Download Rotational Motion and Equilibrium

Newton’s Law of
Universal Gravitation
AP Physics C
Mrs. Coyle
Isaac Newton
• 1666, England (45 years after
Kepler).
Questions
• If the planets are orbiting the sun , what force is
keeping them in orbit?
• What force keeps the moon in its orbit?
• Could the force of gravity be universal?
Newton’s Law of Universal Gravitation
• Any two objects attract each other with a
gravitational force, proportional to the
product of their masses and inversely
proportional to the square of the distance
between them.
• The force acts in the direction of the line
connecting the centers of the masses.
Note
• Newton’s Law is universal, it acts between any
two masses regardless of how large (planets,
stars) or how small (particles, atoms,
neutrons) they are.
• The gravitational force is weaker than the
electrical force.
• The gravitational force is one of the 4
fundamental forces in nature.
Newton’s Law of Universal Gravitation
http://scienceblogs.com/startswithabang/upload/2009/07/meet_our_second_moon/400px-NewtonsLawOfUniversalGravitation.svg.png
The Value of G.
G= 6.67 x 10-11 N m2 / kg2
Vector Form of Newton’s Law of
Universal Gravitation
m1m2
F12  G 2 rˆ12
r
Note
• F12 = -F21
Action-reaction pair.
• Gravitation is a field force.
• Masses are considered point masses.
Henry
Cavendish’s
experiment
determined the
proportionality
constant
G
in 1798.
http://www.newscientist.com/data/images/archive/1639/16390101.jpg
Change of
Gravitational
Force with
Distance
• Law of universal
gravitation is known
as an inverse square
law.
Why does the moon not fall straight
down onto the earth?
2
The gravitational force place the
role of the centripetal force.
v
FM 
rM
Relate Weight and Fg
Example Problem
•
Two spheres of equal mass m are a distance d
apart.
a)If the mass of one is doubled and the
distance between them is reduced to ½d,
how does the force change?
b) If both masses are doubled and the distance
is also doubled how does the force change?
Example
• An object that of mass 5kg is located at a
planet that has 3 times the mass of the earth
and half its radius. What is its weight on this
planet.
The Gravitational Force Inside the
Earth
• Varies linearly with the distance from the
center of the Earth. geff = g r/ REarth
Ex: #3
• A 200kg object and a 500kg object are
separated by 0.400m.
a) Find the net gravitational force exerted by these
objects on a 50.0kg object placed midway
between them.
b) At what position (other than an infinitely remote
one ) can the 50kg object be be placed so as to
experience a zero force?
Ans: a)2.50x10-5 N towards the 500kg object,
b)0.245m
Ex: #5
• Three uniform spheres are 2 kg, 4kg, 6 kg are
located as shown:
2kg
3m
4kg
6kg
4m
• Calculate the resultant gravitational force
acting on the 4kg object.
• Ans: (-10i + 5.93j) x10-11 N