Year 8 Term 2 Science

Work, Energy and Power 3

Name: ( ) Homeroom:

Unit Three – Taking care of our planet

Key concept: Change Related concepts: energy, environment

Global concept: Globalization and sustainability

Significant Concept: Increased consumption and neglect of the environment

can lead to disastrous environmental consequences.

Inquiry question: How can we continue to use natural resources to maintain

our standard of living?

In this chapter, you are going to learn the following equations:

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If the man in the picture is moving the van, we

say he is doing _______________________.

The force opposing the movement of the van is

___________________________.

The man can only do this work if he has some

___________________________.

If the man pushes with a stronger force or moves it a longer distance he will

do more work. In fact the relationship can be shown as follows:

Work done = force × distance moved

(newtons) (metres)

The distance used in this formula must be the distance moved in the

__________________________ of the force.

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If the force is in newtons and the distance is in metres then the work is

measured in _______________________, often written ___________.

1 N.m = 1 Joule Joules are the units for ______________________________.

1 joule is the useful _______________________ transferred, when a force of 1

_______________________ moves an object 1 _______________________ (in the

direction of the force).

Example problems

1. A man lifts a brick of mass 5 kg from the

floor to a shelf 2 metres high. How much

work is done?

The opposing force in this case is the

_______________________of the brick.

Here on Earth a mass of 1 kg weighs 10 newtons.

Make a list of what you know and don’t know.

Then write the formula: Work done(J) = force(N) × distance moved(m)

Then substitute: = 50N × 2m

=100 joules

Where does he get the energy to do this work?

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Could he do this work if he did not eat?

2. If a man pushes a van against a friction force of 300 newtons for a

distance of 10 metres how much work does he do?

Large amounts of work many be measured in _______________________ or even

_______________________. Show your working:

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Power If two cars of the _______________________weight climb up the

_______________________ hill, then they do the _______________________ amount of

work. But if car A climbs the hill in a shorter time than the other car, we say

it has a greater _______________________. Power is the _____________________________

(the rate of transferring energy).

Power= work done(¿ joules)time taken(¿ seconds)

= energy transferredtime taken

The work done is measured in joules, the time taken

is measured in seconds and so power is measured

in _____________________________or ___________________(W).

1 watt (1 W) = 1 joule per second

The power of very powerful engines may be

measured in ___________________________(kW) or even ___________________________

(MW).

1kW = 1 kilowatt = 1000 watts

1MW = 1 megawatt = 1 000 000 watts.

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Example

A crane lifts weighing 3000N through a

height of 5 m in 10 seconds.

What is the power of the crane?

Calculate it in two parts:

Formula first: Work done(J) = force(N) × distance moved(m)

Then put in the numbers: 3000 N × 5 m

=15 000 joules

Formula first: Power=work donetimetaken

Then put in the numbers: 15000 joules10 seconds

= 1500W = 1.5 kW

A family car might develop a power of 50 kW, a racing car perhaps 500kW

and a Moon rocket 1 00 000 MW.

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Calculating Potential Energy (PE)

1. Gravitational Potential Energy

This weight-lifter is lifting a mass of 200kg, up

to a height of 2 metres.

The potential energy of his weights:

gravitational PE = work done So:

change in PE (joules) = weight (N) × change in height (m)

But

weight (in N) = mass (in kg) × g

where g = 10ms-2 here on Earth. So:

change in gravitational PE = mass × g × change in height

(joules) (kg) (N/kg) (m)

g has different values on other _______________________.

2. Elastic Potential Energy (strain energy)

This is the kind of energy stored in a bow, or in a

catapult, or in a spring in a clock.

Energy stored = work done to stretch the bow,

so:

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Elastic energy = average force × distance

(joules) (newtons) (metres)

Example

Robin Hood exerts an average

force of 100 N in pulling back his

bow by 0.5 m . He fires the arrow

(mass = 0.2 kg) vertically upwards.

How much energy is stored in his

bow, and how high does the arrow

go?

Elastic energy = average force × distance

= 100 N × 0.5 m = 50 joules

Since this energy is _______________________, then this must be the

________________________________as the arrow leaves the bow, and it must also

equal the ___________________________ at its highest point:

mass × 10 × height = 50 joules

0.2 × 10 × height = 50

Therefore, height = 25 metres

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Calculating Kinetic Energy (KE)

A running elephant has more kinetic

energy than a running man, because it has

more mass. A racing car has more kinetic

energy than a family car because it has a

higher speed.

In fact, the formula for the kinetic energy is:

Kinetic Energy = ½ × mass × speed squared

(joules) (kg) (m/s) 2

Example 1

An elephant of mass 2000kg travelling at 5m/s has

KE = ½ × 2000 × 5 × 5 = 25 000 joules.

Example 2

Galileo drops a stone from the leaning tower

of Pisa, which is 45 metres high. At what

speed does the stone hit the ground?

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The energy is ___________________________ so, assuming no air resistance:

When the stone hits the ground, the kinetic energy is transferred to heat and

sound energy.

Example 3

A car of mass 800 kg is travelling at 10

m/s. When the brakes are applied, it

comes to rest in 8m. What is the

average force exerted by the brakes?

The car’s KE is transferred to heat the brakes.

Work done = Energy transferred

Force × distance moved = 12 × mass × speed2

Force × 8 = 12× 800 × 102

Therefore, average braking force = 5000newtons

The same method can be used if there is a force _______________________an

object for a certain distance.

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Can you recall those equations?

Work done =

(Joules)

Power =

(W) or (Js-1)

Gravitational PE = work done

Change in PE =

(Joules)

Change in gravitational PE =

(Joules)

Elastic energy =

(Joules)

Kinetic Energy =

(Joules)

Gravitational energy at the top = kinetic energy at the bottom

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Exercises:

WORK

1. A man lifts a parcel weighting 5 newtons from the ground to a shelf 2

meters high. How much work does he do on the parcel?

2. A girl weighing 500N climbs 40m vertically when walking up the stairs

in an office block. How much work does she do against gravity? What

are the energy transfers here?

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3. You’re pulling a chest of drawers over 10 meters, applying a force of 60

newtons. How much work do you do?

4. You’re pushing an out-of-gas car down the road, applying a force of 800

N. How much work have you done in moving the car 10m?

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5. You’re dragging a sled over 1km with a force of 20N. How much work

do you do?

6. You’re pushing a box of dishes across the kitchen floor, using 100J to

move it 10m. What is the force you used?

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POWER

1. A man lifts a weight of 300N through a vertical height of 2m in 6

seconds.

a) How much work does he do? b)What power does he develop?

2. A man weighing 1000N runs up some stairs, rising a vertical height of

5m in 10seconds. What power does he develop?

3. A crane lifts a load of 3000N through a vertical height of 10m in 4

seconds. What is its power in a)watts b) kilowatts?

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4. An electric lamp is marked 100W. How many joules of electrical energy

are transformed into heat and light

a) during each second, and b) during a minute?

KINETIC ENERGY

1. You ‘re ice skating and travelling at 30m/s. If your mass is 65kg, what

is your kinetic energy?

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2. You’re travelling in a car at 88m/s. If you have a mass of 80kg and the

car has a mass of 1200kg, what is the total kinetic energy of you and

the car combined?

3. A 0.5kg football is moving with 4J of kinetic energy. What is its speed?

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4. A 70kg athlete runs with 5040J of kinetic energy. What is his speed?

5. A car of mass 1000kg is moving at 30m/s.

a. What is its kinetic energy?

b. It slows to 10m/s. What is the KE now?

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c. What is the change in kinetic energy?

d. If it takes 80 meters to slow down by this amount, what is the

average braking force?

POTENTIAL ENERGY

1. If you’re in an airplane at 10000m, what is your potential energy of you

have a mass of 50kg?

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2. A 40kg box of books falls off a shelf that’s 4m above the ground.

a. What was its potential energy before it fell?

b. How much kinetic energy does it have as it hits the ground?

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c. How fast is the box travelling when it hits the ground?

3. A flagpole on top of a 300m skyscraper falls off. How fast is it falling

when it strikes the ground? (Hint: Let m be its mass.)

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4. You jump out of an airplane at 1 kilometer, and fall 600 meter before

opening your parachute. What is your speed (neglecting air resistance)

when you open your parachute>

(Hint: PE at the beginning

= PE when you open your parachute

+ KE when you open your parachute)

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Questions (For each question show all your working clearly.)

1. How much work is done in these situations:

a) A man pushes a van against a friction force of

300N for 10m.

b) A mother pushes a pram with a force of 30N

for a distance of 100m.

c) A weight-lifter lifts a weight of 500N through a height of 2m.

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2. A worker pushes a barrow at a steady speed of 2m/s for 10s, using a force

of 100N.

a) How far did he travel?

b)How much work is done?

c) Where does the energy come from?

3. A boy with a mass of 60kg climbs 10m vertically up a ladder.

a) What is his weight?

b) How much work is done?

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c) What are the energy changes here?

4. An archer pulls back the arrow in his bow a distance of 0.5m against and

average force of 200N.

a) How much work is done?

b) What are the energy changes here?

5. A car is travelling along the road

with 40 000 J of kinetic energy.

The brakes are applied and it comes to

rest in 20m.

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a) Calculate the average braking force.

b) What happens to the kinetic energy?

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1. A boy does 500 J of work in 10 seconds. What is his power output?

2. A mother pushes a pram with a force of 30N for a distance of 100m in 50s.

What is her power output?

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3. An electric lamp is marked 60W. How much energy does it

transfer a) in 1 second? b) in 100seconds? c) What are the

energy transfers here?

4. An athlete runs a 100m race in 10s against a friction force (drag) of 100N.

What is his power output?

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5. A weightlifter lifts an object of mass 30kg through a height of 2m in 3

seconds.

a) What is the weight of the object?

b) What is the work done on the object?

c) What is his power output?

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6. A boy weighing 600N runs up the stairs,

a) in 3 seconds, and then

b) in 4 seconds.

The vertical height of the stairs is 4m. What is

his power output in each case?

7. A lift containing 6 people is raised through a height of 20m in 10s. The

total weight of the lift and passengers is 6000N. What is the power of the lift

motor,

a) in watts?

b) in kilowatts?

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Experiment!

Personal Power

Questions:

1. What is your power in kilowatts?

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2. If you were pedaling hard on a bicycle connected to a generator

(dynamo), how many 60W lamps could you keep alight?

3. Estimate the power of (a) a baby, (b) an athlete.

4. What are the energy transfers in this experiment?

5. In what sense does your power come from the Sun?

Questions (For each questions show all your working clearly.)

1. A lot of energy is wasted in a car. For every 100J of chemical energy in the

petrol, only 25J are transferred to useful kinetic energy. The rest just heats

up the engine and the air.

a) Draw an Energy Transfer Diagram for this, to scale.

b) Calculate the efficiency.

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2. The diagram shows the energy

transfers for a Bunsen burner

heating a beaker of water. What is

its efficiency as a water heater?

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3. In a solar cell, for every 80J of solar energy shining on it, only 4J is

transferred to useful energy (as electricity).

a) What happens to the other 76J?

b) What is its efficiency?

c) Draw a Sankey diagram of this, to scale.

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4. A pulley system lifts a load and gives it 6000J of potential energy. The

person pulling on the rope gives it 8000J of energy. What is the efficiency?

5. An electric kettle has a power rating of 2kW and is switched on for 100

seconds. While heating up, it loses 60 000J to the surroundings.

a) How much energy is supplied to the kettle?

(1 kW=1000W=1000 joules per second)

b) How much is given to the water?

c) What is the efficiency of heating water?

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6. An electric motor on a building site has a

power rating of 400W and lifts a load of bricks

weighing 600N through a height of 10m in 20

seconds.

a) How much energy is needed to lift the

bricks?

b) How much energy is supplied to the motor in 20 seconds?

c) What is the efficiency of the motor in doing this job?

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2. The same diver now climbs to the 5m platform, four times as high.

a) What is his change in PE now?

b) What is his speed as he hits the water?

c) What do you notice about this answer?

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3. Another diver, of mass 80kg, climbs to the 5m platform.

a) What is her speed as she hits the water?

b) What do you notice about your answer?

4. A stone is dropped from a window 5m high. At what speed does it hit the

ground?

5. A tennis player hits a ball vertically with a speed of 10m/s. How high does

it go?

6. A car of mass 600 kg is travelling

at 10m/s. when the brakes are

applied, it comes to rest in 10m.

What is the average force exerted by the brakes?

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7. A car of mass 800kg is at rest. The engine exerts a resultant force of

2000N for a distance of 5m.

a) What is then its KE?

b) What is then its speed?

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