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Key points in this lecture are: Gravity, Universal Law of Gravity, Distance-Dependence of Gravity, Weight and Weightlessness, Ocean Tides, Spring Vs Neap Tides, Tides In the Earth, Tides In the Atmosphere, Gravitational Fields, Einstein’s Theory of Gravitation Topics covered in this course "Basic Concepts of Physics" are: Newton’s Laws of Motion, Linear Motion, Momentum, Energy, Rotation, Gravity, Liquids, Gase, Plasmas, Heat, Waves, Sound, Electrostatics, Electric current, Magnetism, Electromag
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Newton: made revolutionaryconnection between the circularmotion of celestial bodies and thedownward falling of objects on theearth: It is the one and the samegravitational force responsiblefor both the apple falling fromthe tree and the moon orbitingaround the earth!
Every mass
m
attracts every other mass 1
m
with a force: 2
m
m 1
2
d^
2
distance between their centers
The greater (either of) the masses, the greater is the attractive force.The closer they are to each other, the greater the force – with aninverse-square dependence.
-^ The constant of proportionality is called the
universal gravitational
constant,
G = 6.67 x 10
N. m
2 /kg
2 = 0.0000000000667 N m
2 /kg
2
G m
m 1
2
d^
2
Tiny!
So gravitational forces between everyday masses at everyday distances(eg you and me) is negligible.
F ~ 1/d
2
Compare with paint-spray burst out from a can: the thickness of thepaint varies in the same inverse-square way i.e. if 1-layer thick at 1m,then is ¼ layers thick at 2 m etc.
Notes (1)
d
= distance between the
center of masses
of the objects.
So when one of the objects is earth, then the relevant distance d^
= radius of the earth + distance of other object from earth’s surface.
6.4 x 10
6 m
(2) Even very very far from earth, its gravitational force is never
actually zero, but it does decrease rapidly and forces from other morenearby objects would overwhelm the grav force from earth.
(Neglect changes in the weight ofthe fuel carried by the shuttle.)
Clicker Question
1. nearly as much. 2. about half as much.3. nearly zero (micro-gravity).4. zero.
(Neglect changes in the weight ofthe fuel carried by the shuttle.)
When at rest on the launching pad,the force of gravity on the spaceshuttle is quite huge—the weight ofthe shuttle. When in orbit, some200 km above Earth’s surface, theforce of gravity on the shuttle is
The gravitational force on the shuttle,whether at rest or in orbit, depends on onlythree things: its mass, the mass of Earth,and its distance from Earth’s center. Theonly variable is distance. On the launchingpad the shuttle is about 6370 km fromEarth’s center. When in orbit it is about 6370+ 200 km from the Earth’s center. In accordwith
the 200-km difference in
distance means a 0.06 fractional differencein force. Discounting the changes in the fuel,the gravitational force on the shuttle in orbitis 94% as much as when on Earth’ssurface—nearly the same.
Answer:1, nearly as much F^
Gm M
/^ R
2
Earlier, we defined weight as force due to gravity,
mg
But if we
accelerate
, we may “feel” heavier or lighter – eg. in an elevator:
If the elevator accelerates upwards, any scales you are standing on willread a higher weight and you feel heavier
larger “apparent weight”; if
accelerates downwards, they read a lower weight and you feel lighter
less “apparent weight”.
Your “apparentweight” depends onyour acceleration
We will now
define apparent weight
to measure this instead --
Define apparent weight = force exerted against a supporting surface or a
weighing scale. (Note: your textbook calls “apparent weight” just weight at this point!)
Answer: BThe gravitational force on you is what we call your weight,mg, provided by your gravitational interaction with the earth.However you feel weightless because there is no supportforce when you are in free-fall – there is therefore noapparent force.
Caused by differences in the gravitational pull of the moon on theearth on opposite sides of the earth.
-^
Moon’s pull is stronger on the side of the earth that it is closest to;weakest on the opposite side, because F decreases with distance.
-^
Why does this result in
two
high-tides (and two low-tides) every
day? Because when the moon is
either
closest or farthest away,
you get a maximum bulge:
Imagine earth to be a ball of jello.If moon’s force was equal at everypoint, then it all accelerates togethertowards moon.But moon’s force is actually more likearrows here: so ball gets elongated – both sides
effectively bulge.
(moon over heresomewhere)
Since earth spins once a day, any point on earth has two high tidesand two low tides (on average, 1-m below average) a day. If moon was not orbiting, then the high-low tide separation would be ¼
day, ie. 6 hours.
-^
But since while the earth spins, the moon moves in its orbit, it turns outthe moon returns to same point in the sky every 24 hours and 50minutes – ¼ of this is what determines the high-low-tide timedifference.
-^
This is why high tide is not at the same time every day
-^
Why are there no tides in lakes?– Because lakes are localized; no part of the lake is a lot closer to
the moon than any other part, so no big differences in moon’s pullin a lake, as opposed to the oceans which span the globe… Note also that due to the earth’s tilt, the two high-tides are not equally high.
The sun’s gravitational force on Earth is 180 times as large as that of themoon’s pull on Earth. So, what about ocean tides due to the sun??Why are these not 180 times as strong as those due to the moon?
Because tides happen due to
differences
in grav pulls on one side of
earth c.f. other side.Because the sun is so far away, the
1/d
2 factor flattens out, so the
are
tides due to the sun, which are
about half as high as those due to the moon(180 x 0.017 % = 3 %, which is about half of 6.7 %)
high-tides are higher
and low tides are lower thanaverage --
Spring
tide (nothing
to do with the season).At full moon or new moon.When lines to the moon and sunare at right angles, then high tidedue to one occurs at low tide dueto other
smaller than average
high tides –
Neap
tide (nothing to
do with your instructor)At time of half-moon
.
