Transcript New Phenomena: Recent Results and Prospects from the Fermilab

Physics 218
Review
Dr. David Toback
Physics 218, Review
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Thought of the day…
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Problem Choices
1. Ball rolling down a hill
2. Ice Skating
3. Apollo 11
4. Mass moving in a circle
5. Hunter in the forest
6. Simple harmonic motion derivation
7. Ski Vacation
8. Rocket Launcher
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Ball Rolling Down a Hill
You are the technical advisor on the new movie:
“The Matrix – Refrozen.” The script has a giant
spherical ice ball, I = 2/5 mr2, where you have
measured m and r. It rolls down a hill (without
slipping) starting from rest right at Morpheus
who is at the bottom. You know the length of the
slope (L) and its angle to the horizontal (q) and
the ball starts from the top of the hill
• Your job is to calculate the speed of the ice ball at
the bottom of the hill (you want to make sure it’s
fast enough to look cool) and
• The time it takes to get down the hill so Morpheus
knows exactly when to dive out of the way.
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Ice Skating
You decide to take up ice-skating and, being athletic, want to
learn all the moves. You are proud of the fact that you have
learned to spin in place on the ice. Your friends video tape
you spinning and then bringing your arms in close to your
body. From the tape you are able to measure your initial and
final moments of inertia, I0, and If = Io/3, as well as your
final angular speed, wf. In terms of I0 and wf, find:
• Your final angular momentum
• Your initial angular speed
• Your initial kinetic energy
• How much work you have to do to bring in your arms.
At the end of your spin, you put your foot down and dig your toe
into the ice and come to a stop. You measure the time it takes
to stop to be t seconds. Assuming constant negative angular
acceleration:
• What is the torque your toe exerts?
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Mass Moving in a Circle
A puck of mass M, attached to a massless string, moves in a circle of
constant radius R about a small hole on a frictionless, horizontal
table. The end of the string is connected to a small block of mass m
through the hole as shown. At t=0 the puck is at (R,0) and moving
in the positive Y-direction. The block and puck may be treated as
particles.
• Draw the force diagram for the puck including the magnitude and
direction of each force.
• Find the speed (v1) of the puck in terms of g, R, M and m
• Is this Simple Harmonic Motion? If so, what is the Amplitude and
w? What is the equation of motion in the X-direction?
• A woman pulls the block (of mass m) down by ½R. Find the
resultant speed, v2, of the rotation in terms of v1. Hint: Use
conservation of angular momentum
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Hunter in the Forest
A hunter aims directly at a target which is a distance R
away. Note that the gravitational acceleration near the
earth’s surface is g. Ignore air friction.
• If the bullet leaves the
gun at a speed of V0, by
how much (vertically)
will it miss the target? In
other words, on the
diagram what is the
value of d.
• Assuming the bullet
leaves at the same speed,
at what angle should the
d
gun be aimed so that the
target will be hit? Hint:
2sinqcosq = sin2q
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Simple Harmonic Motion
A block of mass m sits on a frictionless surface attached to a
spring with spring constant k. We can write down
• Hooke’s law: F=-kx
• Newton’s law: F = ma =md2x/dt2.
• Given that the general equation of motion for the
position, x, as a function of time t is x(t) = Asin(wt+f),
show that this equation is a solution of Hooke’s law and
Newton’s law with w2= k/m.
• At time t=0, the spring is compressed to the position -x0
and released from rest. Using your previous results, find
the amplitude. You may NOT just write down the
solution, rather you must show it to be true
mathematically.
• For the same system, find the phase of the motion
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Ski Vacation
You take a ski vacation to Vale, Colorado. While at
the summit of a large slope, you start from rest
and then ski over two successively lower hills with
known heights H1 = 2H2. The lowest hill is
essentially a semi-circle centered at the 0 level.
You want to leave the lowest hill at its top and fly
through the air. Assume no friction and air
resistance. The magnitude of gravity = g.
How far up the slope must you be when you start
down the hill? Put your answer in terms of g and
H 2.
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Rocket Launcher
You want to simulate the muzzle velocity of a missile fired
by the shoulder-fired “Red-eye launcher.” To simulate
this, you build a small model and test-fire a bullet of
mass M1 and unknown speed directly into a wooden
block of mass M2. The block is suspended by wires from
the ceiling and is initially at rest. The bullet embeds in
the block and the block swings up to a maximum height
(Hmax) above its initial position. Magnitude of gravity =
g. Ignore air friction.
• What is the speed of the bullet, when fired?
• What is the change in mechanical energy after the bullet
gets stuck in the block?
• Is this an elastic or inelastic collision? Why?
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That’s it…
• It’s been a pleasure
• I hope you’ve enjoyed it as well and perhaps
even learned something ;)
• Make sure you get your homework and labs
turned in
• Best of luck on the final…
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Physics 218, Review
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