Download Motion, Energy, and Gravity

Motion, Energy, and Gravity
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Today’s Topics
• Describing Motion
• Mass v. Weight
• Newton’s Laws of Motion
• Energy
• Newton’s Law of Gravitation
Describing Motion
• All objects in the Universe are moving
• Earth is spinning about its axis
• Earth orbits Sun
• Solar System orbits center of Milky Way
• Milky Way and Andromeda galaxy are rushing towards each other
• All galaxies, on the largest scale are moving apart (the Universe is
expanding)
• The two galaxies below are in the process of colliding
Describing Motion
• Three of the fundamental
quantities used to describe
motion are position, velocity,
and acceleration
• Position is how far an object is
(in all dimensions) from a
reference point
• Velocity is the rate of change of
position (speed is the magnitude
of velocity)
• Acceleration is the rate of change
of velocity
• Because velocity has both a
size and direction, an object
can accelerate, even when its
speed doesn’t change!
Mass v. Weight
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Mass is an intrinsic property of an object - how
much of it is there? (measured in kg)
Weight is the force experienced by an object due
to gravity (measured in lbs or Newtons)
Weight, unlike mass, depends on the situation
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In the stationary elevator at right, the weight on the
scale is the same as it would be standing on the ground
If the elevator moves up or down at a constant velocity
the weight on the scale is unchanged
If the elevator accelerates up, the weight on the scale is
higher (you feel heavier)
If the elevator accelerates down, the weight on the scale
is lower (you feel lighter)
If the cable is cut, and the elevator falls freely, you feel
no weight at all (weightlessness)
Pink Panther v. Astronomer Video - 3:30
Pink Panther Quiz
How many “cartoon physics” errors did you detect
in the video?
a) 0
b) 1
c) 2
d) 3
e) More than 3
Mass Quiz
Compared to your mass here on Earth, your mass out in
the space between the stars would be
zero
b) negligibly small
c) much much greater
d) the same
e) the question cannot be answered from the information given
a)
Weightlessness Quiz
Astronauts on the space shuttle feel weightless because
they have no mass in space
b) they are in a constant state of free-fall
c) they are outside the effect of the Earth’s gravity
d) without air there can be no weight
e) all of the above
a)
Newton’s Laws of Motion
• Newton, building on the work of Galileo,
formulated three laws of motion
• 1st Law - an object moves at a
constant velocity (both speed and
direction) unless acted on by a force
• 2nd Law - The acceleration of an
object acted on by a force is
proportional to the force and inversely
proportional to the mass of the object
(a = F/m)
• 3rd Law - For any force, there is an
equal and opposite reaction force
• These laws govern the motion of all
objects in the Universe, except the very
fast (relativity) and the very small (QM)
Example - the Bus and the Bug
• Imagine a bug flying into the windshield of an oncoming bus
• What is the relative size of the forces the bus and bug feel
(Newton’s 3rd Law)
Bus-Bug Quiz I
In a head-on collision between a bus and a bug, which
feels the greater force?
The bus
b) The bug
c) They feel the same force
d) The question cannot be answered from the information given
a)
Example - the Bus and the Bug
• Imagine a bug flying into the windshield of an oncoming bus
• What is the relative size of the forces the bus and bug feel
(Newton’s 3rd Law)
• What is the relative size of the accelerations the bus and the
bug feel (Newton’s 2nd Law)
Bus-Bug Quiz II
In a head-on collision between a bus and a bug, which
feels the greater acceleration?
The bus
b) The bug
c) They feel the same acceleration
d) The question cannot be answered from the information given
a)
Example - the Bus and the Bug
• Imagine a bug flying into the windshield of an oncoming bus
• What is the relative size of the forces the bus and bug feel
(Newton’s 3rd Law)
• What is the relative sizes of the accelerations the bus and the
bug feel (Newton’s 2nd Law)
abus
= Fbug-bus/Mbus
abug = Fbus-bug/m
bug
Circular Motion
• An object in circular motion may have
a constant speed but its velocity is
constantly changing, as its direction of
motion changes
• Newton’s 2nd Law tells us that there
must be a force causing this
acceleration
• In the case of a ball (or donut) on a
string, it is the inward force of the
string that keeps the ball (or donut)
from flying away
• If the string (or donut) breaks, the ball
(or donut) will fly away in a straight
line
(Donut demo)
Forces and Orbits
• An object in orbit feels the force of
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gravity from the central object
Imagine running off a platform on a
very tall tower (above the atmosphere)
You would fall to the Earth, but the
faster you started, the further from the
base of the tower you would land
If, instead of running, you strapped a
rocket to your back, and gave yourself
enough initial velocity (about 8 km/s
near Earth’s surface), you could fall
around the Earth, i.e., you could orbit
All objects in orbit stay in their orbital
path due to the force of gravity
Velocity
Path
Force
Weightlessness Quiz
Astronauts on the orbiting space shuttle feel weightless
because
a)
b)
c)
d)
e)
they have no mass in space
they are in a constant state of free-fall
they are outside the effect of the Earth’s gravity
without air there can be no weight
all of the above
Moon Quiz
The Moon remains in its orbit around the Earth rather
than falling to the Earth because
a) it is outside of the gravitational influence of the Earth
b) it is in balance with the gravitational forces from the Sun
and other planets
c) the net force on the Moon is zero
d) none of these
e) all of these
Energy
• Energy is the central unifying theme
of all science
• Energy comes in many forms
• Kinetic energy (energy of motion)
including motion of atoms (temperature)
- Note: higher speed means more
kinetic energy
• Radiative energy (energy of light)
• Potential (stored) energy, including
mass which is a form of stored energy
(E = mc2)
• Although energy can change from
one form to another, it is always
conserved in total
Gravitational Potential Energy
• When a ball is thrown into the air, it
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starts with kinetic energy
When it reaches the top of its motion,
it momentarily stops
Q: Where did the energy go?
A: Into gravitational potential
energy
The energy is “stored” in the
interaction between the ball and Earth
The evidence for this is that the
energy is (almost) completely
recovered as kinetic energy when the
ball falls back to the ground
High = large GPE Low = small GPE
Gravitational Potential Energy in Orbits
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Recall Kepler’s 2nd Law In a given time, a line connecting the
Sun to the planet will sweep out an area
that is the same in all parts of the orbit
Thus, the planet moves faster when it is
closer to the Sun
We can now understand this in terms of
energy (KE and GPE)
Since the total energy of the planet is
conserved
1. When the planet is closer to the Sun, its GPE
is lower, and its KE (and speed) will be
higher
2. When the planet is further from the Sun, its
GPE is higher, and its KE (and speed) will
be lower
Interactive Figure – Kepler’s 2nd Law
Newton’s Law of Gravitation
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Newton knew that gravity caused objects to fall to the Earth
However, his great achievement was to understand that the same force also held
the Moon in its orbit around Earth
The force acts on both objects in an equal and opposite manner
(Newton’s 3rd Law)
The force is always attractive and has direction (Example: person on Earth)
The correct mathematical relationship is that:
1. The force is proportional to both masses (Newton’s 3rd Law)
2. The force is inversely proportional to the square of the distance between the
objects
The quantity G is a universal constant relating masses, distances, and forces, for
a given system of units
Newton and Kepler’s Laws
• KI – Newton’s force law correctly
predicts that planets will move in
elliptical orbits with the Sun at one
focus
• KII - We have already seen how
gravitational potential energy can
help explain that planets move
faster when close to the Sun and
slower when further from the Sun
• KIII - It is possible to derive this
law (p2 ∝ a3) from Newton’s law
of gravitation
Newton and Kepler’s Laws
There are some differences between Newton’s
and Kepler’s version of planetary (and other)
orbits
1.
The planets do not technically orbit the
Sun; they orbit the center of mass of the
system
The center of mass of the Solar System is
near the edge of the Sun, so the Sun moves
very little, but it does wobble a bit about
the center of mass
2.
All objects with mass will orbit, e.g., binary
stars (Interactive Figure 4.18)
3.
Only bound orbits are elliptical; unbound
orbits are parabolic or hyperbolic
Lecture Tutorial: Newton’s Laws and
Gravitation, pp. 29-32
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Work with one or more partners - not alone!
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Get right to work - you have 20 minutes
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Read the instructions and questions carefully.
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Discuss the concepts and your answers with one another.
Take time to understand it now!!!!
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Come to a consensus answer you all agree on.
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Write clear explanations for your answers.
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If you get stuck or are not sure of your answer, ask another
group.
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If you get really stuck or don’t understand what the Lecture
Tutorial is asking, ask me for help.
Homework
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For homework
• Complete the Lecture Tutorial Newton’s Laws
and Gravitation (if necessary)
• Complete the ranking tasks, Gravity #2-4,
(download from class website)
Gravity Quiz I
How does the gravitational force between two objects
change if the mass of one of the objects triples?
a)
b)
c)
d)
e)
The force increases by a factor of nine
The force increases by a factor of three
The force remains the same
The force decreases by a factor of three
The force decreases by a factor of nine
Gravity Quiz II
How does the gravitational force between two objects
change if the distance between them triples?
a)
b)
c)
d)
e)
The force increases by a factor of nine
The force increases by a factor of three
The force remains the same
The force decreases by a factor of three
The force decreases by a factor of nine