Gravitational Potential and Kinetic Energy

Learning objectives:

• Define Gravitational potential energy + KE and describe factors that affect Gravitational potential energy
• Calculate energy problems using the correct equations
• Rearrange energy equations and convert units when calculating energy problems

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Key Vocabulary:

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Kinetic energy

Gravitational potential energy

Thermal energy

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Starter 1

A stretched a spring is storing 7500J of elastic potential energy. It has a spring constant of 12N/m to an extension of ?

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Starter 2

What is the difference between Gravitational Energy and Kinetic Energy?

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Starter 3

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What factors affect GPE?

Challenge:

What is a possible formula for KE?

Gravitational Potential and Kinetic Energy

Learning objectives:

• Define Gravitational potential energy + KE and describe factors that affect Gravitational potential energy
• Calculate energy problems using the correct equations
• Rearrange energy equations and convert units when calculating energy problems

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Key Vocabulary:

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Kinetic energy

Gravitational potential energy

Thermal energy

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Starter 1

EPE = 1/2 × k × x^2

x=(√2EPE)​​/k

=√15000 / 12

=35.36m

Starter 2

GPE-Energy stored in an object due to its position in a gravitational field.

KE:Energy due to motion

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Starter 3

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Mass, height, gravity

Challenge:

What is a possible formula for KE?

Gravitational Potential Energy

What is gravitational potential energy?

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What factors could affect gravitational potential energy?

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What do you think the equation for gravitational potential energy could be?

Gravitational Potential Energy

Any object raised above the ground has a store of GPE.

GPE is dependent on the mass of the object, the gravitational field strength and the height its raised.

GPE = mass x g x height

1. What are the units for mass, height and GPE?
2. Which has a greater store of GPE – the jug or the plant pot?

12m.

2.3m

0.25kg

0.16kg

ON WB

Gravitational Potential Energy

Mass is measured in kg.

Height is measured in m.

GPE is measured in Joules, because it is an energy.

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Jug: 0.25 x 9.8 x 1.2 = 3J

Plant pot: 0.16 x 9.8 x 2.3 = 3.68J

1.2m

2.3m

0.25kg

0.16kg

• Gravitational potential energy is a stored type of energy.
• The more height an object has the more gravitational potential energy it has.
• If object A has more mass, and is at the same height as object B with less mass, object A will have more gravitational potential energy.

Key words – Stored, Energy, Gravitational potential, mass, height

GPE energy:

Challenge – Create an equation for GPE energy. Think carefully about the variables that will be in there!

Gravitational potential energy equation

Create a triangle for this formula.

Write down the answer AND how you worked it out:

Oliver is stood 20m on top of a building and has a mass of 60kg. If the strength of gravity is 10 N/Kg, what is his Gravitational potential energy?

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Show all working out!

Write down the answer AND how you worked it out:

1. Luke is stood 50m on top of a Cliff and has a mass of 55kg. If the strength of gravity is 9.81 N/Kg, what is his Gravitational potential energy?

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2. Sophia is stood 30m on top of a hill. She has a mass of 65kg. If the strength of gravity is 9.8 N/kg, how much gravitational potential energy does she have? As a challenge: what other form of energy is relevant here and how would we calculate it?

Show all working out!

ON WB

Stretch:Emma is stood on a platform 80m high, and she has a mass of 52kg. The strength of gravity is 9.8 N/kg. If Emma jumps from the platform and falls freely under gravity, how much kinetic energy does she have just before she hits the ground?

Solutions

1)Ep​=mgh

Ep​=55×9.81×50

Ep​=55×490.5=26,477.5J

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2)Ep​=mgh

Ep​=65×9.8×30

Ep​=65×294=19,110J

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Stretch:

Ep​=mgh

g=9.8N/kg

h=80m

m=52

Ep​=52×9.8×80

Ep​=52×784=40768J

Since there is no energy loss (we aren’t counting air resistance), all of Emma's gravitational potential energy will be converted into kinetic energy as she falls.

Kinetic Energy

What is kinetic energy?

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What factors could affect kinetic energy?

What do you think the equation for kinetic energy may be?

Kinetic energy equation

Create a triangle for this formula.

Using the Equation:

What factors could affect kinetic energy?How? Provide an example

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ON WB

1. Mass
1. Kinetic energy is directly proportional to mass. If the mass of the object increases, its kinetic energy will increase, assuming the velocity stays the same.
2. E.g: A truck moving at the same speed as a bicycle will have much more kinetic energy because of its greater mass.

2. Velocity:

• Kinetic energy is proportional to the square of the velocity. This means that even a small increase in velocity results in a much larger increase in kinetic energy.
• E.g: If a car's speed doubles, its kinetic energy increases by a factor of four, because v2 would be four times greater.

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Kinetic energy

1. If Aaron and Kabir are both running at 15m/s towards you, who is going to do more damage/hurt more? Why?

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2) If Aaron runs into you at 20m/s or walks into at 1m/s, which will do more damage/hurt more? Why?

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Aaron

Kabir

Kinetic energy

• Kinetic energy is the energy of something in motion.
• Things moving with a higher velocity have more kinetic energy.
• If object A has more mass, and is moving at the same velocity as object B with less mass, object A will have more Kinetic energy.

Key words – Motion, Energy, Kinetic, Velocity, Mass

What can affect an objects velocity?

AFL Task: Worksheet

Gravitational Energy=mass x gravity x height 

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Write down the answer AND how you worked it out:

Aarav is running 20m/s and has a mass of 55kg. What is his Kinetic energy?

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Show all working out!

Kg

m/s

J

Write down the answer AND how you worked it out:

1. Huda is running 10m/s and has a mass of 48kg. What is her Kinetic energy?

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2. Bhavya has a kinetic energy of 30,000J and is traveling at 20m/s, what is his mass?

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3. Zoya has a kinetic energy of 1200J and has a mass of 60kg. How fast is she moving?

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Recall……

The law of conservation of energy states that:

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Energy cannot be created or destroyed, only transformed from one form to another. It is always conserved.E

Plenary - True/False

• If an object has more height it has more GPE.
• Energy can be created and destroyed as well as transformed.
• A shot put with a mass of 10kg on a shelf 5m high has 500J of GPE.
• The 10kg shot put travelling at 20m/s has 4000J of kinetic energy.

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