Physics A2 Unit4 19 GravitationalFields02

8/11/2019 Physics A2 Unit4 19 GravitationalFields02

1/12


2/12

1. To investigate the value of gon other planets

in our solar system & to practice our graph

drawing and other practical skills

2. To recreate some of Newtons work on

gravitation & to establish Newtons law of

gravitation

3. To use Newtons law to establish the

gravitational force of attraction between two

objects

Book Reference : Pages 59-61


3/12

Using the supplied planetary data complete the following:

1. For each planet complete the table by calculating the value ofm/r2

2. Next plot a good quality line graph for g against m/r2

3. Find the Gradient of your graph

Mass/kg Radius/m g N/kg m/r2

Mercury 3.18E+23 2.43E+06 3.59 5.39E+10

Venus 4.88E+24 6.06E+06 8.87 1.33E+11

Earth 5.98E+24 6.38E+06 9.81 1.47E+11

Mars 6.42E+23 3.37E+06 3.77 5.65E+10

Jupiter 1.90E+27 6.99E+07 25.95 3.89E+11

Saturn 5.68E+26 5.85E+07 11.08 1.66E+11

Uranus 8.68E+25 2.33E+07 11.08 1.60E+11

Neptune 1.03E+26 2.21E+07 14.07 2.11E+11


4/12

You should have a straight line graph. What does

this tell us about

The relationship between g and the mass of

the planet?

The relationship between g and the radius of

the planet?


5/12

The straight line graph tells us that

g is directly proportional to the mass of

the planet

g is inversely proportional to the radius ofthe planet squared

g m

g 1/r2


6/12

We have just short circuited some of Newtons

work on gravitation and for a mass of 1kg wehave shown that the gravitation force F is related

to the mass of and radius of the planet in the

following way

F m/r2

How do we turn a proportionality into anequation we can use?


7/12

We introduce a constant of proportionality

F = Gm1m2

r2

Where Fis the gravitational force between

the two objects, m1& m2are the masses of

the two objects & ris the separationbetween the centres of the masses (think

point masses)


8/12

G is the universal constant of gravitation,

has a value of 6.67 x 10-11Nm2kg-2

Mass m1 Mass m2

Distance r

Force F Force F


9/12

Earlier we showed that the gravitational

force between two objects is governed bythe following

F 1/r2

This is an example of an inverse square

law. The force is inversely proportional to

the square of the separation. In practicethis means that the force reduces quickly as

r increases, we will see many inverse square

laws


10/12

The distance from the centre of the sun to the

centre of the Earth is 1.5x10

11

m & the masses ofthe Earth & sun respectively are 6.0x1024kg &

2.0x1030kg

a) The diameters of the Sun & Earthrespectively are 1.4x109m & 1.3x107m why

is it reasonable to consider them both to be

point masses?

b) Calculate the force of gravitational

attraction between the Earth & the Sun


11/12

The diameters of both are small compared to the

separation. Distance between any part of the sunand Earth is the same within 1%

F = Gm1m2/r2

F = 6.67x10-11x 6.0x1024x 2.0x1030/(1.5x1011)2

F = 3.6x1022N


12/12

Take care with separation between the two

masses... (r).... Consider distances between thecentres and surfaces.

r is the distance between their centres

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Physics A2 Unit4 19 GravitationalFields02