unit 8 law of universal gravitation2008

7/27/2019 Unit 8 Law of Universal Gravitation2008

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ag

g

Do you know the difference??


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Newtons Law of Universal

GravitationEvery body in the universe attracts every other body with

a force that is directly proportional to the product of the

masses of the bodies and inversely proportional to the

square of the distance between the bodies.


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GravitationWhen 2 masses are separated by a distance (r)

r

m1 m2

Fg -Fg

2

21

r

mmGF

The proportionality constant, G is called the universal gravitational

constant. Its value in the SI system of units is,

G = 6.67 10-11Nm2/kg2.

Cavendish link
http://www.physicsclassroom.com/Class/circles/U6L3d.htmlhttp://www.physicsclassroom.com/Class/circles/U6L3d.html


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The Law of Universal gravitation states that

every object in the universe is attracted to every

other object in the Universe!Greater the masses = greater the force of attraction

Greater the distance = smaller the force of attraction


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The more mass an object has, the greater its force of attraction.

You are extremely attractive.


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Sample Problems

So you use the equation

Fg = GMm/r2

Fg = 6.67E-11*.05*.05/.82

Fg = 2.61E-13 N

Find the gravitational attractive force between two

identical 50 g spheres with centers .8 meters apart?

G = 6.67x10-11 N m2/kg2


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Weight and Gravitational Attraction.

Fg = GMm/r2=

6.67E-11(5.98E24 )(75) / (6.37E6)2

Fg = 737.46 N

1. Find the weight of a 75 kg person on the

planet earth.

2. Find the gravitational force of attraction

between a 75 kg person and the Earth?mearth = 5.98 x 1024 kgrearth = 6.37 x 10

6 m

W= 75 X 9.8=735 N


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Acceleration Due to Gravity

Calculate g for planet Earth at sea level.


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Example 6

The mass of the Hubble Space Telescope is 11,600 kg.

Determine the weight of the telescope (a) when it was resting

on the earth and (b) as it is in its orbit 598 km above the

earth's surface.

Mearth = 5.98 x 1024 kg

Rearth = 6.37 x 106 m

G = 6.67 x 10-11 N m2/kg2

Answer: 114, 027 N =25,623 lbs

95,295 N = 21,414 lbs


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INNER SPACEDown in a cave below the surface of the earth there is:

a) More gravity than at the earths surfaceb) Less gravity than at the earths surfacec) The same gravity as at the surface


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Gravitation: Conceptual Questions1. The moon and the Earth are attracted to each other

by gravitational force. Does the more massiveearth attract the moon with a greater force than the

moon attracts Earth? Explain.2. What happens to the gravitational force between

two masses when the distance between the massesis doubled?

3. If the Earth were twice as massive but remainedthe same size, what would happen to the value ofG? g?

4. Jupiter has about 300 times the mass of Earth andabout 10 times earths radius. Estimate the size of

g on the surface of Jupiter.


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Cannonball A cannonball is fired horizontally from a tall

mountain to the ground below. Because of gravity, itstrikes the ground with increased speed. A second

cannonball is fired fast enough to go into circular

orbit but gravity does not increase its speed. Why

Refer to #19 & #23 in conceptual physics


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MOON MOTION

Draw a FBD and sum the forces acting onthe moon as it orbits the earth.

If the moon orbits the earth every 27.3 daysat a radius of 3.8 x 108 meters. Determinethe velocity and the acceleration due togravity that the moon experiences.


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Fg = G =Mem_________

r

____

r

mv2

Speed of a Satellite:


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v = GMer

Speed of a Satellite:


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v = velocity (m/s)G = gravitational constant

Me = mass of Earth (kg)

r = distance to center of

the Earth (m)


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Satellites

What is the minimum velocity needed for a

satellite to stay in orbit at 1500 km above

the earths surface. Given

Mearth = 5.98 x 1024 kg

Rearth = 6.37 x 106 m

And the answer is. 7913.047866 m/s


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TREETOP ORBIT

If the earth had no air (atmosphere) or mountainsto interfere, could a satellite given adequate

initial velocity orbit arbitrarily close to the

earths surface provided it did not touch?

a) Yes, it could.

b) No, orbits are only possible at a sufficient

distance above the earths surface where

gravitation is reduced.

Explain.

unit 8 law of universal gravitation2008

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