Download - 1.1.1 gravitational fields
Topic 9.2
1.1.1 Gravitational Fields
Mass, Weight and Gravity
Remember that mass is a measure of the amount of substance in an object.
Weight is the force of gravity pulling down on the object's mass.
This is expressed as the formula: W=mg
What are the units of each term in this equation?
The Simple Pendulum
A simple pendulum consists of a mass (called a bob) on a light (no mass) string.
The weight of the object causes it to try to return to the lowest position when it is disturbed.
The time taken to make one complete swing (Left to right to Left) is called the TIME PERIOD, T.
Investigating the Simple Pendulum
Set up a simple pendulum as shown.
Investigate the effect of the mass of the bob, m, on the time period, T, of the pendulum.
Identify what variables need to be controlled.
How can you make your time measurement as precise as possible?
Remember keep the angle of swing small for the best results!
What does a graph of T against m show?
mg
l
Investigating the Simple Pendulum
Now investigate the effect of the pendulum length, l, on the period, T. Identify what variables need to be
controlled. How should you measure the length
of the pendulum? What does a graph of T against l
show? What does a graph of T2 against l
show?
Measuring g
•The time period of a simple pendulum is given by the equation:
•This can be written as:
•Calculate g from the gradient of your T2 versus l graph.
g
lT 2
lg
T2
2 4
Gravitational Fields
Gravity can act over large distances, even through space.
To explain this we use the idea of a field. All objects with mass create their own
gravitational field. This field extends to infinity and causes
other objects to be attracted towards the mass.
This is similar to the electromagnetic fields. The gravitational field is much weaker than
the other fields.
Gravitational Fields
Uniform Gravitational Fields
Very close to an object the gravitational field can be considered to be uniform. g has a constant value
Further away the gravitational field becomes weaker. g decreases with distance.
Gravitational Potential Energy
Close to Earth, where g is constant, we know that the energy gained by an object when it is lifted equals the work done on it.
EG
= Work Done = Force x Distance
EG = WΔh = mgΔh
How much GPE is gained when a 65kg object is raised through 7.0m close to the Earth's surface?
Gravitational Potential Energy
Normally, the Earth's surface is defined to have a GPE of 0J.
In space, a new zero must be defined which is the same for everyone.
A point an infinite distance from Earth is defined as having zero GPE.
“Gravitational Potential Energy is a measure of the work done to move an object from infinity to a point within the gravitational field”
Gravitational Potential Energy
If a point an infinite distance from Earth has zero GPE AND lifting an object away from the Earth increases its GPE then GPE MUST ALWAYS BE NEGATIVE!!
i.e. lifting an object makes its GPE less negative!
Gravitational Potential Energy
GPE is given by the formula:
Where G is the Universal Gravitational Constant =6.67x10-11 m3kg-1s-2
What do the other symbols mean?
EG=−GMmR
Gravitational Potential Energy
Calculate the GPE of a 200kg satellite when in low Earth orbit 125km above the Earth's surface.
What is the GPE of a 400kg satellite in a geostationary orbit 36,000km above the Earth's surface?
mEarth
=5.98x1024 kg
rEarth
=6.38x106 m
Gravitational Field Strength
Equating our universal equation for GPE and our close to Earth equation gives on the Earth's surface (radius R):
The acceleration due to gravity is not constant! It falls off with r2.
Notice that g is a vector and that the – sign indicates attraction.
2
0
R
MG=g
R
mMG=Rgm
r
MmG=hmg
Gravitational Field Strength
Gravitational Field Strength
Visit www.nineplanets.org Record values for the mass and
diameter of each of the 8 major planets.
Create a table or use a spreadsheet to calculate values of g for each planet.
g=6.67E-11*mass/(radius^2)
Homework
Read pages 3-4 of Keep It Simple Science
Complete worksheet on page 5.
