Contents

1. Some comments

2. What will be on the test

3. Equation sheet

4. Test format

5. Examples of questions

1. Some comments

On problems, it is important to show how you reasoned from the information given in the problem to your final answer.  The correct final answer with units is only worth 2-3 points.  The remainder of the points are given for the quality of your solution.  You need to include the following to receive full credit:

All the information given in the problem with correct units (This may include a diagram)

A statement of what quantity you are trying to find.

State explicitly what physics principle you are using to solve the problem

Solve for the unknown quantity in symbols explicitly before numberic calculations

Then substitute numbers with units and calculate the numeric answer

Extra credit will be given for checks made to see if the answer is reasonable

Be prepared to make reasonable estimations and state your assumptions when solving problems. Be aware of significant digits in your answers. (Keep lots of digits until the final calculation, then round to the appropriate precision.)

Here are some really good tips on test taking from Dr. Richard Felder's website at North Carolina State University.

If you have ANY questions while taking the test, please be sure to ask the instructor. The purpose of the test is not to give you trick problems to catch you in an error. The purpose is to give you an opportunity to "show what you know" !  The test problems are based completely on the reading, the lectures, and the homework.  If you understand the main ideas and how to apply them, you'll do well.

Be sure to carefully review your notes, especially when we do things that are not covered very well in the book. Looking over the individual class days linked to the calendar on the class website will also help refresh your memory. Although this test is comprehensive, the test will emphasize material from chapters 3, 4, & 5.

For this test, you should be able to do the following things:

Chapter 1 (Measurement, Estimation, and Units)

• Use base SI units and various conversion factors. For example, compute the number of seconds in an hour, day, or year.
• Analyze the units and dimensions of equations; use units in numerical calculations.
• Make order of magnitude calculations.
  
  

Chapter 2 (Concepts and Mathematics of Motion)

• Be able to state, use, and differentiate the definitions of position, distance, displacement, speed, velocity, and acceleration.
• To learn to analyze the motion of an object by using motion diagrams as a tool.
• To learn to identify velocity and acceleration vectors (both direction and relative magnitude) at different points in an objects motion.
• To recognize the relationship between the velocity and acceleration vectors when an object is speeding up, slowing down, curving, or at a turning point.
• To understand and use the basic ideas of the particle model.
• To gain experience with vectors and graphical vector addition and subtraction.
• To begin the process of learning to analyze problem statements and to translate the information into other representations.
• To obtain a clear understanding of the concepts of position, velocity, and acceleration in one dimension and the relationships between them.
• To learn to translate kinematic information between verbal, pictorial, graphical, and algebraic representations.
• To learn the basic ideas of calculus (differentiation and integration) and to utilize these ideas both symbolically and graphically.
• To solve kinematic problems and to interpret the results
  
  

Chapter 3 (Vectors & Coordinate Systems)

• Explain the difference between vectors and scalars, giving examples of each
• To add and subtract vectors both graphically and using components.
• To be able to decompose a vector into it's components and to reassemble vector components into a magnitude and direction. .
• To recognize and be able to use the basic unit vectors..
• To be able to express vectors in two and three dimensions in terms of Cartesian unit vectors i,j,k.
• To be able to work with tilted coordinate systems.
• To understand and use proper significant figures

Chapter 4 (Motion in two dimensions)

• To state and use the definitions of 2D position, displacement, average velocity, average acceleration.
• To state and use use the definitions of 2D instantaneous velocity and acceleration.
• To solve projectile motion problems using constant acceleration equations in 2D.
• To use calculus to develop or check equations for displacement, velocity, and acceleration.
• To sketch velocity and acceleration vectors for uniform circular motion; calculate the magnitude of a from v.
• To identify the acceleration vector and its components for curvilinear motion

Chapters 5 & 6 Force and Motion

Chapter 9 & 10: Momentum, Impulse, Systems of Particles, and Center of Mass

• To be able to explain what is meant by a "system of particles," and give examples of some "systems" including "rigid bodies".
• To be able to determine the center of mass of various systems of particles and use symmetry if appropriate.
• To be able to determine the velocity of the center of mass of various systems of particles using its connection to the total linear momentum of the system.
• To be able to state the relation between the rate of change of the total linear momentum and the net external force on the system, and state the condition necessary for conservation of linear momentum of a system of particles.
• To understand iteractions from the new perspective of momentum and impulse.
• To begin the process of understanding conservation laws
• To learn what is meant by an isolated system
• To apply conservation of momentum in simple one-dimensional situations
• To understand the basic ideas of inelastic collisions, and recoil

Equations:You will need to know the following equations and under what conditions they can be applied. When you do calculations you will typically be expected to start with one of these equations and to derive what you need for the specific problem. See comments in Section 1 above.

Should also know formulas for:

• area & circumference of a circle
• area & volume for cube & sphere
• average speed

Conversions (rules of thumb):

• yard => meters
• miles => km
• inches => cm
• kg => lb
• quarts => liters

Numbers to know:

• your height and weight/mass in English and SI units
• The size of your hand
• The number of people who live in the Orlando Metropolitan Area
• The number of people in the US
• The distance from LA to New York
• The distance from Orlando to Miami
  

You will need to be able to derive specific equations you need from these equations listed above. You will be given any additional constants and conversions you need. Unless told otherwise, you may use - 10 m/s^/s for the gravitational constant.

4. Test Format:

Final Exam will be from 4-8 PM on Friday, December 6, 2002

 

Part I	(30 points)
Group Problem using GOAL Protocol	30 points
Part II	(40 points)
Multiple Choice Section (no explanation required, but no partial credit either)	(40 points)
Part III	(80 points)
Problem 1: Estimation Problem	20 points
Problem 2: Short Essay ( Mainly looking for an answer in words - about 1/2-1 page paragraph, but equations, diagrams, and graphs OK. No calculations allowed)	10 points
Problems 3, 4, & 5: Problems based on Homework and Class (15-20 points each)	50 points
Total	150 points

If the overall test average of your entire group is 75% or above, every member of your group will receive a bonus of 5%.

Bonus points for problems 1, 3, 4, & 5 are awarded for showing work to check your answer for reasonableness or for using GOAL.

Note: The test will be printed single sided so you should not run out of room. If you need more than a single page, please use the back of the previous problem.

5. Examples of questions

Practice Test 3 / Practice Test 3 Solution / Practice Final

Additional Practice Questions

To test your understanding of key concepts, try the multiple-choice problems here.  This NC State website has practice problems for a class similar to ours. Tests 1, 2, & 3 have material relevant to this test.

Also Note:

• Additional Questions can be found in the practice tests
• Test Questions that the class has done badly on in previous tests may reappear on the Final Exam
• The Questions below have appeared on Dr. Saul's exams in the past

Essay Questions

1) The conservation of momentum is useful in some situations and not in others. Describe how you obtain the impulse-momentum theorem from Newton's second law and what situations lead to momentum conservation. How would you decide if conservation of momentum could be used in a particular problem?

2) Energy conservation is sometimes a useful principle in helping us solve problems concerning the motion of objects. Suppose a single object is moving subject to a number of forces. Describe how you would know whether energy conservation would hold for the given example and in what kinds of problems you might find it appropriate to use it.

3) Discuss the difference between the physical content of the two laws F = ma and F = mg. (Do NOT just give a one sentence statement describing each. Think about what they mean and how they are used. Are they similar in some ways? Are they different in some ways? What I am looking for here is a thoughtful discussion that shows some insight into what these laws mean.)

4) Student A says: Galileo said all objects fall with the same speed. I know that's not true. If I drop a balloon and a billiard ball the balloon falls more slowly. Galileo was wrong.

Student B says: No. Galileo only said two heavy objects fall with the same speed. If I drop a steel ball and a wooden ball they hit the ground at the same time.

Discuss these student's statements. Which one do you agree with? If either or both are wrong, explain why.

5) In our readings about mechanics we encounter the following equations:

For each equation, discuss the following questions:

• What is the physical system being described by this equation?
• What does each symbol represent?
• Under what conditions does the equation hold?

Sketch on your paper a diagram in which you put each of the equations in a box. Connect with an arrow any pair of equations when one equation can be easily derived from another by considering a special case. (The arrow should point from the more general to the more specific equation.)

 

Estimation Questions

1) The mass of the earth is about 6x10^24 kg. Estimate the kinetic energy it has as a result of its orbiting the sun.

2) According to some recent highly accurate measurements made from satellites, the continent of North America is drifting at a rate of about 1 cm per year. Assuming a continent is about 50 km thick, stimate the kinetic energy the continental US has as a result of this motion.

3) Suppose an elevator with a mass of 1000 kg lifts 3 people from the 2nd to the 4th floor of a building. The elevator is connected by a cable to an electric motor at the top of the shaft.

• How much work is done by the cable on the elevator?
• How much work is done by the Earth's gravity on the elevator?
• What is the net work done on the elevator?

4) Suppose you are visiting some relatives in Maryland during winter break when you are hit by a snow storm. You offer to shovel the walk but your host tells you not to bother since you are not used to it. Estimate the amount of work your host does shoveling the walk after a snow storm. Among your estimates, you may use the following:
- The length of a typical path from a house to a street is 10 meters.
- Assume the snow fell to a depth of 4 inches
- Assume the snow was only moderately packed so that its density was equal to 0.2 g/cm3 - about one fifth that of water.
In doing this problem, you should estimate any other numbers you need to one significant figure. Be certain to state what assumptions you are making and to show clearly the logic of your calculation.