Assignment #4 Reading, Objectives, & Problems
A. Availability and Due Dates
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Assignment #4 is available Tuesday, September 28, 2004. The target date for its successful completion is Tuesday, October 12, 2004. In any event, all of the Type A problems from Assignment #4 must be successfully completed and turned in by 5:00 pm on Friday, October 15, 2004. If this requirement is not met, the student will not be allowed to take Quiz 2, to be given in class on Tuesday, October 19, 2004. |
B. Reading
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As preparation for completing the problems in Assignment #4, read Chapters 8 & 9 in Cohen's The Fundamentals of College Physics, Volume IA. |
C. Objectives
In addition to the Objectives listed on Assignments 1- 3, after completing Assignment #4, the student should
[1] Know what the static frictional force is, and realize that the static frictional force acts only when it has a force to oppose. The student should also be able to describe a microscopic mechanism responsible for the existence of the static frictional force.
[2] Realize that the magnitude of the static frictional force can never exceed the magnitude of the net force it is opposing, and realize why.
[3] Realize that there is a limit to the strength of the static frictional force between two surfaces. Know that, for a wide variety of materials, this limit depends on the magnitude of the normal force between the surfaces and on the composition of the two surfaces. The student should be able to give a qualitative discussion of why the maximum strength of the static frictional force depends on these two quantities.
[4] Know what the coefficient of static friction is, know the conventional symbol for it, and know how to use it to determine the maximum possible static frictional force in arbitrary situations.
[5] Know what the kinetic frictional force is, and realize that, like static friction, the kinetic frictional force acts only when it has a force to oppose. The student should also be able to describe a microscopic mechanism responsible for the existence of the kinetic frictional force, and should be able to give a qualitative explanation for the fact that, given two surfaces, the kinetic frictional force between them is typically less than the maximum static frictional force between them.
[6] Know what the coefficient of kinetic friction is, know the conventional symbol for it, and know how to use it to determine the kinetic frictional force acting in arbitrary situations.
[7] Be able to solve arbitrary problems involving only gravitational, frictional, normal, and tension forces.
[8] Be able to use the fundamental definition of acceleration to determine the velocity of an object at some point in time if its acceleration is constant, and its acceleration and velocity at some other point in time are both known.
[9] Know what is meant by the term terminal velocity. Be able to describe why some falling objects achieve a terminal velocity.
[10] Realize that velocities make sense only as relative quantities, that is, as quantities given relative to some reference frame.
[11] Given the velocities of two different reference frames, be able to add and or subtract them as necessary in order to determine the relative velocity between the two frames.
[12] Realize that, for objects experiencing constant acceleration, the average velocity during some time interval is simply equal to the average of the initial and final velocities. Realize, and this is very important, that this fact is not generically true!
[13] Be able to use the fact alluded to in Objective [12] above to relate positions, velocities, and times for objects experiencing constant acceleration.
[14] Know what is meant by the term kinematics, and be able to recognize and utilize kinematic equations in situations in which accelerations are constant.
[15] Know what is meant by the term projectile motion, and be able to analyze the motion of particles in arbitrary problems involving projectile motion.
[16] Understand that one of the key features of two (or three) dimensional motion is that the dimensions may be analyzed completely independently. Realize that this fact turns any single problem in multiple dimensions into multiple problems in one dimension.
[17] Realize that solving a system of equations for n unknowns requires the existence of at least n independent equations.
D. Type A Problems
[1] Problem 8.1 on pp. 182-183 of Cohen.
[2] Problem 8.2 on p. 183 of Cohen.
[3] Problem 9.1 on p. 228 of Cohen.
[4] Problem 9.3 on p. 228 of Cohen.
[5] Problem 9.4 on p. 228 of Cohen.
E. Type B Problems
[6] Rope 1 is connected between the ceiling and the top of a 50 kg mass. The bottom of the 50 kg mass is attached to rope 2, which then hangs down to the top of a 60 kg mass. Finally, the bottom of the 60 kg mass is attached via rope 3 to the top of a 70 kg mass. All of these masses and ropes hang at rest.
Determine the tensions in each of the three ropes.
[7] Suppose that an object having mass 1000 kg is pushed out of an airplane and falls to earth. Suppose also that, while it falls, it experience a force due to air resistance that has magnitude: Fair resistance = 2v2 , where v is the speed of the object measured in m/s, and the force due to air resistance is measured in Newtons.
Determine the terminal velocity of this object.
[8] Suppose that the current in a river flows at speed 5 m/s. A boat that travels at a top speed of 10 m/s in calm water sets out to cross the river by pointing itself directly across the river (perpendicular to the river bank) and turning its engines on full.
Determine the speed of the boat with respect to the shore.