Here are the assigned problems. The
problem solving handout gives specific instructions
on how to solve these problems (as well as others you may encounter in
other coruses or later in life).
Due January 26:
After our many days & weeks of rain, you decide to take advantage
of the nice weather and head down to the Santa Monica Pier for a stroll.
You are walking on the pier on your way back to your car, toward the beach.
The sidewalk is crowded with many people. When you are halfway back to
the beach, you notice a jogger approaching you wearing a t-shirt with
writing on it. You read the first two lines, but are unable to read the
third and final line before he passes. You wonder, "Hmm, if he continues
to the end of the pier and returns, I bet I'll see him again. Since we’ll
both be going the same way then, I should anticipate the time when he’ll
pass me so I can turn around and see the t-shirt." You look at your
watch and it is 2:17 p.m. You recall that the pier is 1600 feet long.
You estimate your walking speed to be 2 or 3 miles per hour and
the jogger’s speed to be about 7 miles per hour. (Solution
Due February 2
The police department asks you
to assist in the prosecution of a robbery suspect. The prosecuting attorneys
contend that the while the robber was fleeing from the police, he went
to the roof of a building. There he allegedly threw the bag of money to
a waiting accomplice on the roof of a nearby building so as not to be
caught with the evidence. However, the defense attorney contends that
in order to reach the roof of the other building, the defendant would
have to throw the bag with a minimum horizontal velocity of 10 m/s. But
in a test, the defendant could throw the bag with a maximum velocity of
no more than 5 m/s. What do you tell the prosecuting attorney? (The building
on which the suspect was caught is 200 m tall, and the other, which is
20 meters away, is 50 m tall.)
While you are watching the
Superbowl you decide to look for interesting physics. Even the opening
kickoff grabs your attention. The receiver is standing on his goal line,
65 yards from where the ball is kicked. It looked like the ball left the
kicker's foot at an angle close to 45° (relative to the ground). You
notice that the receiver runs up 10 yards to catch the ball (on the fly).
As soon as the receiver is brought down at the 25-yard line, the next
barrage of commercials begins, during which you estimate the speed of
the football as it left the kicker’s foot. (Solutions
Due Feb 18
You are helping with set design of the latest play on campus. In the script
there is a scene, which calls for the male lead to rise into the air,
as if ascending into the clouds. Your plan involves attaching a rope to
a harness that the actor will wear. The rope is then put over a pulley
and a counterweight is attached to the other end. When the weight is released
the actor will be pulled upward. The director has told you that he wants
the actor to ascend the 20 feet in 3 seconds. As part of your planning
you weigh the actor and find that he has mass of 70kg. You first make
some calculations to determine how much concrete to buy (for the counterweight)
and which rope to buy. (Your production is on a tight budget and the stronger
rope costs more than the thinner, weaker rope. You need to optimize your
budget by buying the cheapest rope, which will not result in the actor
plummeting to the stage.)
Over the break you head up
to San Francisco to visit a friend from your dorm. Since this is the first
time you’ve visited this friend, you find yourself constant looking
down at the map which she emailed you. (You might guess where this is
going.) As you are driving up a hill, you glance down at the map for just
a moment to check the house number when a kid runs out in the street.
You look up just in time to slam on your brakes and skid to a stop without
harming the kid. While the kid goes on his way, as if he doesn’t
even notice you, a police officer did notice you and your 30-foot skid
mark. He promptly marches over and writes a ticket for speeding in a 25
mph zone. While you weren’t watching your speedometer you didn’t
think you were speeding. Perhaps physics can come to the rescue. You determine
that the street makes an angle of 20° with the horizontal. Your car
manual tells you that the mass of your car is 1430 kg. Will you fight
the ticket in court? (Solutions
Due March 11
You and a friend charter a small plane to take a tour of the desert. Unfortunately,
there are mechanical difficulties during the flight and the pilot is forced
to make a crash landing on the top of a mesa that stands 250m above the
surrounding plain. The pilot fixes the plane and wants to take off again,
but the only reasonably smooth road that could be used for a runway is
not long enough. The pilot estimates that the maximum speed the plane
is likely to reach before going off the edge of the mesa is about 45 mph,
but the plane needs an airspeed of about 120mph before the wing’s
lift becomes significantly larger than the plane’s weight. Noting
that the side of the mesa is essentially a vertical cliff, the pilot thinks
about deliberately driving the plane off the edge and diving downward
and forward. By doing this he hopes to pick up enough air speed to pull
out of the dive before hitting the ground. Seeing how your life is at
stake in this attempt, you decide to do your own calculations.
To raise money for the proposed
science and engineering building, you want to have the Dean bungee-jump
from a crane if $100,000 is contributed. To add some interest, the jump
will be made from 40 meters above the surface of a 2.5-meter deep pool
of raspberry Jell-O. A 25-meter long bungee cord would be attached to
the Dean’s ankles. First, you must convince the Dean that the plan
is safe for a person of his mass (80 kg). You figure that as the bungee
cord begins to stretch, it will behave more or less like a spring. Your
plan has the Dean stepping off a platform and being in free fall for the
25 m before the spring begins to stretch. You must determine the elastic
(spring) constant of the bungee cord so that it stretches only 13 m, enough
to just keep the Dean’s head out of the Jell-O. (Solutions
Due April 1
A small asteroid of mass 2.6 x 109kg is discovered traveling
at a speed of 18 km/s on direct heading for a starbase, which is in deep
space, far from our solar system. The inhabitants of the starbase don’t
have sufficient weaponry to destroy the asteroid, and instead develop
a plan to deflect it with a probe. The probe has a total mass of 25,000
kg and a top speed of 85 km/s, after the fuel has been exhausted. The
plan requires the asteroid to be deflected 1800 m away from its original
path by the time it reaches the starbase. You must now determine when
the probe needs to strike the asteroid.
You are once again in court
as a technical advisor. This time you are working with the defense in
a murder case. The victim was killed with a single bullet. A second bullet,
which missed the victim, was found embedded in the victim’s chair.
The lawyer for whom you’re working is currently questioning one
of the police officers who investigated the crime scene.
Lawyer: In what type of chair
did you find the bullet?
Detective: A leather reading chair with wooden legs.
L: How massive was the chair?
D: Forty pounds.
L: How did the chair respond to being struck with the bullet?
D: It slid across the floor.
L: How do you know this?
D: The floor had a small amount of dust, except near the chair legs where
they had cleared the floor as they slid.
L: How long were these scuffs?
D: Two inches.
L: What kind of floor was in the room?
D: It’s a hardwood floor made from oak boards.
L: What was the mass of the bullet retrieved from the chair?
D: Three-tenths of an ounce.
L: How far did this bullet penetrate into the chair?
D: Two inches
L: Have you tested the gun you found in my client’s possession the
night of the murder?
L: What is the muzzle velocity of the bullets fired from that gun?
D: The muzzle velocity is one thousand miles per hour.
L: Thank you. I have no more questions.
As the lawyer sits down, what
do you tell her?
Due April 18
You are working in a research group investigating more energy efficient
city busses. One option is to store energy in the rotation of a flywheel
when the bus stops and then use it to accelerate the bus. The flywheel
under consideration is disk of uniform construction except that it has
a massive, thin rim on its edge. Half the mass of the flywheel is in the
rim. When the bus stops, the flywheel needs to rotate at 20 revolutions
per second. When the bus is going at its normal speed of 30 miles per
hour, the flywheel rotates at 2 revolutions per second. The material holding
the rim to the rest of the flywheel has been tested to withstand an acceleration
of up to 100g but you are worried that it might not be strong enough.
To check, you calculate the maximum radius of the rim for the case when
the flywheel reaches 20 revolutions per second just as the bus going 30
miles per hour makes an emergency stop in 0.50 seconds.
want to hang a shelf on your wall that can support 40 CDs (including the
cases) using a wood board that is 1” thick, 6” wide and 24”
long. Your creative design has two thin wires attached to two corners
of the board. These wires are the only means of support for the shelf.
(You don’t want to make too many holes in the walls, so you can
get back your security deposit.) You want the wires to make a 45°
with the wall. Which wire should you purchase at the hardware store? (Will
your shelf be able to hold the CDs?)