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Problem exercises

(a) Calculate Earth's mass given the acceleration due to gravity at the North Pole is 9.830 m /s 2 size 12{9 "." "830"`"m/s" rSup { size 8{2} } } {} and the radius of the Earth is 6371 km from center to pole.

(b) Compare this with the accepted value of 5 . 979 × 10 24 kg size 12{5 "." "979" times "10" rSup { size 8{"24"} } `"kg"} {} .

a) 5.979 × 10 24 kg size 12{ {underline {5 cdot "979" times "10" rSup { size 8{"24"} } " kg"}} } {}

b) This is identical to the best value to three significant figures.

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(a) Calculate the magnitude of the acceleration due to gravity on the surface of Earth due to the Moon.

(b) Calculate the magnitude of the acceleration due to gravity at Earth due to the Sun.

(c) Take the ratio of the Moon's acceleration to the Sun's and comment on why the tides are predominantly due to the Moon in spite of this number.

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(a) What is the acceleration due to gravity on the surface of the Moon?

(b) On the surface of Mars? The mass of Mars is 6.418 × 10 23 kg size 12{6 "." "418" times "10" rSup { size 8{"23"} } `"kg"} {} and its radius is 3 . 38 × 10 6 m size 12{3 "." "38" times "10" rSup { size 8{6} } `m} {} .

a) 1.62 m / s 2 size 12{1 cdot "62"" m"/s rSup { size 8{2} } } {}

b) 3.75 m / s 2 size 12{1 cdot "62"" m"/s rSup { size 8{2} } } {}

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(a) Calculate the acceleration due to gravity on the surface of the Sun.

(b) By what factor would your weight increase if you could stand on the Sun? (Never mind that you cannot.)

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The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the center of Earth. (This is 1690 km below the surface.)

(a) Calculate the magnitude of the acceleration due to the Moon's gravity at that point.

(b) Calculate the magnitude of the centripetal acceleration of the center of Earth as it rotates about that point once each lunar month (about 27.3 d) and compare it with the acceleration found in part (a). Comment on whether or not they are equal and why they should or should not be.

a) 3.42 × 10 –5 m / s 2 size 12{3 cdot "42" times "10" rSup { size 8{"-5"} } m/s rSup { size 8{2} } } {}

b) 3.34 × 10 –5 m / s 2 size 12{3 cdot "34" times "10" rSup { size 8{"-5"} } m/s rSup { size 8{2} } } {}

The values are nearly identical. One would expect the gravitational force to be the same as the centripetal force at the core of the system.

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Solve part (b) of [link] using a c = v 2 / r size 12{a rSub { size 8{c} } =v rSup { size 8{2} } /r} {} .

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Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one's birth. The only known force a planet exerts on Earth is gravitational.

(a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child).

(b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some 6 . 29 × 10 11 m size 12{6 "." "29" times "10" rSup { size 8{"11"} } `m} {} away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)

a) 7.01 × 10 –7 N size 12{7 cdot "01" times "10" rSup { size 8{"-7"} } N} {}

b) 1.35 × 10 –6 N size 12{1 cdot "35" times "10" rSup { size 8{"-6"} } N} {} , 0.521 size 12{0 cdot "521"} {}

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The existence of the dwarf planet Pluto was proposed based on irregularities in Neptune's orbit. Pluto was subsequently discovered near its predicted position. But it now appears that the discovery was fortuitous, because Pluto is small and the irregularities in Neptune's orbit were not well known. To illustrate that Pluto has a minor effect on the orbit of Neptune compared with the closest planet to Neptune:

(a) Calculate the acceleration due to gravity at Neptune due to Pluto when they are 4 . 50 × 10 12 m size 12{4 "." "50" times "10" rSup { size 8{"12"} } `m} {} apart, as they are at present. The mass of Pluto is 1 . 4 × 10 22 kg size 12{1 "." 4 times "10" rSup { size 8{"22"} } `"kg"} {} .

(b) Calculate the acceleration due to gravity at Neptune due to Uranus, presently about 2 . 50 × 10 12 m size 12{2 "." "50" times "10" rSup { size 8{"12"} } `m} {} apart, and compare it with that due to Pluto. The mass of Uranus is 8 . 62 × 10 25 kg size 12{8 "." "62" times " 10" rSup { size 8{"25"} } " kg"} {} .

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(a) The Sun orbits the Milky Way galaxy once each 2 . 60 x 10 8 y size 12{2 "." "60 x 10" rSup { size 8{8} } " y"} {} , with a roughly circular orbit averaging 3 . 00 x 10 4 size 12{3 "." "00 x 10" rSup { size 8{4} } } {} light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the centripetal acceleration of the Sun in its galactic orbit. Does your result support the contention that a nearly inertial frame of reference can be located at the Sun?

(b) Calculate the average speed of the Sun in its galactic orbit. Does the answer surprise you?

a) 1.66 × 10 –10 m / s 2 size 12{1 cdot "66" times "10" rSup { size 8{"-10"} } m/s rSup { size 8{2} } } {}

b) 2.17 × 10 5 m/s size 12{2 cdot "17" times "10" rSup { size 8{"5"} } m/s} {}

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Unreasonable Result

A mountain 10.0 km from a person exerts a gravitational force on him equal to 2.00% of his weight.

(a) Calculate the mass of the mountain.

(b) Compare the mountain's mass with that of Earth.

(c) What is unreasonable about these results?

(d) Which premises are unreasonable or inconsistent? (Note that accurate gravitational measurements can easily detect the effect of nearby mountains and variations in local geology.)

a) 2.94 × 10 17 kg size 12{2 cdot "94" times "10" rSup { size 8{"17"} } kg} {}

b) 4.92 × 10 –8 size 12{4 cdot "92" times "10" rSup { size 8{"-8"} } } {}

of the Earth's mass.

c) The mass of the mountain and its fraction of the Earth's mass are too great.

d) The gravitational force assumed to be exerted by the mountain is too great.

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Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
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what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
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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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