Download - 6.1 - Gravitational Force and fields
6.1 - Gravitational Force& Fields
Newtonโs Universal Law of GravitationEvery single point mass attracts every other point mass with a force directly proportional to the product of the masses and inversely proportional to the square of their separation.
๐นโ๐1๐2๐นโ
1
๐ 2
Universal Constant of Gravitation: G= 6.6742 x 10-11 m3kg-1s-2
Newtonโs Universal Law of GravitationNewton calculated (using calculus) that Spheres also follow the same rule as long as the separation is between their centre of mass.
The Centre of Mass is a point that represents the total mass of a body and is where gravity can be said to act. For regular shapes itโs in the middle.
r
http://phet.colorado.edu/en/simulation/gravity-force-lab or click on the picture
Newtonโs Universal Law of Gravitation on PhET
Use this to check Newtonโs Law of Gravitation. What happens to the force if you double the distance? or double either of the masses?
Acceleration due to Gravity
Newtonโs 2nd Law
๐น=๐๐+ m
M
a
๐=๐บ๐๐ 2
Newtonโs Law of Gravitation
๐น=๐บ๐๐๐2
On Earth: a = 9.81ms-2 Newton was right. This is correct!
Orbits: Centripetal Force & Gravity
๐น=๐บ๐๐๐2
๐น=๐๐ฃ2
๐
Assuming the orbits are circular.
Gravity causes the centripetal force
๐บ ๐๐๐2
=๐๐ฃ2
๐
๐๐
๐๐
+
๐ฃ=โ๐บ๐๐
This is the speed of the orbiting object
Orbits: Centripetal Force & Gravity (cont)
๐ฃ=โ๐บ๐๐
1. The speed of the earth in orbit around the sun:
m1 = mass of the sun = 1.99 x 1030 kgr = distance between Sun and Earth = 1.49 x 1011mG = 6.6742 x 10-11 m3kg-1s-2
= 29 846 ms-1
2. The time for the earth to orbit around the sun:
๐ฃ=๐ ๐ก
๐ =2๐ ๐๐ก=2๐ ๐๐ฃ ๐ก=3.14ร107๐
Newton was right again โ 1 Year
Orbits: Centripetal Force & Gravity
http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html
My Solar SystemGravity and Orbits
http://phet.colorado.edu/en/simulation/gravity-and-orbits
or click on the pictures
Try out these two great simulations to understand gravity even more.
Gravitational Field StrengthDefinition: The force per unit mass experienced by a small test mass* placed in the field.
units: Nkg-1
๐น=๐บ๐๐๐2
๐=๐บ๐๐ 2
For the mass m:
* A small test mass is used because any larger mass might change the field.
Field LinesThese show the direction that a mass would accelerate if placed in the field, and help us to imagine the field.
Around a spherical mass the field lines are closer together nearer the surface, so the field strength is larger.
Near the Earth the field lines are almost parallel.
The field is uniform.
Wherever you are near the surface of the earth you are pulled down with the same Force/Kilogram
Field Strength is a vector, so two values of g can be added together