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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?.

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Presentation Transcript
isaac newton
Isaac Newton
  • 1666, England (45 years after Kepler).
questions
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 gravitation4
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.
slide5
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 gravitation6
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
The Value of G.

G= 6.67 x 10-11 N m2 / kg2

slide9
Note
  • F12 = -F21Action-reaction pair.
  • Gravitation is a field force.
  • Masses are considered point masses.
henry cavendish s experiment determined the proportionality constant g in 1798
Henry Cavendish’sexperiment determined the proportionality constant G in 1798.

http://www.newscientist.com/data/images/archive/1639/16390101.jpg

change of gravitational force with distance
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
Why does the moon not fall straight down onto the earth?

The gravitational force place the role of the centripetal force.

example problem
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
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
The Gravitational Force Inside the Earth
  • Varies linearly with the distance from the center of the Earth. geff = g r/ REarth
slide17
Ex: #3
  • A 200kg object and a 500kg object are separated by 0.400m.
    • Find the net gravitational force exerted by these objects on a 50.0kg object placed midway between them.
    • 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

slide18
Ex: #5
  • Three uniform spheres are 2 kg, 4kg, 6 kg are located as shown:
  • Calculate the resultant gravitational force acting on the 4kg object.
  • Ans: (-10i + 5.93j) x10-11 N

2kg

3m

4kg

4m

6kg