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In the figure, there is a circular stand at the floor holding two weight bars over it attached through an inverted cup shape object fitted over the stand. The first bar over this is a horizontal flat panel and contains two spheres of mass M at its end. Just over this bar is a stick shaped bar holding two spherical objects of mass m at its end. Over to this bar is mirror at the center of the device facing east. The rotation of this device over the axis of the stand is anti-clockwise. A light source on the right side of the device emits a ray of light toward the mirror which is then reflected toward a scale bar which is on the right to the device below the light source.
Cavendish used an apparatus like this to measure the gravitational attraction between the two suspended spheres ( m size 12{m} {} ) and the two on the stand ( M size 12{M} {} ) by observing the amount of torsion (twisting) created in the fiber. Distance between the masses can be varied to check the dependence of the force on distance. Modern experiments of this type continue to explore gravity.

Test prep for ap courses

Jupiter has a mass approximately 300 times greater than Earth's and a radius about 11 times greater. How will the gravitational acceleration at the surface of Jupiter compare to that at the surface of the Earth?

  1. Greater
  2. Less
  3. About the same
  4. Not enough information

(a)

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Given Newton's universal law of gravitation (Equation 6.40), under what circumstances is the force due to gravity maximized?

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In the formula g = G M r 2 , what does G represent?

  1. The acceleration due to gravity
  2. A gravitational constant that is the same everywhere in the universe
  3. A gravitational constant that is inversely proportional to the radius
  4. The factor by which you multiply the inertial mass to obtain the gravitational mass

(b)

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Saturn's moon Titan has a radius of 2.58 × 10 6 m and a measured gravitational field of 1.35 m/s 2 . What is its mass?

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A recently discovered planet has a mass twice as great as Earth's and a radius twice as large as Earth's. What will be the approximate size of its gravitational field?

  1. 19 m/s 2
  2. 4.9 m/s 2
  3. 2.5 m/s 2
  4. 9.8 m/s 2

(b)

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4. Earth is 1.5 × 10 11 m from the Sun. Mercury is 5.7 × 10 10 m from the Sun. How does the gravitational field of the Sun on Mercury ( g SM ) compare to the gravitational field of the Sun on Earth ( g SE )?

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Section summary

  • Newton's universal law of gravitation: Every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In equation form, this is
    F = G mM r 2 , size 12{F=G { { ital "mM"} over {r rSup { size 8{2} } } } } {}

    where F is the magnitude of the gravitational force. G size 12{G} {} is the gravitational constant, given by G = 6 . 673 × 10 –11 N m 2 /kg 2 size 12{G=6 "." "673" times "10" rSup { size 8{"-11"} } `N cdot m rSup { size 8{2} } "/kg" rSup { size 8{2} } } {} .

  • Newton's law of gravitation applies universally.

Conceptual questions

Action at a distance, such as is the case for gravity, was once thought to be illogical and therefore untrue. What is the ultimate determinant of the truth in physics, and why was this action ultimately accepted?

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Two friends are having a conversation. Anna says a satellite in orbit is in freefall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not 9.80 m /s 2 size 12{9 "." "80"`"m/s" rSup { size 8{2} } } {} . Who do you agree with and why?

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Draw a free body diagram for a satellite in an elliptical orbit showing why its speed increases as it approaches its parent body and decreases as it moves away.

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Newton's laws of motion and gravity were among the first to convincingly demonstrate the underlying simplicity and unity in nature. Many other examples have since been discovered, and we now expect to find such underlying order in complex situations. Is there proof that such order will always be found in new explorations?

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Questions & Answers

If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
Anurag Reply
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
Jaydie Reply
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
Princewill Reply
how can I read physics...am finding it difficult to understand...pls help
rerry Reply
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju
I have a exam on 12 february
David Reply
what is velocity
Jiti
the speed of something in a given direction.
Ju
what is a magnitude in physics
Jiti Reply
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
Practice Key Terms 4

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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