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**Newton’s Law of Universal Gravitation**

AP Physics C

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Isaac Newton 1666, England (45 years after Kepler).

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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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**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.

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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.

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**Newton’s Law of Universal Gravitation**

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The Value of G. G= 6.67 x N m2 / kg2

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**Vector Form of Newton’s Law of Universal Gravitation**

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**Note F12 = -F21 Action-reaction pair. Gravitation is a field force.**

Masses are considered point masses.

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**Henry Cavendish’s experiment determined the proportionality constant G in 1798.**

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**Change of Gravitational Force with Distance**

Law of universal gravitation is known as an inverse square law.

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**Why does the moon not fall straight down onto the earth?**

The gravitational force place the role of the centripetal force.

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**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?

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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.

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**The Gravitational Force Inside the Earth**

Varies linearly with the distance from the center of the Earth. geff = g r/ REarth

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**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

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**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 j) x10-11 N 2kg 3m 4kg 4m 6kg

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C H A P T E R 4 Forces and Newton's Laws of Motion

C H A P T E R 4 Forces and Newton's Laws of Motion

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