gpe and ke · 2015. 10. 6. · what factors does the gpe depend on? what factors does the ke depend...

P G . 1 4 4 & 1 4 5 , S Y L L A B U S 4 . 1 1 & 4 . 1 2

GPE AND KE

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STARTER: MULTIPLE-CHOICE QUIZ


TODAY’S LEARNING OBJECTIVES ARE TO…

End

Calculate (a)  The kinetic energy of objects (b)  Changes in gravitational potential energy of objects

Starter: (1 minute) How do you increase: a)  The kinetic energy of an object b)  The gravitational potential energy of an object


What factors does the GPE depend on?

What factors does the KE depend on?

Which has the most KE? Which has the most GPE?

800kg car travelling at 6 m/s

0.7kg ball travelling at 60 m/s

A 3000 kg helicopter hovering at 20 m

An 80kg man at the top of a 60m ladder

A 0.1kg bullet travelling at 675 m/s

A 20 kg child on top a 300m building


KEY WORDS

Kinetic Energy 운동 에너지

Mass 큰 덩어리

Speed 속도

Energy 중력 위치 에너지

Gravity 중력

Height 높이


A LONG WAY DOWN… How would you describe a bungee jumper?

As someone who is:

l  full of gravitational potential energy (GPE).

l  brave

l  unwise

l  energetic

GPE is the amount of energy an object has because of its position above the ground, i.e. its height.


l  When a bungee jumper starts to fall he starts to lose GPE.

l  As the elastic cord pulls the bungee jumper back up, he gains GPE.

The gravitational potential energy (GPE) of an object on Earth depends on its mass and its height above the Earth’s surface.

WHAT IS GRAVITATIONAL POTENTIAL ENERGY?


HOW IS GPE CALCULATED? The GPE of an object can be calculated using this equation:

GPE = mass × gravitational field strength × height GPE = m x g x h

l  Height is measured in metres (m).

l  Mass is measured in kilograms (kg).

l  GPE is measured in joules (j).

l  Gravitational field strength is measured in newtons per kilogram (N/kg), usually taken as 10 N/kg on Earth.


An osprey with a mass of 2 kg flies at a height of 200 m above the ground.

CALCULATING GPE QUESTION 1

How much gravitational potential energy does the osprey have?

= 2 × 10 × 200

GPE = mass × gravitational field strength × height

= 4,000 J


An apple with a mass of 200 g falls 3 m from its branch to the ground.

CALCULATING GPE QUESTION 2

How much GPE will the apple have lost when it reaches the ground?

= 0.2 × 10 × 3

= 6 J

= mass × gravitational field strength × GPE lost

change in height


QUESTION 3

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 is the energy an object has because it is moving.

WHAT IS KINETIC ENERGY?

The word ‘kinetic’ comes from the Greek word ‘kinesis’, meaning motion.

All moving things have kinetic energy, but the amount of energy they have is not just dependent on how fast they are moving.

What other factors affect the kinetic energy of a moving object?


HOW IS KINETIC ENERGY CALCULATED?

The kinetic energy (KE) of an object can be calculated using this equation:

l  Velocity is measured in metres per second (m/s).

l  Mass is measured in kilograms (kg).

l  KE is measured in joules (j).

KE = ½ × mass × velocity2

= ½mv2


kinetic energy = ½ × mass × velocity2

A car with a mass of 1,500 kg travels at a velocity of 20 m/s.

CALCULATING KINETIC ENERGY QUESTION

What is the kinetic energy of the car?

= 300,000 J = 300 kJ

= ½ × 1,500 × 202


Sometimes it is necessary to rearrange the kinetic energy equation in order to calculate the mass or the velocity of a moving object.

KE = ½mv2

What are the rearranged versions of this equation for calculating mass and velocity?

m = 2KE v2 v = √ 2KE

m

REARRANGING THE KE EQUATION


A lorry has a mass of 20,000 kg. If its kinetic energy is 2.25 MJ, at what velocity is it travelling?

CALCULATING VELOCITY QUESTION

KE = ½ × mass × velocity2

= 15 m/s

velocity = √2KE

mass

= √ 2 × 2,250,000 20,000


THE KINETIC ENERGY OF CARS


Use the KE = ½mv2 equation to fill in the kinetic energy values in the table below for two cars each travelling at two different velocities.

Which factor – mass or velocity – has the greatest effect on the kinetic energy of a moving object?

DANGEROUS SPEEDING?

KE = 800 kJ KE = 1600 kJ

1,000 kg 2,000 kg

20 m/s

40 m/s

KE = 200 kJ KE = 400 kJ

Doubling the mass causes the KE to double.

Doubling velocity causes the KE to quadruple.


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 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


What factors does the GPE depend on?

What factors does the KE depend on?

Which has the most KE? Bullet: 22780J Car: 14400J Ball: 1260J Which has the most GPE? Helicopter: 600 000J Child: 60 000J Ladder: 4800J

800kg car travelling at 6 m/s

0.7kg ball travelling at 60 m/s

A 3000 kg helicopter hovering at 20 m

An 80kg man at the top of a 60m ladder

A 0.1kg bullet travelling at 675 m/s

A 20 kg child on top a 300m building


TASK: 15 MINUTE WS

End


ANSWERS

•  KE •  1. 50KJ •  200KJ •  3. 0.442J •  4. 23.66m/s •  GPE •  2. 125J •  3. 1632J •  4a) 120m •  4b) 15360J


COMPLETE kinetic 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 g 4 m/s

8

6

5

6.4

400

Answers Plenary


gpe and ke · 2015. 10. 6. · what factors does the gpe depend on? what factors does the ke depend...

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