Transcript Document 7523740

What do you remember from
Physics 53?
Review
Newton’s Law of Universal
Gravitation
Every particle in universe attracts every other particle with a
force that is proportional to the product of their masses and
inversely proportional to the square of the distance between
them. This force acts along the line joining the two particles.
F = G m1m2/r2
Question
1. The Moon falls around the Earth than straight into it.
If tangential velocity were zero, how would the
Moon move?
2. According to the equation for gravitational force,
what happens to the force between two bodies if the
mass of one of bodies is doubled? If both masses are
doubled?
The Universal Gravitational
Constant G
F = Gm1m2/d2
G = 6.67 10-11 Nm2/kg
Questions
1. If there is an attractive force between all objects, why do we
not feel gravitating toward massive buildings in out
vicinity?
2. Consider an apple at the top of the tree that is pulled by
Earth’s gravity with a force of 1 N. If the tree were twice as
tall, would the force of gravity be only ¼ as strong? Defend
your answer.
Question
In what sense is drifting in space far
away from all celestial bodies like
stepping off the table?
Momentum
When we combine the ideas of inertia
and motion we are dealing with
momentum
By momentum we mean inertia in
motion. More specifically momentum is
defined as the product of the mass of an
object and its velocity, that is:
momentum = mass x velocity
When direction is not important
momentum = mass x speed.
Impulse
Impulse = Force x Time interval
Assume that your friend jumps from the roof of
the garage and lands on the ground. How will
the impulses the ground exerts on your friend
compare if the landing is on grass or on
concrete?
Conservation of Momentum
To change a momentum we must apply some
impulse…
In other words, the force or impulse must be
exerted on the object or any system of objects
by something external to the object.
Questions
1. A high-speed bus and an innocent bug have a head-on collision.
The sudden change of momentum for the bug spatters it all over
the windshield. Is the change in momentum of the bus greater,
less or the same as the change in momentum experienced by the
unfortunate bug?
2. The Starship Enterprise is being in space by a Klingon warship
moving at the same speed. What happens to the speed of the
Klingon ship when it fires a projectile at the Enterprise? What
to the speed happens of the Enterprise when it returns the fire?
1. How does the padding (or air pockets) in the soles
of running shoes reduce the forces on your legs?
Explain your answer in terms of impulse and
momentum.
2. Two identical objects moving at the same speed
collide head-on. If the two objects stick together
after the collision, will they move to the right, left
not at all?
1. An astronaut training at the Craters of the Moon in Idaho
jumps off platform in full space gear and hits the surface at
5 m/s. If later, on the Moon, the astronaut jumps from the
landing vehicle and hits the surface at the same speed, will
the impulse be larger, smaller, or the same as that on Earth?
Why?
2. An object of mass m and an object of mass 3m, both
moving at the same speed, collide head-on. If the two
objects stick together after the collision, will they be moving
to the left, to the right or not at all?
Some times a star “dies” in an enormous
explosion know as a supernova. What happens
to the total momentum of such a star?
Work
For the simplest case, where the force is constant and the
motion takes place in a straight line in the direction of the
force we define the work done on an object by applied
force as a product of the force and the distance through
which the object is moved. In shorter form
Work = force x distance
Conceptual Question
Does Earth do work on Moon?
Important: Definition of work
involves both a force and a
distance.
Units of Work
1J=1Nm
Power
Power = work done/time interval
Units of Power
1 W = 1J/s
Mechanical Energy
We can define energy as “the ability
to do work”.
Conservation of Kinetic Energy
Question
Are the collisions of billiard balls perfectly elastic?
Important: The change in potential energy
between any two points does not depend on
the choice of reference level.
Important: The changes in gravitational
potential energy depend only on the change in
vertical height and not on the path taken.
PE of Elastic Spring
Important: Potential energy
belongs to a system, and not to a
single object alone!!!! The
potential energy is a property of a
system as a whole.
Mechanical Energy and its
Conservation
If no frictional (or other dissipative)
forces are involved, the total
mechanical energy of a system
neither increases nor decreases in any
process. It stays constant – it is
conserved.
Conceptual Example: Speeds on
Two Water Slides
Two water slides at a pool are shaped differently, but have the
same length and start at the same height h. Two riders, Paul
and Kathleen, start from rest at the same time on different
slides.
(a) Which rider, Paul or Kathleen, is traveling faster at the
bottom?
(b) Which rider makes it to the bottom first?
1. In tryouts of the national bobsled team, each competing team
pushes a sled along a level, smooth surface for 5 meters. One
team brings a sled that is much lighter than the others.
Assuming that this team pushes with the same force as the
others, compare the kinetic energy of the light sled to that of
the others after 5 meters . Compare the momentum of the
light sled to that of the others after 5 meters.
2. Suppose the rules were changed in previous question so that
the teams pushed for a fixed time of 5 seconds rather that a
fixed distance of 5 meters. Compare the momentum of the
light sled to that of the others after 5 seconds. Compare the
kinetic energy of the sled to that of the others after 5 seconds.
1. Does a car consume more fuel when its air conditioner is
turned on? When its lights are on? When its radio is on while
it is sitting on the parking lot?
2. Rows of wind-powered generators are used in various windy
locations to generate electric power. Does the power
generated affect the speed of the wind? That is, would
locations behind the “windmills” have more wind if the
windmills weren’t there?
1. Mountain highways often have emergency ramps for truckers
whose brakes fail. Why are these covered with soft dirt or
sand rather that paved?
2. A physics textbook is launched up a rough inline with a
kinetic energy of 200 J. When the book comes momentarily to
rest near the top of incline, it has gained 180J of gravitational
potential energy. How much kinetic energy will it have when
it returns to the launch point?
1. When you get your power bill, you are charged for the
number of kilowatt-hours that you have used. Is kilowatthour a unit of power or a unit of energy?
2. Athletes will sometimes run along the beach to increase the
effect of their workouts. Why is running on soft sand so
tiring?
3. Which of the following is not a unit of energy: joule,
Newton-meter, kilowatt-hour, watt?
Rotational Motion
Question
On a rotating platform, if you sit halfway between the
rotating axis and the outer edge and have a rotational speed
of 20 RPM and tangential speed of 2 m/s, what will be the
rotational and tangential speeds of your friend, who sits on
the outer edge?
Questions
1. Consider balancing a hammer upright on the tip of your
finger. If the head of hammer is heavy and the handle
long, would it be easier to balance with the end of the
handle on your finger so that the head is at the top, or the
other way around with the head at your fingertip and the
end of the handle on the top?
2. Consider a pair of meter sticks standing nearly upright
against the wall. If you release them, they’ll rotate to the
floor in the same time. But what if one has a massive
hunk of clay stuck to its top end? Will it rotate to the
floor in a longer or shorter time?
1. A figure skater is spinning with her arms held straight out. Which
has greater rotational speed, her shoulders or her fingertips?
Why?
2. You are looking down on a merry-go-round and observe the it is
rotating clockwise. What is the direction of the merry-go-round
rotational velocity? If the merry-go-round is slowing down, what
is the direction of its rotational acceleration?
3. What is the direction of rotational velocity of Earth?
1. Earth rotational speed is slowing due to tidal influences of
the Sun and Moon. What is the direction of Earth’s
rotational acceleration?
2. Two flywheels have the same mass but one of them is much
thinner than the other so that its radius is twice that of the
other one. If both flywheels are spinning about their axes at
the same rate, which one would be harder to stop? Why?
Torque
Balancing a Seesaw
Newton’s first Law for Rotation
The angular velocity of an object remain
constant unless acted on by an
unbalanced torque.
Newton’s Second Law for
Rotation
St = Ia
Conceptual Example: Who’s
fastest?
Several objects roll without slipping down an inline of vertical
height H, all starting from rest at the same moment. The objects
are: thin hoop, a marble, a solid cylinder an empty soup can. In
addition a greased box slides down without friction. In what order
do they reach the bottom of the incline?
Angular Momentum and its
Conservation