Some Revision• What is Work?

– “Work is done when an object moves in the direction of a force applied to it”

– Work is the transfer of energy

• Scalar quantity

• Units of Joules (J) or Newton metres (Nm)

FsW

Force (N)

Distance, s (m)

Gravitational Potential Energy (GPE)

• Definition:

Gravitational Potential Energy, Ep is the energy of a

mass due to its position within a gravitational field.

Close to Earth:

Ground, defined as zero gravitational potential energy (GPE)

MassEp = 0

Mass

Height = h

Work done = Fs = mgh = GPE

GPE = mgh

m = mass (kg)g = gravitational field vector (ms-2)h = height (m)

Gravitational Potential Energy (GPE, Ep)

Think, Pair, Share Question: Why can we only use GPE = mgh near the surface of a planet?

Answer: g, gravitational field strength varies as you move away from the surface of the planet. Close to the surface of the planet ie. where we live, the field can be approximated as constant but this is not valid if we are considering the physics on a larger scale

– g is higher

– g is lower

g is ‘constant’

GPE on a Large ScaleThink Q. Consider the Earth’s gravitational fieldWhere is the field zero?

221

d

mmGF

F is only zero when d = ∞ (infinity)

So g is only zero when a mass is at infinity distance compared to the Earth

Hence infinity is chosen as the point of zero gravitational potential energy on a larger scale.

d = ∞

Zero GPE

GPE on a Large ScaleAlternative definition for large scale: • GPE is defined as the work done to move an object from infinity to a

point within a gravitational field.

Imagine mass at d = ∞

What happens to the GPE of the mass as it moves closer to the planet?

It decreases, hence it’s Ep is less than zero or a negative number!

This is a weird consequence of defining GPE as zero at ∞

Formula for GPEGPE (Ep) is defined as the work done to move an object from infinity to a point

within a gravitational field.

d

mGm

dd

mGm

sF

doneWorkEp

21

221

But we know Ep has a negative value so the formula is

r

mGmEp

21

Formula for GPE

r

mGmEp

21

Ep = Gravitational Potential Energy (J)

G = Universal Gravitation Constant

m1 = mass of planet (kg)

m2 = mass of object (kg)

r = distance separating the centre of the masses (m)

Note that on the data sheet the formula uses r and not d. Another interesting quirk of our Physics Syllabus!

Formula for GPEThink Q:A mass can move either with or against a

gravitational field.

(a) When does an external force need to be applied?

(b) When does the gravitational field do the work?

Example Calc

Given the data below determine the gravitational potential energy of the Moon within the Earth’s gravitational field.

Data: Mass of the Earth = 5.97 x 1024 kgMass of the Moon = 7.35 x 1022 kgEarth – Moon distance = 3.84 x 108 m on average

Equation:

)..3(1062.7

106217777.7

1084.3

1035.71097.51067.6

28

28

8

222411

21

figssig

JE

r

mGmE

p

p

Example Calc

What does this actually mean?

If the Moon was moved from infinity to its current position it would require – 7.62 x 1028 J of work. The negative sign means that the field does the work and that no external force needs to be applied to make the Moon move over that distance.

Conversely it also means that if the Moon is to escape the Earth’s gravitational field 7.62 x 1028 J of energy would be required.

)..3(1062.7 28 figssigEp

Time for Some Practice Questions

• Complete questions 1 to 12 from WU.