Homework Problems

 

 
 

           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).  The exercises will (until further notice) be handed out in class.

 

Kinematics Unit

Due January 29
Because of your technical background, you have been given a job as a student assistant in a University research laboratory that has been investigating possible accident avoidance systems for oil tankers. Your group is concerned about oil spills in the North Atlantic caused by a super tanker running into an iceberg. The group has been developing a new type of down-looking radar which can detect large icebergs. They are concerned about its rather short range of 2 miles. Your research director has told you that the radar signal travels at the speed of light which is 186,000 miles per second but once the signal arrives back at the ship it takes the computer 5 minutes to process the signal. Unfortunately, the super tankers are such huge ships that it takes a long time to turn them. Your job is to determine how much time would be available to turn the tanker to avoid a collision once the tanker detects an iceberg. A typical sailing speed for super tankers during the winter on the North Atlantic is about 15 miles per hour. Assume that the tanker is heading directly at an iceberg that is drifting at 5 miles per hour in the same direction that the tanker is going. (Solution )

 

Due February 5
Because of your knowledge of physics, and because your best friend is the third cousin of the director, you have been hired as the assistant technical advisor for the associate stunt coordinator on a new action movie. In this exciting scene, the hero pursues the villain up to the top of a bungee jumping apparatus. The villain appears trapped but to create a diversion she drops a bottle filled with a deadly nerve gas on the crowd below. The script calls for the hero to quickly strap the bungee cord to his leg and dive straight down to grab the bottle while it is still in the air. Your job is to determine the length of the unstretched bungee cord needed to make the stunt work. The hero is supposed to grab the bottle before the bungee cord begins to stretch so that the stretching of the bungee cord will stop him gently. You estimate that the hero can jump off the bungee tower with a maximum velocity of 10 ft/sec. straight down by pushing off with his feet and can react to the villain's dropping the bottle by strapping on the bungee cord and jumping in 2 seconds.

Since your previous stunt went off without any problems, you’ve been asked to consult on another. In this scene, the script calls for a large package to be dropped onto the bed of a fast moving pick-up truck from a helicopter that is hovering above the road, out of view of the camera. The helicopter is 235 feet above the road, and the bed of the truck is 3 feet above the road. The truck is traveling down the road at 40 miles/hour. You must determine when to cue the assistant in the helicopter to drop the package so it lands in the truck. The director is paying $20,000 per hour for the chopper, so he wants you to do this successfully in one take.

(Solution )

 

Dynamics Unit

Due February 21
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 slide down a rope. The director has told you that he wants the actor to slide down the rope as slowly as possible. As part of your planning you weigh the actor and find that he has mass of 70kg. The rope that you are planning on using is rated as having a maximum tension of 100 lbs. If the rope is 10 m long, what should you tell the actor? How much time can he take to slide down the rope?

While riding Space Mountain at Disneyland, you contemplate the physics involved in the ride. Obviously there is a lot of physics involved, but the ride is only a few minutes long, so you concentrate on trying to understand the launch system. You want to know the strength of the cable, which propels the 3000kg car up the initial ramp. You remember that the car accelerated from rest to its maximum speed at the top of the 30° ramp in just under 2 seconds. By looking at the lights & other decorations around you, you figure that the ramp is around 65 feet long.

(Solution )


Energy Unit

Due March 14

1. 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.

2. After graduation you decide to join the circus. (It’s always been your dream.) Since you have taken physics courses, your supervisors give you the task of helping to design the human cannonball stunt. Your task is to design a stunt in which a man, who weighs 170 pounds, will be shot out of a cannon that is elevated 40° from the horizontal. The “cannon” is actually a 3-foot diameter tube that uses a stiff spring and a puff of smoke rather than an explosive to launch the man. The manual for the cannon states that the spring constant is 985 Newtons/meter. A motor compresses the spring until its free end is level with the bottom of the cannon tube, which is 5 feet above the ground. A small seat is attached to the free end of the spring for the man to sit on. When the spring is released, it extends 8 feet up the tube. Neither the seat nor the chair touch the sides of the 12-foot long tube. After a drum roll, the spring will be released and the stunt man will fly through the air with the appropriate sound effects and smoke. Currently, the circus is only traveling with an airbag which is 4-feet thick. You know that the airbag will exert an average retarding force of 2750 Newtons in all directions. You need to determine if this airbag is thick enough to stop the human cannonball safely.

(Solution )

Energy Unit

Due March

1. You are helping to investigate a mishap in a mountain railroad. One night, a railroad car was left parked at the top of a hill above another car of the same mass. In the morning, both cars are found coupled together in a lake. The supervisor claims that the engineer must have not set the brake on the upper car, and that during the night it rolled down, hit and coupled with the lower car, carrying both into the lake. The engineer disputes this, saying that someone must have released the brake and then pushed the upper car. After you study the map of the terrain (which also shows the positions of the cars the night before), you submit your findings which say that…?

2. This year you have a summer job working for the National Park Service at Yosemite. Since they know that you have taken physics, they start you off in the laboratory which tests possible new equipment. Your first job is to test a small cannon. During the winter, small cannons are used to prevent avalanches in populated areas by shooting down heavy snow concentrations overhanging the sides of mountains. In order to determine the range of the cannon, it is necessary to know the velocity with which the projectile leaves the cannon (muzzle velocity). The cannon you are testing has a weight of 700 lbs and shoots a 40-lb projectile. During the lab tests the cannon is held horizontally in a rigid support so that it cannot move. Under those conditions, you measure the magnitude of the muzzle velocity to be 400 m/s. When the cannon is actually used in the field, however, it won’t be able to be secured, meaning that it is free to move (recoil) when it is fired. Your boss asks you to calculate the projectile's speed leaving the cannon under field conditions, when it is allowed to recoil. She tells you to take the case where the cannon is fired horizontally using cannon shells that are identical to those used in the laboratory test.

(Solution )

 

Rotation Unit

Due April 16

1. After graduation you have landed a job at the CalTech Seismological Laboratory. One project that you are working on is to estimate the density of the earth’s core. You know that NASA has used various satellites to measure the earth’s moment of inertia to be 8.010 x 1037 kg m2. Interestingly, this works out to be 0.33 M R2 (rather than the expected 0.4 M R2 for a uniform sphere), where M is the earth’s total mass and R is the earth’s radius. Your simplified model is that the earth has two sections- a central core and the mantel which comprises the rest of the earth. The density of the mantel is known to be 4500 kg/m3. From the analysis of earthquake waves it is known that the core has a radius of 2.8 x 106 m. (This is done by studying how the different P and S waves propagate through the earth. Seismic waves will bend and reflect at the interfaces between different materials, just like the prism below refracts and scatters light waves at its faces.)

2. On the weekend you find yourself engaged in serious physics experiments- bowling. You will throw the ball straight down the alley. When it starts, its center of mass will have a speed of 5m/s and it is sliding without rotating. You guess that the coefficient of friction between the ball and the floor is 0.1. Before you actually throw the ball, you decide to determine how far the ball will go down the alley before it starts rolling without slipping.

(Solution )