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Lesson_4.5_Printable

# Lesson_4.5_Printable - Newtons Law of Gravitation Every...

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Newton’s Law of Gravitation Every object attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. m 1 m 2 r 1 2 2 m m F r If the distance between the centers of two objects of masses m 1 and m 2 is r, each will attract the other with a force given by 1

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G is called the universal gravitational constant. 1 2 2 g m m F G r = Can you figure out the unit of G? G has the same value everywhere in the universe given by: G = 6.67 × 10 -11 Nm 2 kg -2 2
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Weight of an object on the surface of the earth is a measure of the gravitational force on it by the earth. R e M e If the mass of the earth is represented as M e and its radius R e : Weight of an object The gravitational force on an object of mass m on the surface of the earth can be written as: 2 e g e M m F G R = F g is the weight of the object But weight = mg where g is the acceleration due to gravity. F g = mg 4
2 e e M g G m m R = An average value of g on the surface of the earth can be obtained by using the known values of M e and R e 2 e e M g G R = GM e = gR e 2 M e = 5.98 × 10 24 kg R e = 6.38 × 10 6 m ( 29 24 11 2 6 5.98 10 6.67 10 6.38 10 g - × = × × × = 9.8 ms -2 5

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g at an altitude h The value of g will change as the object is taken away from the surface of the earth. At an altitude h from the surface of the earth g is given by: ( 29 2 e e M g G R h = + Find the value of g at a height 200 km from the surface of the earth. ( 29 24 11 2 6 6 5.98 10 6.67 10 6.38 10 0.2 10 g - × = × × × + × = 9.2 ms -2 6
Gravitational Field The statement of the law of gravitation implies that an object placed outside the earth’s surface experiences a force towards the earth. This is true no matter where the object is placed, it will experience a force towards the earth. This is equivalent to saying that that there is a gravitational force field around the earth. The gravitational force field is a vector earth quantity that has a magnitude and direction. The direction is towards the center of the earth as indicated by the arrows in the figure The magnitude or strength of the force field is greater where the vectors are closer (at the surface of the earth), and becomes weaker as the vectors get separated (away from the surface of the earth). 7

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The strength of the gravitational field at a point is defined as the force per unit mass placed at that point. The force experienced by a unit mass placed at a height h above the surface of the earth is given by: = g The gravitational field at a point is a measure of the acceleration 2 e g e M F G R = -g -g -g -g -g due to gravity at that point. Gravitational field can be represented using vector notation as F g = - g j The unit of gravitational field is Nkg -1 which is the same as ms -2 -g -g -g -g -g -g -g -g -g -g -g 8
What is the gravitational field at a point where the weight of a 3.0-kg object is –15 N j Gravitational field at a point is force per unit mass.

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