Gravitational Gravitational Potential and Kinetic Potential and Kinetic EnergyEnergyGCSE PhysicsGCSE Physics

Learning IntentionsLearning Intentions

By the end of the lesson we will be able By the end of the lesson we will be able to…to…

- State how State how Work DoneWork Done and and GPE GPE are are linkedlinked

- Recall the Recall the equationsequations for calculating for calculating PotentialPotential and and KineticKinetic energy energy

- Solve some simple problems related to Solve some simple problems related to GPE and Kinetic energyGPE and Kinetic energy

What is Gravitational What is Gravitational Potential Energy (GPE) ?Potential Energy (GPE) ?

An object lifted up An object lifted up vertically has the vertically has the ability to fall back ability to fall back to its original to its original position, it has the position, it has the potential to potential to movemove. We say the . We say the object has gained object has gained GPEGPE..

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GPE in action…GPE in action…

GPE linked to Work DoneGPE linked to Work Done

Consider the stone lifted up- what is the Consider the stone lifted up- what is the work donework done on the stone? on the stone?

Wd = F x dWd = F x d

= (2 x 10) x 5= (2 x 10) x 5

= 100 J= 100 J

This is also equal to This is also equal to potential energy potential energy gainedgained by the stone. by the stone.

5 m

2 kg

Equation for GPEEquation for GPE

GPE = Weight x Height above the groundGPE = Weight x Height above the ground

Joules (J) = Newton (N) x metre (m)Joules (J) = Newton (N) x metre (m)

Important Note- it is the height lifted Important Note- it is the height lifted against gravity that mattersagainst gravity that matters

5 m

2 kg

Wor

d

Equat

ion

Units

Newton’s CradleNewton’s Cradle

Newton’s cradle can help us understand the Newton’s cradle can help us understand the factors that effect GPEfactors that effect GPE

If we increase the height the ball is released If we increase the height the ball is released from, what will happen to show that the GPE from, what will happen to show that the GPE has also increased?has also increased?

When we lift up more than one ball and release When we lift up more than one ball and release them what happens?them what happens?

Which factor does this show effects GPE?Which factor does this show effects GPE?

What is Kinetic Energy?What is Kinetic Energy?

Any object which is Any object which is in motionin motion has kinetic has kinetic energy.energy.

Speed around the Sun –107 000 km/hr or 66 500 mph

Fastest man on the planet over 100 metres

10.32 m/s or 23.1 mph

What does KE depend What does KE depend on?on?

Consider a flying pig heading towards you- if Consider a flying pig heading towards you- if you had to you had to stop the pigstop the pig what two factors (or what two factors (or variables) would you be concerned about?variables) would you be concerned about?

The The speedspeed it is moving towards you it is moving towards you The The massmass of the pig of the pig

Equation for KEEquation for KE

Kinetic Energy = ½ x Mass x SpeedKinetic Energy = ½ x Mass x Speed22

KE KE = ½ = ½ xx mm xx vv22

JoulesJoules = = kg x metre/secondkg x metre/second

Wor

d Equ

atio

n

Units

Dim

ensi

ons

KE linked to Work DoneKE linked to Work Done

Consider a stone of mass m kilograms, Consider a stone of mass m kilograms, increasing in speed from 0 to v m/s in time t increasing in speed from 0 to v m/s in time t secondsseconds

Work Done = Work Done = ForceForce x x DistanceDistance ForceForce = Mass x Acceleration = Mass x Acceleration

= = m x (v / t)m x (v / t) DistanceDistance = Average Velocity x Time = Average Velocity x Time

= = ½ v x t½ v x t Work DoneWork Done = = m x (v / t)m x (v / t) x x ½ x v x t½ x v x t

= = ½ x m x v½ x m x v22

Kinetic Energy = Work Done= ½ x m x vKinetic Energy = Work Done= ½ x m x v22

t = 0 t = t

v0

Example Question on KEExample Question on KE

What is the KE of a football of mass 0.4 What is the KE of a football of mass 0.4 kg moving at a speed of 10 m/s?kg moving at a speed of 10 m/s?

KE = ½ x m x vKE = ½ x m x v22

= 0.5 x 0.4 x 10= 0.5 x 0.4 x 1022

= 20 J= 20 J

Back to Earth…Back to Earth…

Mass is 5.98 x 10Mass is 5.98 x 102424 kg kg Speed is 30 000 m/sSpeed is 30 000 m/s

KE = ½ x m x vKE = ½ x m x v22

= 0.5 x (5.98x10= 0.5 x (5.98x102424) x 30 000) x 30 00022

= 26.9x10= 26.9x103232 J J

26 900 000 000 000 000 000 000 000 000 000 000 J

Your turn…Your turn…

Page 16Page 16 Try question 25Try question 25

Learning IntentionsLearning Intentions

By the end of the lesson we will be able By the end of the lesson we will be able to…to…

- Recall how Recall how GravitationalGravitational PotentialPotential and and KineticKinetic energy are linked energy are linked

- Solve some simpleSolve some simple problems problems relating relating GPE and Kinetic energyGPE and Kinetic energy

- State how to calculate the State how to calculate the efficiencyefficiency of a of a systemsystem

Conservation of EnergyConservation of Energy

Energy cannot be made or destroyed but it can Energy cannot be made or destroyed but it can change form, change form, total energy stays constanttotal energy stays constant

Consider a marble at the top of a ramp with 2.5 Consider a marble at the top of a ramp with 2.5 J of energy…J of energy…

GPEGPE = 2.5 J

KEKE = 0 JGPEGPE = 0 J

KEKE = 2.5 J

GPEGPE = 1.25J

KEKE = 1.25 J

Total Energy- 2.5 J 2.5 J 2.5 J

a

b

c

cba

Ignoring heat energy losses!

Conservation of EnergyConservation of Energy

When a falling object ‘loses’ GPE it is When a falling object ‘loses’ GPE it is transformed to KE ‘gained’transformed to KE ‘gained’

GPEGPElostlost = KE = KEgainedgained

Example QuestionExample Question

A stone of mass 3 kg is dropped from a A stone of mass 3 kg is dropped from a height of 60 cm onto the ground.height of 60 cm onto the ground.

a) Calculate its GPE before it is droppeda) Calculate its GPE before it is dropped

b) When it hits the ground how much GPE b) When it hits the ground how much GPE does it have? How much KE does it does it have? How much KE does it have?have?

c) At what c) At what speedspeed will it hit the ground? will it hit the ground?

AnswerAnswer

a)a) GPE = Weight x heightGPE = Weight x height= (3 x 10) x 0.6= (3 x 10) x 0.6= 18 J= 18 J

b) GPE is zero as its height off the ground is b) GPE is zero as its height off the ground is zero. KE is 18 J, all the GPE has been zero. KE is 18 J, all the GPE has been converted into KEconverted into KE

c) KE = ½ x m x vc) KE = ½ x m x v22

18 = ½ x 3 x v18 = ½ x 3 x v22

12 = v12 = v22

3.46 m/s = v3.46 m/s = v

Question TimeQuestion Time

Page 16 Question 27Page 16 Question 27

GPE = Weight x heightGPE = Weight x height

KE = ½ x m x vKE = ½ x m x v22

GPEGPElostlost = KE = KEgainedgained

total energy stays constanttotal energy stays constant