energy

In windy places, wind is used to turn turbines that convert kinetic energy to electrical energy.

• Moving objects have kinetic energy.

• Kinetic energy can be used to do work.


6.1 Energy

Potential Energy

• Energy that is stored is known as potential energy.

• Potential energy can be converted to kinetic energy and vice versa.

• Potential energy exists in many forms.


Chemical Potential Energy

• Food contains chemical potential energy which is converted from solar energy via photosynthesis.

• These can be converted to kinetic energy.

6.1 Energy

How energy is transferred from the sun to humans and animals.


Chemical Potential Energy

• Chemical potential energy is also stored in fossil fuels like coal and oil.

• A battery also stores chemical potential energy that can be converted to electricity.

6.1 Energy


Elastic Potential Energy

• A spring or rubber band possesses elastic potential energy when it is compressed or stretched.

• This energy is converted to kinetic energy when the spring or rubber band is released.

6.1 Energy

An archer makes use of the elastic potential energy stored in the bow to propel the arrows. A fully flexed bow stores about 300 J of energy.


Gravitational Potential Energy

• An object has gravitational potential energy when it is raised to a certain height above the ground.

• When released, it falls and gravitational potential energy is converted to kinetic energy.

6.1 Energy

When a ball is being dropped from a height, it falls and the gravitational potential energy it has is converted to kinetic energy.


Principle of Conversation of Energy

Energy can neither be created nor destroyed in any process. It can be converted from one form to another or transferred from one body to another, but the total amount remains constant.

6.1 Energy

When energy is converted from one form to another, the total amount remains constant.

20 J energy in one form

20 J energy in another form


Conversion of Energy

Diver on a diving board

Stored chemical energy in the body of a diver allows him toexert a push to bend the diving board. This causes the bentdiving board to store elastic potential energy which is thenconverted to kinetic energy that helps push the diver upwards.

6.1 Energy

Elastic potential energy is converted to kinetic energy, helping to push the boy upwards.



Hammering a nail

A raised hammer possesses gravitational potential energy. When it falls, this energy is converted to kinetic energywhich is used to do work in driving the nail into the woodblock. Sound and thermal energy are also produced andreleased by the block, nail and hammer.

6.1 Energy

When the hammer falls, gravitational potential energy is converted to kinetic energy.



Burning of Fuels

By burning fuels, the stored chemical energy in these fuelsis converted to thermal and light energy.

6.1 Energy

Burning charcoal in a barbecue pit emits a lot of thermal energy to cook food.



In real life, energy is easily dissipated into the surroundings.This makes it difficult for us to compare the amount ofenergy before and after conversion in order to study thePrinciple of Conservation of Energy effectively.

6.1 Energy


Principle of Conservation of Energy and the ideal pendulum

6.1 Energy


6.1 Energy

Principle of Conservation of Energy and the non-ideal pendulum

In the real world, frictional forces convert some of the total energy of a swinging pendulum to thermal energy.

This thermal energy is dissipated to the surroundings and cannot be converted back into kinetic or gravitational potential energy of the pendulum.


6.1 Energy

Principle of Conservation of Energy and the non-ideal pendulum

The pendulum eventually comes to a stop.

Height gained is lower than the original because some of the energy has been converted to thermal energy.


6.1 Energy


Efficiency

From the Principle of Conservation of Energy, the totalenergy output by a machine must be equal to its energyinput.

In real life, energy output is always less than energy inputas energy is dissipated, due to friction, or as a form ofsound and thermal energy.

This energy lost is considered wasted energy output.

6.1 Energy


6.1 Energy

Efficiency

Energy input = useful energy output + wasted energy

100% inputenergy

outputenergy useful Efficiency =


6.1 Energy

Key Ideas

1. Energy is the capacity to do work.

2. Energy can be converted from one form to another.

3. The Principle of Conservation of Energy states that energy can neither be created nor destroyed in any process. It can be converted from one form to another or transferred from one body to another but the total amount remains constant.


6.1 Energy

Test Yourself 6.1

1. A softball player throws a ball into the air and catches it on the way down. State the energy conversions that take place.

K.E

partly K.E,partly G.P.E

G.P.E

partly K.E,partly G.P.E

K.EA

B

C

D

E

Answer:• When the ball left the player’s hand

(at A), it has kinetic energy.

• As it rises up (at B), part of the K.E. is converted into gravitational potential energy.

• At the point of maximum height (at C), the ball has grav. P.E.

• As it is falling down (at D), part of the grav. P.E. is converted into K.E.

• When the ball reaches the player’s hand (at E) it will have only K.E.


6.1 Energy

Test Yourself 6.1

2. A cyclist pedals up to the top of a hill at a steady speed. Whatkind of energy is being used to do work against gravity? Statethe type of energy the cyclist has at the top of the hill. Whenthe cyclist moves downhill without pedaling, what type ofenergy does he gain?

The cyclist uses his stored chemical energy. The chemical energy is converted into gravitational potential energy as he rises up the hill.

When he moves downhill, the G.P.E. is converted into kinetic energy. Without him pedaling, he is gaining K.E as he moves downhill.

Answer:


6.1 Energy

Test Yourself 6.1

3. Using the Principle of Conservation of Energy, explain:

a) What happens to the stored chemical energy of a dry cell when it is connected to a light bulb?

Answer:The chemical energy in the dry cell is converted into electrical energy that drives a current round the circuit.The light bulb converts the electrical energy into light energy as well as thermal energy.

b) Why a ball released from rest at a certain height above the floor bounces up to a lower and lower height until it finally comes to a stop?

Answer:Every time the ball hits the floor, some of the kinetic energy of the ball is converted into sound energy and heat energy. Hence, the ball will rise to a lower height after each bounce.


6.2 Work

Learning Outcomes

In this section, you will be able to:

• Understand the concept of work and apply the relationship W = F s to solve problems

• Apply the relationships

to solve problems 1h g m Eand vm

2 E 2

k == p


6.2 Work

Work Done

Definition: Work done by a constant force on an object is givenby the product of the force and the distance moved by the objectin the direction of the force.

W = F s

where W = the work done (in J), F = the constant force (in N) s = the distance moved in the direction of the force (in m)


6.2 Work

The SI unit of work is the joule (J).

Definition: One joule (J) is defined as the work done by a force

of one newton (N) which moves an object through a distance of

one metre (m) in the direction of the force.

one joule = one newton one metre1 J = 1 N m


6.2 Work

Example of work being done: Lady pushing a pram


6.2 Work

No work is being done when:

1. The direction of the applied force and the direction in which the object moves are perpendicular to each other.

A man carrying a load while walking. No work is done on the load in the upward direction as the load is only moving horizontally.


6.2 Work

No work being is being done when:

2. The force is applied on the object (such as the wall or the pile of books) but the object does not move.

Boy pushing against a solid wall.

A girl holding a heavy pile of books in a stationary position does no work.


6.2 Work

How is energy related to work and force?

We need energy to move an object, run and climbstairs.

To move a stationary object, we need to applyforce to them.

For a moving object, we also need to apply force toincrease its speed.

Hence, work is done when we move a stationaryobject or make a moving object move faster.


6.2 Work


6.2 Work

Mechanical Energy

There are two types of mechanical energy:

1. Kinetic energy

2. Gravitational potential energy

A roller coaster uses a motor-and-chain system to pull the riders up the first hill before letting gravity take over the rest of the ride.


6.2 Work

Kinetic energy and work done

A moving body has kinetic energy. When a force movesan object, it does work and the object gains kineticenergy.

Kinetic energy is defined as:

)s m (inbody the of speed

and kg) (inbody the of mass

J), (inenergy kinetic E where

1

1–

k

=

=

=

v

m

2 E

k= mv2


6.2 Work

Gravitational potential energy and work done

Potential energy is stored energy• Gravitational potential energy (G.P.E) is the energy a body

has due to its position• To find G.P.E. of an object near surface of Earth, we need to

consider its mass and its height above the ground.

An object of mass m raised to a height h above ground level possesses G.P.E. of mgh.


6.2 Work

Gravitational potential energy and work done

Gravitational potential energy is defined as:

m) (in height

)kg N (in strength field nalgravitatio

where

1–

=

=

J), (inenergy potential nalgravitatio E p =

h

g

kg) (inbody the of mass =m

g E p = hm


6.2 Work


6.2 Energy, Work and Power

Figure 6.23


6.2 Work

Key Ideas

1. Force, work and energy are interrelated.

2. Work done W by a constant force F is given by the product of the force F and the distance moved in the direction of the force, i.e. W = F s.

3. The SI unit of work is the joule (J), which is the same as the SI unit of energy.


6.2 Work

Key Ideas

4. No work is done when

a. The direction of the applied force and the direction in which the object moves are perpendicular to each other

b. The force is applied on the object but the object does not move.

5. Moving objects have kinetic energy. The kineticenergy of an object of mass m in kilograms andspeed v in m s–1 is given in joules by the expression:

2

k 21 E mv=


6.2 Work

Key Ideas

6. An object of mass m kg at height h has gravitational potential energy given by Ep = mgh where g is the

gravitational field strength (10 N kg–1).

7. Potential energy can be converted to kinetic energy and

vice versa. The total energy in a system is fixed. If all the

gravitational energy is converted to kinetic energy or all

the kinetic energy is converted to gravitational potential

energy, the equation is true.2

21 mvmgh =


6.2 Work

Test Yourself 6.2

1. (a) Define the joule.

Answer: One joule is defined as the work done by aforce of one newton which moves an object through adistance of one metre in the direction of the force.

(b) Complete the table by filling in the missing quantities (in bold).

Force exerted

Distance moved in the direction of force

Work done

(i) 20.0 N 10 m 200 J

(ii) 0.1 N 10 m 1 J

(iii) 0.04 N 20 m 0.8 J

(iv) 500 N 7200 m 3.6 106 J


6.2 Work

Test Yourself 6.2

2. A block of mass 4 kg slides fromrest through a distance of 30 mdown a frictionless slope, asshown in the diagram. What isthe kinetic energy of the blockat the bottom of the slope?

Answer:

At the top, the block has G.P.E

G.P.E = m g h= 4 10 5 = 200 J

At the bottom, the G.P.E is converted into K.E.Hence, the K.E of the block at the bottom is 200 J.

5 m4 kg

30 mG.P.E

K.E


6.2 Work

Test Yourself 6.2

3. If the speed of a springboard diver decreases by half on entering the water, by how much will his kinetic energy decrease?

2imv

21K.E Initial

Answer:

Let the initial speed of the diver just before he hit the water be vi ,

and the final speed after he entered the water be vf . Since speed

is decreased by half, i.e.

2i

2

i

mv21

41

2v

m21 K.E Final

Hence, the final K.E is now one quarter of the initial K.E.

12

vf = vi


6.2 Work

Test Yourself 6.2

4. A package of 5 kg is lifted vertically through a distance of 10 m at a constant speed. Taking acceleration due to gravity to be 10 m s–2, what is the gravitational potential energy gained by the package?

Answer:Gravitational P.E = m g h

= 5 10 10= 500 J

Hence, the package gained 500 J of gravitational potential energy.

5 kg

10 m

G.P.E


6.3 Power

Learning Outcomes

In this section, you will be able to:

• Recall and apply the relationship to solve problems. taken time

donework power


6.3 Power

What is power?

Power is defined as the rate of work done or rate ofenergy conversion.

s) (in taken time t

and J) (in converted energy E

J) (in donework W

power P where

tE

tW P


6.3 Power

The SI unit of power is the watt (W). One watt (W)is defined as the rate of work done or energyconversion of one joule per second.

1-s J 1 W 1second onejoule one

watt one


6.3 Power


6.3 Power

Key Ideas

1. Power is the rate of work done or energy converted.

2. The SI unit of power is the watt (W). One watt is the rate of work done at 1 joule per second.


6.3 Power

Test Yourself 6.3

1. (a) Define the watt.

Answer: One watt is defined as the rate of work done or energy conversion of one joule per second.

(b) What is meant by power?

Answer: Power is defined as the rate of work done or rate of

energy conversion.


6.3 Power

Test Yourself 6.3

1. (c) In the following situations, calculate the power involved.

(i) A force of 50 N moves through a distance of 10 m in 5 s.

Answer:== W 100

510 50

ts F

tW

P ==

(ii) An object of mass 1 kg is lifted up vertically through 5 m in 10 s.

Answer:

W 5 10

5 10 1

tmgh

tEP

==

==


6.3 Power

Test Yourself 6.3

2. An electric motor in a washing machine has a poweroutput of 1.0 kW. Find the work done in half an hour.

Answer:Given Power P = 1.0 kW = 1000 W and

Hence, the work done W = 1.8 106 J

12

time t = = 0.5 60 60 = 1800 shour

J101.8

1800 1000

t PW

tW

P

6=

=

=

=

physics matters for gce ‘o’ level unit 6: energy, work and power

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elastic potential energy

chemical potential energy

thermal energy state