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). 

Kinematics Unit
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 )

 

Dynamics Unit
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 )

 

Energy Unit
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 )

 

Momentum Unit
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?
D: Yes
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?
(Solutions )

 

Rotation Unit
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.

You 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?)
(Solutions )