Transcript Gravity and mass

Key Areas covered
• Gravitational field strength of
planets, natural satellites and stars.
• Calculating the force exerted on
objects placed in a gravity field.
• Newton’s Universal Law of
Gravitation.
What we will do today
• State the difference between mass and
weight
• Explain star and planet formation with
reference to the force of gravity
• Describe how space travel makes use of
the ‘slingshot effect’
• Carry out calculations using Newton’s
Inverse Square Law of Gravitation
Gravity and mass
BBC Universe - Gravity
What’s the difference between mass and weight?
• Mass is how much matter (material) is in
an object and is measured in kg.
• Weight is the force of gravity acting on
an object (of known mass) and is
measured in N kg-1.
Gravity demonstration
• Place a large rubber sheet or bin bag etc on a table this is space.
• As you travel from one end to the other it takes time
– this is the space-time continuum.
• Place a tennis ball (a planet) and a marble (a moon) on
the sheet and lift it up.
• You will see the marble move towards the tennis ball.
• Repeat again only this time add in a football (the
Sun).
• You will see that the marble and tennis ball are
attracted to the Sun.
• The bigger the mass, the bigger the gravitational pull.
Thinker???
• Why don’t we constantly move towards
the Sun if it has such a strong gravity?
• More on this later
Where can you find gravity?
• Everything that has a mass has its own
gravitational field strength, the bigger the
mass the bigger the field strength.
• This explains why planets orbit the Sun and
why the asteroid belt is close to Jupiter.
• This is why different planets have different
values of gravity.
• BBC Universe - Gravity: See Brian Cox’s zero
G flight
Gravity and star formation
• Scientists believe that stars were formed by the
gravitational attraction between hydrogen molecules
in space.
• This attraction built up over time, a large enough
mass of gas such that the forces at the centre was so
big that it caused the hydrogen molecules to fuse
together, generating energy (the centre of the Sun).
• This energy radiating outwards counteracts the
gravitational force moving trying to compress the Sun
inwards.
• Eventually the Hydrogen will be used up and the Sun
will collapse under its own gravity (in about 4 billion
years time)
Gravity and planet formation
• Once a star is formed there will be a
debris orbiting around it.
• This debris may join together to form
planets, again due to the gravitational
attraction between the particles.
• This is the most common explanation to
explain the formation of our solar
system.
• We are all made of stars.
How can we make use of gravity?
• Another application of the gravitational force
is the ‘slingshot’ method used by space craft.
• Basically an space craft is sent close to a
planet, where it accelerates due to its
gravitational field.
• If the trajectory is right then the craft
speeds past the planet with increased speed,
if not, then it will crash into the planet.
• The slingshot method was used by Apollo 13
when it used the field strength of the Moon
to accelerate back towards the Earth.
What causes gravity?
• In short, we don’t know.
• One popular theory is that there is a particle
called a graviton that has an attractive force
that draws things toward the centre of a
mass.
• If this particle was ever discovered and could
be reproduced it could help with long distance
space travel.
• Zero gravity is bad for human health as it
causes huge muscle wastage.
Newton’s Inverse Square Law
of Gravitation
This law states that there is a force of attraction between
any two objects in the universe.
The size of the force is proportional to the product of the
masses of the two objects, and inversely proportional to the
square of the distance between them.
Gm1m2
F
2
r
m1 and m2 are the masses of
the two objects, and r is the
distance between them.
G = gravitational constant =
6.67 x 10-11 Nm2kg-2
Example 1
• What is the force of • F = Gm1m2
attraction between
r2
two pupils of average
= 6.67 x 10-11 x 60 x 60
mass (60 kg) sitting
1.52
1.5 metres apart?
= 1.07 x 10-7 N
Value of r
• It is important to realise that the value
for r, the distance between two masses,
is the distance between the centre of
the two masses.
i.e. if we consider the force between
the Earth and the Moon then the value
of r is the distance from the centre of
the Earth to the centre of the Moon.
Example 2
• Taking the radius of the Earth to be 6.4 x 106 m, find
the force of attraction on a 250 kg satellite that is
orbiting at a height of 36 000 km above the Earth.
• (mass of Earth = 6.0  1024 kg)
•
1.
This question should be broken down into two parts.
First of all, find the distance, r, between the two
objects.
2. Use Newton’s Universal Law
Example 2
1. r
= radius of Earth + the height above the Earth
= 6.4 x 106 + 36 000 x 103
= 4.24 x 107 m
2. F
= Gm1m2
r2
= 6.67 x 10-11 x 6.0  1024 x 250
(4.24 x 107)2
=
55.7N
2012 Revised Higher
2015 CfE Higher
2015 CfE Higher
2013 Revised Higher
Open-ended question
• Experiment:
• Use bathroom scales and a metre stick
to come up with an answer for above.
Questions
• Activity sheets:
• Gravity and mass
• You should now be able to answer all
questions in class jotter
Answers
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Gravity and mass
1. Teacher Check
2. Teacher Check
3. 2·67 × 10−4 N
4. 3·61 × 10−47 N
5. 3·53 × 1022 N
6. 4·00 × 10−15 m