<< Chapter < Page Chapter >> Page >

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)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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)

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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)

Got questions? Get instant answers now!

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 )?

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
can you send the book attached ?
Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
explain standard reason why economic is a science
innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
scares means__________________ends resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 4

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask