Transcript Part II - Otterbein University

You are a passenger in a car and not wearing
your seat belt. Without changing its speed, the
car makes a sharp left turn, and you find
yourself colliding with the right-hand door.
Which is the correct analysis of the situation?
• Before and after the collision, there is a
rightward force pushing you into the door.
• Starting at the time of the collision, the door
exerts a leftward force on you.
• Both of the above
• Neither of the above
Your little brother wants a ride on his sled. On
flat ground, should you push or pull him if
you want to use the least force ?
• Pull
• Push
• Not enough information
In the 17th century, Otto von Guericke, a physicist in
Magdeburg, fitted two hollow bronze hemispheres
together and removed the air from the resulting sphere
with a pump he invented. Two eight horse teams could
not pull the halves apart, even though the hemispheres
fell apart when air was admitted. Suppose he had tied
both teams of horses to one side and bolted the other side
to a heavy tree trunk. In this case, the tension on the
hemispheres would be (…) what it was before.
•
•
•
•
twice
exactly the same
half
Not enough information
Consider a frictionless Atwood’s
machine. Can we assume that the
magnitudes of the accelerations of
the elevator car and the
counterweight are the same?
• Yes
• No
• Not enough information
Identifying Forces
1. Divide the problem into “system” and “environment”. The
system is just the object whose motion we wish to study.
2. Draw a picture of the situation, showing the object and
everything in the environment that touches the object. Ropes,
springs, surfaces, etc. are all parts of the environment.
3. Draw a closed curve around the system, with the object inside
the curve and everything else outside.
4. Locate every point on the boundary of this curve where the
environment touches or contacts the system. These are the
points where the environment exerts contact forces on the
object. Don’t leave any out!
5. Identify by name the contact forces at each point of contact
(there may be more than one!), then give each an appropriate
symbol.
6. Identify any long-range forces (for us: gravity) acting on the
object and write its symbol beside your picture.
Analyze the following two situations: a)
a mass of 10 kg hangs vertically from a
pulley attached to a spring scale which is
attached to the wall. b) the wall is
replaced by another mass hanging from a
second pulley. Which is correct?
• The scale shows a larger force in a)
• The scale shows a larger force in b)
• The scale shows the same force in a) & b)
Johannes Kepler–The Phenomenologist
• Key question:
How are things happening?
Major Works:
• Harmonices Mundi (1619)
• Rudolphian Tables (1612)
• Astronomia Nova
• Dioptrice
Johannes Kepler (1571–1630)
Kepler’s First Law
The orbits of the planets are ellipses, with
the Sun at one focus
Ellipses
a = “semimajor axis”; e = “eccentricity”
Kepler’s Second Law
An imaginary line connecting the Sun to any planet sweeps
out equal areas of the ellipse in equal times
Why is it warmer in the summer than
in the winter in the USA?
• Because the Earth is closer to the Sun
• Because the Sun rises higher in the sky in
the summer
• None of the above
Kepler’s Third Law
The square of a planet’s orbital period is proportional to the cube of its
orbital semi-major axis:
P 2  a3
a
P
Planet Orbital Semi-Major Axis Orbital Period
Mercury
0.387
0.241
Venus
0.723
0.615
Earth
1.000
1.000
Mars
1.524
1.881
Jupiter
5.203
11.86
Saturn
9.539
29.46
Uranus
19.19
84.01
Neptune
30.06
164.8
Pluto
39.53
248.6
(A.U.)
(Earth years)
Eccentricity
0.206
0.007
0.017
0.093
0.048
0.056
0.046
0.010
0.248
P2/a3
1.002
1.001
1.000
1.000
0.999
1.000
0.999
1.000
1.001
“Strange” motion of the Planets
Planets usually move from W to E relative to the stars,
but sometimes strangely turn around in a loop, the so
called retrograde motion.
The heliocentric Explanation of
retrograde planetary motion
The Planets from Otterbein
Venus
Mars
The Planets from Otterbein
Jupiter
The Planets from Otterbein
Saturn
The Planets from Otterbein
Uranus
Neptune
The Planets from Otterbein
The Moon
Isaac Newton – The Theorist
• Key question:
Why are things happening?
• Invented calculus and physics
while on vacation from college
• His three Laws of Motion,
together with the Law of
Universal Gravitation, explain all
of Kepler’s Laws (and more!)
Isaac Newton (1642–1727)
Isaac Newton (1642–1727)
Major Works:
• Principia (1687)
[Full title: Philosophiae naturalis
principia mathematica]
• Opticks [sic!](1704)
• Major findings:
– Three axioms of motion
– Universal gravity
Law of Universal Gravitation
Mman
MEarth
R
Force = G Mearth Mman / R2
Which of the following depends on
the inertial mass of an object (as
opposed to its gravitational mass)?
• The time it takes on object to fall from a certain
height
• The weight of an object on a bathroom-type
spring scale
• The acceleration given to the object by a
compressed spring
• The weight of the object on an ordinary balance
Orbital Motion
Cannon “Thought Experiment”
• http://www.phys.virginia.edu/classes/109N/more_stuff/Appl
ets/newt/newtmtn.html
Suppose Earth had no atmosphere, and a ball were
fired from the top of Mt. Everest in a direction
tangent to the ground. If the initial speed were high
enough to cause the ball to travel in a circular
trajectory around Earth, the ball’s acceleration
would be…
•Much less than g (b/c the
ball doesn’t fall to the
ground)
•Be approximately g
•Depend on the ball’s speed
•None of the above
Two satellites A and B of the same mass are
going around Earth in concentric orbits. The
distance of satellite B from Earth’s center is
twice that of satellite A. What is the ratio of
centripetal force acting on B to that acting on
A?
•
•
•
•
1/8
¼
½
1
You lift up a stone to a new height.
In the energy-money analogy this is
like …
•
•
•
•
Receiving a check from the stone
Writing a check to the stone
Putting money in your bank account
Taking out cash from an ATM
Two marbles, one twice as heavy as the
other, are dropped to the ground from
the top of a building. Just before hitting
the ground, the heavier marble has…
•
•
•
•
…as much kinetic energy as the lighter one.
…twice as much kinetic energy as the lighter one.
…half as much kinetic energy as the lighter one.
…four times as much kinetic energy as the lighter
one.
A car is connected to a hanging weight
by a string on a pulley. What happens
to the kinetic energy of the car as it is
released?
•
•
•
•
increases
decreases
stays the same
Impossible to tell
A car is connected to a hanging weight
by a string on a pulley. What is the
change in kinetic energy?
•
•
•
•
∆K = 0
∆K > 0
∆K < 0
Impossible to tell
A car is connected to a hanging weight
by a string on a pulley. The car is
accelerated due to the tension. What
work does tension do on the car?
•
•
•
•
None
Positive work
Negative work
Impossible to tell
A car is connected to a hanging weight
by a string on a pulley. The car is
accelerated due to the tension. Is the
net work done on the car …?
•
•
•
•
Zero
Positive
Negative
Impossible to tell
A car is connected to a hanging weight by a
string on a pulley. The car is now pushed to
the left, lifting the mass. What happens to
the kinetic energy of the car before it stops
and turns around?
•
•
•
•
increases
decreases
Stays the same
Impossible to tell
A car is connected to a hanging weight by a
string on a pulley. The car is now pushed to
the left, lifting the mass. What is the
change in kinetic energy of the car before it
stops and turns around?
•
•
•
•
∆K = 0
∆K > 0
∆K < 0
Impossible to tell
A car is connected to a hanging weight by a
string on a pulley. The car is now pushed to
the left, lifting the mass. What work does
tension do on the car before it stops and
turns around?
•
•
•
•
None
Positive work
Negative work
Impossible to tell
A car is connected to a hanging weight by a
string on a pulley. The car is now pushed to
the left, lifting the mass. What is the net
work done on the car before it stops and
turns around?
•
•
•
•
Wnet = 0
Wnet > 0
Wnet < 0
Impossible to tell
A car is connected to a hanging weight by a
string on a pulley. The car is now pushed to
the left, lifting the mass. What is correct
analysis of the situation before the car stops
and turns around?
•
•
•
•
Change in K and net work done are negative
Change in K is pos., net work done negative
Change in K is neg., net work done positive
Change in K and net work done are positive
Potential Energy
• Work done around any closed path is zero
for conservative forces
• For conservative forces a function exists
that describes the amount of energy stored
in a certain configuration involving these
forces
– We can calculate how much work it took to
configure the configuration
– Analogy: building a building costs money
because it takes work to build it.
Gravitational potential energy
• Lifting up a stone we do work against
gravity: W=Fd=mgh
• This is energy transferred into the system
and stored int the configuration “stone sits
at height h above the Earth”
Potential energy of a spring
• Compressing a spring we do work against
the elastic forces in the wire: W=1/2 k x2
• This is energy transferred into the system
and stored int the configuration “spring is
compressed by a distance x”
Potential energy & work-energy
theorem
• Change in potential energy will be equal to
the work done ON the system
ΔU=U2-U1 =Wsystem,external = Wext
• System defined by ITS forces, define
potential energy as work AGAINST the
forces of the system
ΔU=-Wexternal, system = -Wsystem
A ball is pushed up an incline. What
work does gravity do on the ball?
•
•
•
•
Positive
Zero
Negative
Depends on angle
A ball is pushed up an steeper
incline. What work does gravity do
on the ball compared to the
shallower incline?
•
•
•
•
Same
More negative
Less negative
More positive
Energy Problem Solving
1. Draw a picture
2. Determine the system: objects and forces on
them
3. What is the unknown?
4. Choose initial and final positions
5. Choose convenient reference frame for potential
energy
6. Draw an energy bar chart
7. If mech. Energy is conserved: K+U=K+U
8. Solve for the unknown
Dissipative Forces
• Non-conservative forces at work means
mechanical energy is not conserved, but
energy still is
K1+U1= K2+U2+ Wnon-conservative
– Example: Friction has
Wnon-conservative = Ffriction d
Group Work
• A 60kg skateboarder starts up a 20 degree
slope at 5m/s, then falls and slides up the
hill on his kneepads. The coefficient of
friction is 0.30. How far does he slide
before stopping?