Physics 101 Chapter 9 Gravity

7/27/2019 Physics 101 Chapter 9 Gravity

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Chapter 9

Gravity


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Newton and gravity

Before Newton: gravity was thought to be

unique to earth.

But 2ndLaw told Newton that the planets

orbits required a centripetal force.

Does one set of natural laws apply to the

apple and the moon?


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Fig. 9.2

ig. 9.1


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Newtons hypothesis verified: Earth moon distance was about 60 x earths radius

Newton could calculate ac= v

2

/r. v is orbital speed of the moon, v = dist./time

The centripetal acceleration of the moon was 1/3600

of 9.8 m/s2

.

s

m

hrday

hr

days

m

T

r

T

C

t

dv 1023

)min1

sec60

)(1

min60

)(1

24

)(3.27(

)000,000,384(22

2

22

/002725.0000,000,384

)/1023(sm

m

sm

r

va

c

3600

1

/8.9

/002725.02

2

sm

sm


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Newtons hypothesis verified: (cont.)

Recall the distance was 60 times greater

So60 times greater distance and 3600 (602)

less accelerationand thus 3600 times less

force means... F 1/d2

But also, from the 3rdLaw of motion: if the

force depended on the mass of the earth, it

should also depend on the mass of the moon.

So Fm1x m2. > > > > >


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XXXLaw of Universal Gravitation

Newtons Form:

Note: d is center to center distance for the twomasses.

Equation Form:

Could the value of G be found?

There is an attractiveforce between any twoobjects!

2

21

d

mmF

2

21

d

mGmF


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Universal Gravitational Constant, G

Could be found if the force between two knownmasses was measured.

100 years later Henry Cavendish and later Jolly

Magnitude of G is identical to the force betweentwo 1kg masses 1 m apart or .0000000000667 N!

G = 6.67 x 10-11Nm2/kg2

We can explain why force is small for even largeobjects like an aircraft carrier and a battleship.

Gravity is the weakest of the four known forces innature, but it is in effect over great distances

Gravitational forces are always attractive.


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Fig. 9.4


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The inverse squarerelationship

Recall last chapter we saw a direct square

relationship between kinetic energy and speed.

KE

(J)

1 2 3

Speed (m/s)

9

4

1

2

2

1mvKE

KE v2


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Fig. 9.6


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Gravitational force between the

rocket and the earth decreases

with distance squared

Fig. 9.3


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Weight, not mass

decreaseswith distancebetween the centers of mass

Fig. 9.7


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Gravitational Force

Q. Planet A and B orbit the same star at the same distance,

but planet B has 6 times the mass of planet A. How does the

gravitational force on planet B compare with the gravitational

force on planet A?

Mass B = 6x mass A

6 x MOREForce acting on B than acting on A

These are action reaction pairs!

d2

m1x m2GF =


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Gravitational Force

Q. Planet A and B orbit the same star at the same distance,

but planet B has 6 times the mass of planet A. How does the

gravitational force on planet B compare with the gravitational

force on planet A?

A. Mass B = 6x mass A

6 x MOREForce acting on B than acting on A

These are each action reaction pairs!


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Gravitational Force

Q. What is the persons weight when the star shrinks to

half its original radius?

A.2

21

d

mmGF 2

2

1

21

d

mmGF

So? . . .

F = or 4 X ?


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Gravitational Force

Q. What is the persons weight when the star shrinks to

half its original radius?

A. . . . = 4X !!!


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Weight and Weightlessness

True weightlessness?

Astronauts: apparentweightlessness.

You might appear to be weightless if we sayyour weight is the force a supporting scale on

a supporting surface exerts on you. See fig 9.8

and 9.9.


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Fig. 9.8

There has to be a support

Force to measure weight!


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Fig. 9.9


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Fig. 9.11


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Orbiting objects, the space station, the

space shuttle and the astronauts inside

See Figure

9.10

Are in free fall!


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The moon is really in free fallaround the earth!

Fig. 9.2

Physics 101 Chapter 9 Gravity

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