Physics 101- Introduction to Mechanics
Homework Assignments & Solutions

 

 

 
             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 28:
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 automobiles. You have just begun a study of how bats avoid obstacles. In your study, a bat is fitted with a transceiver that broadcasts the bats velocity to your instruments. Your research director has told you that the signal travels at the speed of light which is 1.0 ft/ nanosecond (1 nanosecond is 10-9 seconds). You know that the bat detects obstacles by emitting a forward going sound pulse (sonar) which travels at 1100 ft/s through the air. The bat detects the obstacle when the sound pulse reflects from the obstacle and that reflected pulse is heard by the bat. You are told to determine the maximum amount of time that a bat has after it detects the existence of an obstacle to change its flight path to avoid the obstacle. In the experiment your instruments tell you that a bat is flying straight toward a wall at a constant velocity of 20.0 ft/ s and emits a sound pulse when it is 10.0 ft from the wall.

Due February 4:
1. You are part of a citizen's group evaluating the safety of a high school athletic program. To help judge the diving program you would like to know how fast a diver hits the water in the most complicated dive. The coach has his best diver perform for your group. The diver, after jumping from the high board, moves through the air with a constant acceleration of 9.8 m/s2. Later in the dive, she passes near a lower diving board, which is 3.0 m above the water. With your trusty stop watch, you determine that it took 0.20 seconds to enter the water from the time the diver passed the lower board. How fast was she going when she hit the water?

2. You have a summer job working for a research group investigating the causes of the ozone depletion in the atmosphere. The plan is to collect data on the chemical composition of the atmosphere as a function of the distance from the ground using a mass spectrometer located in the nose cone of a rocket fired vertically. To make sure the delicate instruments survive the launch, your task is to determine the acceleration of the rocket before it uses up its fuel. The rocket is launched straight up with a constant acceleration until the fuel is gone 30 seconds later. To collect enough data, the total flight time must be 5.0 minutes before the rocket crashes into the ground.
 

Dynamics Unit
Due February 20:
1. You are planning to build a log cabin near Big Bear.  (Youíve decided that youíd rather spend the rest of your life skiing than suffering through another LA commute.)  You will pull the logs up a long, smooth hill to the building site by means of a rope attached to a winch.  You need to buy a rope for this purpose, so you need to know how strong the rope must be.  Stronger ropes cost more. You know that the logs weigh a maximum of 200 kg.  You measure that the hill is at an angle of 30° with respect to the horizontal, and the coefficient of kinetic friction between a log and the hill is 0.90.  When pulling a log up the hill, you will make sure that the rope stays parallel to the surface of the hill and the acceleration of the log is never more than 0.80 m/s2.  How strong a rope should you buy?

2. You are flying to Chicago when the pilot tells you that the plane can not land immediately because of airport delays and will have to circle the airport. This is standard operating procedure. She also tells you that the plane will maintain a speed of 400 mph at an altitude of 20,000 feet while traveling in a horizontal circle around the airport. To pass the time you decide to figure out how far you are from the airport. You notice that to circle, the pilot "banks" the plane so that the wings are oriented at 10° to the horizontal. An article in your in-flight magazine explains that an airplane can fly because the air exerts a force, called "lift," on the wings. The lift is always perpendicular to the wing surface. The magazine article gives the weight of the type of plane you are on as 100 x 103 pounds and the length of each wing as 150 feet. It gives no information on the thrust of the engines or the drag of the airframe.
 

Energy Unit
Due March 13
1. The Navy wants a new airplane launcher for their aircraft carriers and you are on the design team.  The launcher is effectively a large spring that pushes the plane for the first 5 meters of the 20 meter long runway.  During that same time, the planeís jet engines supply a constant thrust of 5.4 x 104 N for the entire length of the runway. The 2000 kg planes need to have a velocity of 45 m/s by the end of the runway.  What should be the spring constant for the launcher?

2. You have landed a summer job with a company that has been given the contract to design the ski jump for the next Winter Olympics in Italy.  The track is coated with snow and has an angle of 25° from the horizontal.  Basically, a skier zips down the ski jump ramp so that he leaves it at high speed and travels as a great of distance as possible.  Your task is to determine the height of the starting gate above the end of the ramp, which will determine the mechanical structure of the ski jump facility.  You have been told that the typical ski jumper pushes off from the starting gate at a speed of 2.0 m/s.  For safety reasons, your design should be such that for a perfect run down the ramp, the skier's speed before leaving the end of the ramp and sailing through the air should be no more than 80 km/hr.  You run some experiments on various skies used by the jumpers and determine that the coefficient of static friction between the snow and the skis is 0.10 and its coefficient of kinetic friction is 0.02.  Since the ski jumpers bend over and wear very aerodynamic suits, you decide to neglect the air resistance to make your design.
 

Rotation Unit
Due April 1
While working on your latest novel about settlers crossing the Great Plains in a wagon train, you get into an argument with your co-author regarding the moment of inertia of an actual wooden wagon wheel. The 70-kg wheel is 120-cm in diameter and has heavy spokes connecting the rim to the axle. Your co-author claims that you can approximate using I = MR2 (like for a hoop) but you anticipate I will be significantly less than that because of the mass located in the spokes. To find I experimentally, you mount the wheel on a low-friction bearing then wrap a light cord around the outside of the axle to which you attach a 20-kg bag of sand. When the bag is released from rest, it drops 3.77-m in 1.6-s during which time the wheel rotates through an angle of 21-radians.
 

Momentum Unit
Due April 17
1. Because of your physics background, you have been hired as a technical advisor for a new James Bond adventure movie.  In the script, Bond and his latest love interest, who is 2/3 his weight (including skis, boots, clothes, and various hidden weapons), are skiing in the Swiss Alps.  She skis down a slope while he stays at the top to adjust his boot.  When she has skied down a vertical distance of 100 ft, she stops to wait for him and is captured by the bad guys.  Bond looks up and sees what is happening.  He notices that she is standing with her skis pointed downhill while she rests on her poles.  To make as little noise as possible, Bond starts from rest and glides down the slope heading right at her.  Just before they collide, she sees him coming and lets go of her poles.  He grabs her and they both continue downhill together.  At the bottom of the hill, another slope goes uphill and they continue to glide up that slope until they reach the top of the hill and are safe.  The writers want you to calculate the maximum possible height that the second hill can be relative to the position where the collision took place.  Both Bond and his girl friend are using new, top-secret frictionless stealth skis developed for the British Secret Service.

2. You have been able to get a part time job with a medical physics group investigating ways to treat inoperable brain cancer.  One form of cancer therapy being studied uses slow neutrons to knock a particle (either a neutron or a proton) out of the nucleus of the atoms which make up cancer cells.  The neutron knocks out the particle it collides with in an inelastic collision.  The heavy nucleus essentially does not move in the collision.  After a single proton or neutron is knocked out of the nucleus, the nucleus decays, killing the cancer cell.  To test this idea, your research group decides to measure the change of internal energy of a nitrogen nucleus after a neutron collides with one of the neutrons in its nucleus and knocks it out.  In the experiment, one neutron goes into the nucleus with a speed of 2.0 x 107 m/s and you detect two neutrons coming out at angles of 30o and 15o with respect to the incoming neutron.  You can now calculate the change of internal energy of the nucleus.
 

 


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Jeff Phillips
phillips@lmu.edu
Loyola Marymount University
Spring 2002