PHY 2020 Chapter Notes - Chapter 9: Tide, Gravitational Constant, Weightlessness

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9 Feb 2017
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Chapter 9 Notes- Gravity
The Universal Law of Gravity
- A force of gravity might account for the motions of the planet.
- Newtonian synthesis: the force between Earth and an apple is the same force
that pulls moons and planets and everything else in our universe, was a
revolutionary break with the prevailing notion that there were two sets of
natural laws: one for earthly events and another, altogether different, for
motion in the heavens.
- Newton realized that the Moon falls in the sense that it falls away from the
straight line it would follow if there were no forces acting on it.
- Law of universal gravity: Every body in the universe attracts every other
body with a force that, for two bodies, is directly proportional to the product
of their masses and inversely proportional to the square of the distance
between their center: F=G (m1m2/d^2)
o Force~mass1 x mass2/distance^2
- Figure 9.2: The tangential velocity of the Moon about Earth allows it to fall
around Earth rather than directly into it. If this tangential velocity were
reduced to zero, what would be the fate of the Moon?
- Checkpoint 1: (1) In Figure 9.2, we see that the Moon falls around Earth
rather than straight into it. )f the Moon’s tangential velocity were zero, how
would it move? (2) According to the equation for gravitational force, what
happens to the force between two bodies if the mass of one of the bodies is
doubled? If both masses are doubled? (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?
o (1) The Moon would fall straight down and crash into Earth
o (2) When one mass is doubled, the force between it and the other
mass doubles. If both masses double, the force is 4 times as great.
o (3) The answer goes back to Chapter 4. Recall Figure 4.12m in which
heavy and light bricks fall with the same acceleration because both
have the same ratio of weight to mass. Newton’s second law reminds
us that greater force acting on greater mass does not result in greater
acceleration.
The Universal Gravitational Constant, G
- Universal gravitational constant: the proportionality form of the universal
law of gravitational can be expressed as an exact equation when the constant
of proportionality G is introduced
o F=G (m1m2/d^2)
- Figure 9.3: As the rocket gets farther from Earth the gravitational pull of each
on the other decreases.
- The gravitational force between the two masses was measured by the weight
needed on the opposite end of the balance to restore equilibrium.
- The force of attraction between you and Earth however can be measured: It
is your weight.
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- Checkpoint 2: If there is an attractive force between all objects, why don’t we
feel ourselves gravitational toward massive buildings in our vicinity?
o Gravity certainly does pull us toward 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.
Gravitational and Distance: The Inverse-Square Law
- Inverse-square law: a law that relates 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.
o The inverse-square law holds for gravity and for all phenomena for
which the effect from a localized source spreads uniformly throughout
the surrounding space.
- Checkpoint 3: (1) By how much does the gravitational forces between two
objects decrease when the distance between their centers is doubled?
Tripled? Increase tenfold? (2) Consider an apple at the top of trees that is
pulled by Earth’s gravity with a force of  N. )f the tree is twice as tall, will the
force of gravity be ¼ as strong? Defend your answer.
o (1) The force decreases to ¼, 1/9, and 1/100 the original value.
o (2) 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 Earth’s radius for the apple’s weight at its top to reduce to ¼
N. Before its weight decreases by 1%, an apple or any object must be
raised 32 km- nearly 4 times the height of Mt. Everest. So, as a
practical matter, we disregard the effects of everyday changes in
elevation.
- Figure 9.7: According to Newton’s equation, the girl’s weight decreases as she
increases her distance from Earth’s center.
Weight and Weightlessness
- Weight: the press against Earth
- Figure 9.8: When you step on a weighting scale, two forces act on it: a
downward force of gravity, mg, and an upward support force. These two
forces are equal and opposite when no acceleration occurs, and they squeeze
a spring-like device inside the scale that is calibrated to show your weight.
- So a broader definition of weight experienced by something is the force it
exerts against a supporting surface.
- Weightless: there is still a gravitational force acting on you that causes your
downward acceleration.
o But gravity now is not felt as weight because there is no support force.
- Figure 9.9: Your weight equals the fore with which you press against the
supporting floor. If the floor accelerates up or down, your weight varies
(even through the gravitational force mg that acts on you remains the same)
- Figure 9.10: These astronauts are in free fall. They feel weightless because
they aren’t pressed against anything that provides a support force.
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