Physics Chp. 9 Gravity
Universal Gravitation Review What percentage of the universe is presently speculated to be composed of: 1. Dark Matter 2. Dark Energy
1. 23% 2. 73%
Ocean Tides 1. Complicated tidal motions are cause by 2. In many places, the tides break up into smaller "basins of circulation" where a tidal bulge travels like a circulating wave that moves around in a small basin of water that is titled. For this reason
1. land masses and friction with the ocean floor. 2. the high tide may be hours away from an overhead Moon. example: the range is greatest in some Alaskan fjords and is most notable in the basin of the Bay of Fundy, between New Brunswick and Nova Scotia in eastern Canada, where tidal differences sometimes exceed 15 m. This is largely due to the ocean floor, which funnels shoreward in a V-shape. A person cannot outrun this tide
Gravitational Field inside a Planet Check Point Halfway to the center of Earth, would the force of gravity on you be less than at the surface of Earth?
1. less because there is less mass of Earth below you, which pulls you with less force.
Ocean Tides The tilt of Earth's axis causes
1. two daily high tides and unequal in most parts of the ocean 2. Inequalities of tides vary with the positions of the moon and the sun
The Universal Gravitational Constant, G Once the value of G was known, the mass of the Earth was easily calculated as
6 x 10^24 kg
Ocean Tides Review Distinguish between spring tides and neap tides.
A spring tide—refers to the 'springing forth' of the tide during new and full moon. Making the high tides higher than average and the low tides lower than average A neap tide—Tides that occur when the Moon is midway between new and full, in either direction. Tides due to the Sun and the Moon partly cancel, making the high tides lower than average and the low tides higher than average.
Universal Gravitation
Every object in the universe attracts every other object 1. Earth has attracted itself together as far as it can a. no corners ~ every part of the surface is equidistant from the center of gravity. b. law of gravitation: Sun, Moon, and Earth are spherical 2. Planets pull on each other a. effect is small in comparison with the pull of the Sun b. perturbation = interplanetary forces causing wobbling 3. dark energy a. recent evidence suggest that the universe is expanding and acceleration outward b. antigravity c. 73% of the universe d. late 20th and 21st century discovery 4. dark matter a. 23% of the yet-to- be discovered particles b. late 20th and 21st century discovery 5. Ordinary matter: a. stars, cabbages, kings
The Universal Gravitational Constant, Review What is the magnitude of the gravitational force between Earth and a 1kg body?
Given: Mass of earth M=6×1024 kg Mass of object m=1 kg Radius of earth R=6.4×106 m Force of gravitation between them, F=R2GMm F=(6.4×106)26.67×10−11×(6×1024)×1=9.77 N
Black Holes Review Why is a black hole invisible?
The escape velocity of the black hole is greater than the speed of light
Einstein's Theory of Gravitation Review Newton viewed the curving of the path of a planet as being caused by a force acting upon the planet. How did Einstein view the curved path of a planet?
The gravitational field as the warping of 4-dimensional space and time.
Weight and Weightlessness Review Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was moving upward at constant velocity? Downward at constant velocity?
There would be no more compression and no more expansion for both upward and downward motion
Gravity and Distance: The Inverse-Square Law
a law relating the intensity of an effect to the inverse square of the distance from the cause. Gravity follows an inverse-square law, as do the effects of electric, magnetic, light, sound, and radiation phenomena. formula = i/d^2
Gravity and Distance: The Inverse-Square Law Checkpoint By how much does the gravitational force between two object decrease when the distance between their centers is: a. doubled b. tripled c. tenfold
a. i/2^2=1/4 b. i/3^2=1/9 c. i/10^2=1/1000
Weight and Weightlessness Review Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated: a. upward? b. downward
a. more compressed. therefore, you would weigh more b. less compressed. therefore, you would weigh less.
Weight and Weightlessness Review a. Give an example of when you weight is more than mg. b. Give an example when it is zero
a. when you are accelerating upward b. when you are floating in space ~ freefall
Tidal Bulges on the Moon Review Why is there a torque about the Moon's center of mass when the Moon's long axis is not aligned with Earth's gravitational field?
b/c the elongated Moon's center of gravity is slightly displaced from its center of mass.
Tides in Earth and Atmosphere Review Why are all tides greatest at the time of a full Moon or new Moon?
because the Sun and Moon are in line with the Earth
The Universal Law of Gravity
every body attracts every other body with a force that, for any two bodies, is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them. formula: force ~ (mass1 x mass2)/distance^2 formula sh: f ~ (m1 x m2)/d^2
Gravity and Distance: The Inverse-Square Law Review How does the thickness of paint sprayed on a surface change when the sprayer is held twice as far away?
p. 154 i/2^2 = 1/4
Gravity and Distance: The Inverse-Square Law Review Where do you weigh more-at the bottom of Death Valley or atop one of the peaks of the Sierra Nevada? Why?
p. 155 In theory, you would weigh more in the valley than in the mountain because the pull of gravity is calculated on the center of mass of the two objects (you and the earth). The closer the two objects are, the stronger the pull - although, in this case, it would of course, be minimal.
Weight and Weightlessness Review When is your weight measured as mg?
p.155 For a non-accelerating mass near the surface of Earth ????
Ocean Tides Jell-O example
the ball stays spherical when all parts are pulled equally in the same direction. When one side is pulled more than the other, it is elongated.
Weight and Weightlessness Weight
the force that an object exerts on a supporting surface (or, if suspended, on a supporting string), which is often, but NOT always, due to the force of gravity. examples: 1.bathroom scale on a stationary floor (Newton's 3rd law ~ compression of the springs is considered your weight), 2.moving elevator (going upward, weight increases like the compression on a bathroom scale's springs, accelerate downward ~ decrease in weight)
Ocean Tides Gravitational force between the Moon and Earth is stronger on the side of Earth nearer to the moon, and it is weaker on the side of Earth that is farther from the Moon. This is simple because the gravitational force is ??? with ??? distance.
weaker, increased
The Universal Gravitational Constant, G The value of G shows that gravity is the ??? of the presently known 4 fundamental forces (the other 3 are the electromagnetic force and two kinds of nuclear forces)
weakest
The Universal Gravitational Constant, Review What do we call the gravitational force between Earth and your body?
weight = the force that an object exerts on a supporting surface (or, if suspended, on a supporting string), which is often, but NOT always, due to the force of gravity.
Tides in Earth and Atmosphere Review Do tides occur in the molten interior of Earth for the same reason that tides occur in the oceans?
yes, the Moon-Sun tidal forces produce Earth tides
Weight and Weightlessness Weightlessness
Being without a support force, as in free fall.
The Universal Gravitational Constant, G Calculating G alone was done by the English Physicist ??? in 1798, a ??? after Newton's time.
Henry Cavendish, century (100 years)
Ocean Tides
Seafaring people have always known that there is a connection between the ocean tides and the Moon. Newton produced the theory two explain 2 high tides per day. caused by differences in the gravitational pull of the moon on opposite sides of the earth. picture: two tidal bulges produced by differences in gravitational pulls remain relatively fixed relative to the Moon, while Earth spins daily beneath them.
Gravity and Distance: The Inverse-Square Law The Inverse-Square Law
The greater the distance from Earth's center, the less the weight of an object.. For greater distances, force is less
Gravitational Fields Review What is a gravitational Field and how can its presence be detected?
The influence that a massive body extends into the space around itself, producing a force on another massive body. It is measured in newtons per kilogram (N/kg) Its presence can be detected by a force field/magnetic field.
Black Holes Review What happens to the strength of the gravitational field at the surface of a star that shrinks?
The strength of the gravitational field would become stronger if the star kept shrinking.
Ocean Tides Review Why do both the Sun and the Moon exert a greater gravitational force on one side of Earth than the other?
The sun is half effective as the as the moon, the sun pulls 180 times harder on earth than the moon, sun pulls almost as hard on the far side of earth as it does on the near side.
What is the Newtonian synthesis?
The union of terrestrial laws and cosmic laws example: the force of gravity that pulls an apple off a tree is the same force on a planet that is pulled or directed toward the sun.
The Universal Law of Gravity Check Point 1. The moon falls around earth rather than straight into it. If the tangential velocity were zero, how would it move?
If the moon's tangential velocity were zero, it would fall straight down and crash into the earth!
The Universal Law of Gravity Check Point 2.a. According to the equation for gravitational force, what happens to the force between two bodies is the mass of one of the bodies is doubled? 2.b. If both masses are doubled?
2.a. the force between it and the other one is doubled f ~ (2m1 x m2)/d^2 2.b. the force is 4 x as much f ~ (2m1 x 2m2)/d^2
The Universal Gravitational Constant, Review When G was first measured by Henry Cavendish, newspapers of the time hailed his experiment as the "weighing Earth experiment." Why?
This was the first time the mass of the Earth was calculated.
Do tides depend more on the strength of gravitational pull or on the difference in strengths? Explain.
Tides depend only on the difference in strengths. The Moon is closer to the Earth and therefore has greater gravitational force.
Ocean Tides Neap Tides
Tides that occur when the Moon is midway between new and full, in either direction. Tides due to the Sun and the Moon partly cancel, making the high tides lower than average and the low tides higher than average.
Gravity and Distance: The Inverse-Square Law Review How does the force of gravity between two bodies change when the distance between them is doubled?
i/2^2 = 1/4
Ocean Tides Spring Tides
1. Definition: High or low tides that occur when the Sun, Earth, and the Moon are all lined up so that the tides due to the Sun and the Moon coincide, making the high tides higher than average and the low tides lower than average 2. occur at the times of a new or full Moon a. full moon = earth is between the sun & moon = lunar eclipse (full moon passes into Earth's shadow) b. full moon = moon is between the sun & earth = solar eclipse (moon blocks the sun) 3. not equally high b/c Earth-Moon, Earth-Sun distances vary 4. highest tides occur when the Moon and Sun are closest to Earth
What did Newton discover about gravity?
1. Newton did not discover gravity as commonly thought 2. Newton discovered that gravity extends beyond earth. 3. That it is a universal force. Everything pulls on everything. examples: it pulls planets toward the sun, raises ocean tides, and accounts for the shapes of galaxies
Einstein's Theory of Gravitation
1. The gravitational field as the warping of 4-dimensional space and time. 2. bodies put dents in space and time somewhat like a massive ball placed in the middle of a large waterbed dent the 2-dimensional surface.
The Universal Gravitational Constant, G
1. The proportionality form of the universal law of gravitation can be expressed as an EXACT equation: F = G((m1*m2)/d^2) 2. The units of G make the force come out in Newtons formula: G = 6.67 x10⁻¹¹ N*m²/ kg²
Ocean Tides low tide
1. When the Earth makes a 1/4 turn ~ occurs 6 hours after high tide 2. the lowest point on shore that the ocean reaches (occurs when the sun and moon are not in line) ~ 1 m below sea level 3. picture: (occurs when the sun and moon are NOT in line)
Tides in Earth and Atmosphere Tides in Earth
1. because Earth is a semi-molten liquid covered by a thin, solid, and pliable crust, the Moon-Sun tidal forces produce Earth tides 2. the solid surface of Earth rises and falls as much as 1/4 m 3. Earthquakes and volcanic eruptions have a higher probability of occurring during a spring tide or near full or new Moon .
Ocean Tides two high tides and two low tides each day is caused by:
1. different pulls of the Moon stretch Earth 2.this stretch is evident in ocean bulges on opposite sides of Earth 3. ocean bulges on average are nearly 1 m above the average surface level of the ocean.
Universal Gravitation Review 1. What was the cause of perturbations discovered in the orbit of the planet Uranus? 2. What greater discovery did this lead to?
1. discovery of an unknown 8th planet (Neptune) 1840's Englishman (JC Adams) and Frenchman (Urbain Leverrier) 2. discovery of Pluto ~ dwarf planet 1930
Tides in Earth and Atmosphere Tides in Atmosphere
1. do not NOTICE tides at the BOTTOM of the atmosphere. (bottom of ocean) 2. Upper part of atmosphere = ionosphere a. ionosphere produce electric currents that alter the magnetic field that surrounds the Earth = MAGNETIC TIDES b. magnetic tides regulate cosmic rays that penetrate into the lower atmosphere c. magnetic tides are highest and lowest during spring tides-near the full and new Moon
Ocean Tides 1. Ocean tides do not occur in ponds because 2. Ocean tides do not occur in fluids in your body because
1. no part of the pond is significantly closer to the Moon or Sun than any other part. With no differences in pulls, no tides are produced 2. any tides caused by body fluids that are cause by the moon are negligible; not tall enough for tides. picture, p. 159, 9.20: the tidal force difference due to a 1-kg body 1 m over the head of an average height person is about 60 trillionths (6 x 10^-11) N/kg. For an overhead Moon, it is about 0.3 trillionth (3 x 10^-13) N/kg. So...holding a melon over head produces about 200 times as much tidal effect in your body as the moon does.
Tidal Bulges on the Moon
1. two tidal bulges 2. the near and far sides of each body are pulled differently ~ same as Earth's tidal bulges. 3. goes from a spherical shape into a football shape (long axis pointing toward Earth 4. differs from Earth's tidal bulges: a. fixed locations b. no daily rising and falling of tides. 5. takes the moon 27.3 days to make a single revolution on its own axis a. occurs b/c the elongated Moon's center of gravity is slightly displaced from its center of mass. b. if the Moon's long axis is not lined up toward Earth, Earth exerts a small torque on the Moon c. the Moon is twisted aligning it with Earth's gravitational field ~ like the torque that aligns a compass needle with a magnetic field. d. why the Moon always shows us its same face ~ tidal lock 6. Tidal lock also works on Earth. a. day are getting longer by 2 milliseconds per century. (In a few billion years, days = 1 month and the Moon will still show us the same face.
Gravitational Field inside a Planet Check Point Suppose you stepped into a hole bored clear through the center of Earth and made not attempt to grab the edges at either end. Neglecting air drag, what kind of motion would you experience?
1. you will go back and forth. 2. Earth = an ideal sphere of uniform density ~ no air drag 3. called simple harmonic motion 4. roundtrip = 90 minutes or 45 minutes for a one way trip
Ocean Tides high tide
1.Any part of the earth that passes beneath one of the bulges 2.the tide when the water is highest ~ 1 m above sea level 3. picture: (occurs when the sun and moon are in line)
Gravitational Fields
Definition: The influence that a massive body extends into the space around itself, producing a force on another massive body. It is measured in newtons per kilogram (N/kg) 1. action at a distance = Earth and Moon interact with each other without being in contact. 2. Moon is in contact with Earth's gravitational field 3. it is an example of a force field. a magnetic field is a force field 4. follows the inverse square law ~ strongest near Earth's surface and weakens with increasing distance from the Earth. examples: above large subterranean lead deposits, the field is stronger; above large caverns, the field is weaker. picture: field lines represent the gravitational field about Earth. Where the field lines are closer together, the field is stronger. Farther away, where field lines are father apart, the field is weaker.
Black Holes
Definition: a concentration of mass resulting from gravitational collapse, near which gravity is so intense that not even light can escape. 1. weight at the surface is determined by the inverse square law a. if a star collapses to half its radius and there is no change in its mass, gravitation at is surface is multiplied by 4 2. non-aggressive. a. gravitational fields are no stronger than the original fields about the stars before collapse ~ EXCEPT: i.at distances smaller than the original star radius ii. when too close 3. Anything that falls into a black hole is crushed out of existence. 4. only mass, angular momentum, and electric charge are retained by the black hole 5. WORMHOLE = an enormous distortion of space and time. a. does not collapse toward an infinitely dense point b. it opens out again in some other part of the universe or in some other universe. c. black holes have been confirmed ~ wormholes are speculative 6. cannot see a black hole so how is it detected? a. gravitational influence on nearby matter and on neighboring stars. b. binary star systems have black hole like properties c. massive black holes at the center of many galaxies, including our own galaxy and the Sun.
The Universal Gravitational Constant, G Checkpoint If there is an attractive force between all objects, why do we not feel ourselves gravitating toward massive buildings in our vicinity?
Gravity certainly does pull us to massive buildings and everything else in the universe. The forces between buildings and us are relatively small because their masses are small compared with the mass of Earth. The forces due to the stars are extremely tiny because of their great distances from us. These tiny forces escape our notice when they are overwhelmed by the overpowering attraction to Earth. Physicist Paul A. M. Dirac, 1933 Nobel Prize recipient put it this way: "pick a flower on Earth and you move the farthest star!"
Weight and Weightlessness Check point In what sense is drifting in space far away from all celestial bodies like stepping down off a stepladder?
In both cases, you'd experience weightlessness. Drifting in deep space, you would REMAIN weightless because no discernable force acts on you. Stepping form a stepladder, you would be only momentarily weightless because of a momentary LAPSE of support force.
The Universal Law of Gravity, Review In what sense does the Moon "fall"?
It falls away from the straight path that it would follow if there were no forces acting on it.
The Universal Law of Gravity In what sense does the Moon "fall"?
It falls away from the straight path that it would follow if there were no forces acting on it. Because of its tangential velocity, it "falls around" the round earth.
Black Holes Review If Earth shrank with no change in it mass, what would happen to your weight at the surface?
It would increase p. 163, fig. 9.27
The Universal Law of Gravity Check Point 3. Gravitational force acts on all bodies in proportion to their masses. Why, then, doesn't a heavy body fall faster than a light body?
Newton's 2nd law: (a = f/m) reminds us that greater force acting on greater mass does not result in greater acceleration. (chp. 4, f. 4.12)
Gravity and Distance: The Inverse-Square Law Checkpoint Consider an apple at the top of a tree that is pulled by Earth's gravity with a force of 1N. If the tree were twice as tall would the force of gravity by 1/4 as strong? Defend your answer.
No, because an apple at the top of the twice-as-tall apple tree is not twice as far from Earth's center. The taller tree would need a height equal to the Earth's radius (6,370 km) for the apple's weight at its top to reduce to 1/4 N. Before its weight decreases by 1% an apple or any object must be raised 32 km. The everyday changes in elevation are disregarded.
Ocean Tides check point We know that both the Moon and the Sun produce our ocean tides. We know the Moon plays the greater role because it is closer. Does its closeness mean that it pulls on Earth's oceans with more gravitational force than the sun?
No, the Sun's pull is much stronger. But the difference in lunar pulls is more than the difference in solar pulls. So our tides are due primarily to the Moon.
The Universal Gravitational Constant, Review What is the magnitude of gravitational force between two 1-kg bodies that are 1 m apart?
Two formulas needed: F = G((m1*m2)/d^2) G = 6.67 x10⁻¹¹ N*m²/ kg² F = (6.67 x 10⁻¹¹ N*m²/ kg² (1kg)(1kg))/m²) = F = 6.67 x 10⁻¹¹ = F = 0.0000000000667N F = very weak
Tidal Bulges on the Moon Review Is there a torque about the Moon's center of mass when the Moon's long axis is aligned with Earth's gravitational field? Explain how this compares with a magnetic compass
Yes, if the Moon's axis is not aligned, the Earth's gravitational field exerts a torque on the Moon to realign the axis, just like the torque that aligns a compass of a needle with a magnetic field.
Gravitational Field inside a Planet Review What would be the magnitude of the gravitational field anywhere inside a hollow, spherical planet?
Zero N/kg p. 161, fig. 9.25
The Universal Law of Gravity, Review State Newton's law of universal gravitation in words. Then do the same with one equation.
every body attracts every other body with a force that, for any two bodies, is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them. formula: force ~ (mass1 x mass2)/distance^2 formula sh: f ~ (m1 x m2)/d^2
Gravitational Field inside a Planet Review For a planet of uniform density, how would the magnitude of the gravitational field halfway to the center compare with the field at the surface?
g/2m/s^2 p. 161, fig 9.24
Gravitational Field inside a Planet Review What is the magnitude of the gravitational field at Earth's center?
zero N/kg p. 161, fig. 9.23