EXAM III, PHYSICS 1408, July 29, 2009, Dr. Charles W. Myles

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EXAM III, PHYSICS 1408, July 29, 2009, Dr. Charles W. Myles

EXAM III, PHYSICS 1408, July 29, 2009, Dr. Charles W. Myles

INSTRUCTIONS: Please read ALL of these before doing anything else!!!

  1. PLEASE put your name on each sheet of paper & write on 1 side of the paper only!! This wastes paper, but makes my grading easier! PLEASE DON’T write on the exam sheets, there isn’t room!
  2. PLEASE show all work, writing the essential steps in the solutions. Write formulas first, then put in numbers. Partial credit will be LIBERAL, provided that essential work is shown. (If you don’t show your work, how will I be able to give you partial credit?) Organized, logical, easy to follow work will receive more credit than disorganized work.
  3. The setup (PHYSICS) of a problem counts more heavily than the math of working it out.
  4. PLEASE write neatly. PLEASE: Before handing in your solutions, a) number the pages & put the pages in numerical order, b) put the problem solutions in numerical order, & c) clearly mark your final answers. If I can’t read or find your answer, you can't expect me to give it the credit it deserves.
  5. The words “EXPLAIN”, “DISCUSS”, “DEFINE” below mean to answer mostly in ENGLISH, NOT symbols! Answers to such questions containing ONLY symbols will get NO CREDIT!

NOTE: I HAVE 37 EXAMS TO GRADE!!! PLEASE HELP ME GRADE THEM EFFICIENTLY BY FOLLOWING THESE INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY RESULT IN A LOWER GRADE!! THANK YOU!!

An 8.5’’ x 11’’ piece of paper with anything written on it & a calculator are allowed. Number 1, Conceptual Questions IS REQUIRED! You may work any three (3) of the remaining 4 problems for four (4) problems total. Each problem is equally weighted & worth 25 points, for 100 points on this exam.

  1. MANDATORY CONCEPTUAL QUESTIONS!!! Answer briefly. Most answers should be a few complete, grammatically correct English sentences. Keep formulas to a minimum. Use WORDS instead! If you insist on using a formula, DEFINE ALL symbols used. NO credit will be given for answers with ONLY symbols!
  1. State Newton’s Universal Law of Gravitation.
  2. State ANY ONE of Kepler’s Three Laws (for planetary orbits).
  3. State the Work-Energy Principle. In class, when discussing this Principle, I stated that it is actually an already familiar Law re-expressed in energy language. What Law was I referring to?
  4. Near the end of the gravitation discussion, we discussed the “effective weightlessness” experienced by astronauts when they are orbiting the Earth. (If you were in class last week when we discussed this, you likely will be able to answer this. If you skipped class, as some of you often do, you likely won’t be able to answer it.) It is also discussed in detail the book (Sect.6-4). I ended the discussion stating that media reporters are VERY wrong when they say things such as “the space shuttle has escaped the Earth’s gravity & is now in orbit.” In a few complete, grammatically correct sentences, EXPLAIN the reason that this statement by reporters is VERY wrong. (Hint: Can the gravitational force between two massed ever be zero?)

NOTE: The items in parts e & f AREN’T in the book! If you were in class when I discussed them, you’ll likely be able to answer them. But, if you skipped when I discussed them, you probably won’t be able to answer them!!

  1. 3 BONUS POINTS! When starting the Ch. 6 (Gravitation) discussion, I emphasized that Newton was the first one to do Gravitation theory. I also said that he used his Gravitation theory (plus his 2nd Law of Motion + his Calculus!) to make predictions which were in Excellent Agreement with certain well-known observations. Tell me, as briefly as possible, exactly what the observations were that Newton explained with his theory. This result also eventually came to be called Newton’s “Greatest Achievement”. (It’s also a major reason why he is often called “the Greatest Scientist who Ever Lived”! ). Correct answers should give some details of the problem he successfully applied his Gravitation Law to. Note: Answers ONLY stating that he developed the Universal Gravitation Law aren’t sufficient (this is obvious!) & will get ZERO credit. Also, the problem I am referring to here is NOT the same as Newton’s idea for putting objects into orbit around Earth. I ask about that in part f! Answers here that discuss that idea will get ZERO credit.
  2. 2 BONUS POINTS! Near the end of the Ch. 6 (Gravitation) discussion, I talked about small masses orbiting larger ones, like artificial satellites around Earth. In this discussion, I told you about an idea (impractical) that Newton had (in the 1600’s!) about how to launch projectiles into orbit around Earth. Tell me, as briefly as possible, specifically what his idea was. (Hint: There were no rockets in England in the 1600’s, so Newton didn’t know about them. So, answers which state that his idea was about using a rocket to launch an object into orbit will get ZERO credit!).

NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!

  1. See figure. YOU MUST use scientific (power of 10) notation to do this. PLEASE be careful of large & small numbers! Planet X (assumed to be a sphere of constant density) has a mass of M = 1.2  1025 kg. It has a moon of mass m = 7.9  1022 kg in a circular orbit of radius r = 3.3  108 m (from X’s center) at constant speed v around X. G = 6.67  10-11 N m2/kg2. (The masses are similar in size to Earth & our Moon & the orbit radius is similar in size to that of our Moon’s orbit. Other resemblances to Earth & our Moon are coincidental!)
  1. The moon’s orbit is circular, so it experiences a centripetal acceleration.

With words (not equations, which will get ZERO credit!) tell me the cause of

this acceleration. (Hint: See part b!)

  1. Calculate the gravitational force between the moon & the planet. (Hint: This should be huge! For example, the gravitational force between Earth & our moon is ≈ 2  10 20 N! If your result isn’t similar in size to this, you’ve done something wrong!) What is the “centripetal force” on the moon? (Hint: You don’t need the moon’s speed to answer this!).
  2. Calculate the centripetal acceleration experienced by the moon. What is it’s direction? (Hint: This should be very small, definitely much, much smaller than the gravitational acceleration g = 9.8 m/s2 on the Earth’s surface! If your result is larger than or similar in size to g, you’ve done something wrong! You don’t need the moon’s speed to answer this!).
  3. Calculate the speed of the moon in orbit. (Hint: Einstein taught us that the largest speed possible for any mass is the speed of light c = 3 × 108 m/s! If your v is larger than c, or even a significant fraction of it, you’ve done something wrong! v should be large enough for the moon to go the HUGE distance around the orbit in a reasonable time. For example, our moon’s orbital speed around Earth is ≈ 1.0  103 m/s. If your v is much larger or much smaller than this, you’ve done something wrong!)
  4. Calculate the period of the moon’s orbit. (Hint: This should be reasonable for a moon orbiting a planet similar to Earth. For example, our moon’s period is 27.3 Earth days = ≈ 2.4  106 s. If your T is much larger or much smaller than this, you’ve done something wrong!)

NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!

  1. For parts a & b, see Figure A. A car, mass m = 1750 kg, drives at constant speed v = 20 m/s on a straight road. It passes over a hill of circular cross section. The hill’s radius of curvature is r = 25 m.
  1. Calculate the car’s centripetal acceleration & the

“centripetal force” on it when it is at the top of the hill.

What is the direction of this acceleration & of this force?

  1. Sketch the free body diagram for the car, properly labeling all forces. Don’t forget the car’s

weight & the normal force FN due to the road when the car is at the top of the bump. Use Newton’s 2nd Law for the car at the top of the hill to calculate the normal force FN on the car due to the road at that point. Is FN there equal & opposite to the car’s weight? WHY or WHY NOT?

For parts c, d, e, see Figure B. (What follows is a different problem than in parts a & b, but it is about the same car!) The car moves past the hill & down the road. It rounds a curve on a flat portion of the road at speed v = 20 m/s. Figure B is a top view. The curve’s radius of curvature is R = 136 m. There (static) friction between the road & the car tires, or the car wouldn’t stay on the curve.

  1. Calculate the centripetal acceleration on the car & the resulting “centripetal force”.

What physical phenomenon causes this force? (Hint: See part e.)

  1. Calculate the normal force FN between the road & the tires at this point. Is FN there

equal & opposite to the car’s weight? WHY or WHY NOT? (Hint: FN at this point CANNOT be the same as the one calculated in part b!!).

  1. Calculate the (static) frictional force between the tires & the road. (Hint: Use the results

of part c.). If the given speed v = 20 m/s is known to be the maximum speed for this curve for

which a car will not skid, use the frictional force you’ve just found along with the results of part d

to calculate the coefficient of static friction μs between the tires & the road.

NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!

  1. See figure. Note: This problem can be solved using the Newton’s 2nd Law methods of Chs. 4 & 5 OR the Energy Methods of Ch. 7. This exam is partially over Ch. 7, so you must USE ENERGY METHODS to solve this problem! No credit will be given for using the Chs. 4 & 5 methods! This problem can be solved using only Ch. 7 methods. Another way to solve parts of it is to use the potential energy concept & the methods of Ch. 8. This exam is only through Ch. 7, so, I don’t expect you to know the Ch. 8 methods yet. But, if you know these methods, & you’re sure that you know what you are doing, you may use Ch. 8 methods.

An ideal spring has spring constant k = 335 N/m.

  1. Calculate the work required to compress it from it’s relaxed length (x = 0) a distance x = 0.3 m.

The figure is the free body diagram of a mass m = 4.5 kg on a flat horizontal table. It is placed against the same spring as in part a & pushed to the left, compressing it a distance x = 0.3 m. It’s best to take the positive x-axis to the left in the figure. In part b only, assume that the table is frictionless (so the force FD = 0 in the figure).

  1. If the mass is released so that the spring shoves it to the right,

calculate it’s kinetic energy & velocity just after it separates from the spring at x = 0. What Physical Principle did you use to do this calculation?

In parts c & d, assume that the table is NOT frictionless but that there is a constant friction force FD = 5 N acting to the left which slows the mass down as the spring shoves it to the right.

  1. Calculate the work done on the mass by the drag force FD as the spring moves the mass to the right from x = 0.3 m to x = 0.
  2. For the case in part c, calculate the kinetic energy & speed of the mass when it separates from the spring at x = 0. What Physical Principle did you use to do this calculation?

NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!!

  1. See figure. Note: This problem can be solved using the Newton’s 2nd Law methods of Chs. 4 & 5 OR the Energy Methods of Ch. 7. This exam is partially over Ch. 7, so you must USE ENERGY METHODS to solve this problem! No credit will be given for using the Chs. 4 & 5 methods! This problem can be solved using only Ch. 7 methods. Another way to solve parts of it is to use the potential energy concept & the methods of Ch. 8. This exam is only through Ch. 7, so, I don’t expect you to know the Ch. 8 methods yet. But, if you know these methods, & you’re sure that you know what you are doing, you may use Ch. 8 methods. To solve this problem with energy methods, you don’t need to resolve forces into components. The angle θ is not needed in parts a & b! A block of mass m = 150 kg, initially at rest, slides down an inclined plane. Initially, it’s height is h = 3.5 m above the floor.
  1. Calculate the work done by gravity in moving the block down the incline from y = h = 3.5 m to the floor at y = 0.
  2. Assuming that the incline is frictionless, calculate the kinetic energy & speed of the block at the bottom of the incline. What Physical Principle did you use to do this calculation?
  3. Suppose that, instead of the frictionless incline of part b, there is friction force Ff = 10 N acting up the plane as the block slides down it. For an incline angle of θ = 30º, calculate the work done by this friction force as the block moves from the top of the incline to the bottom.
  4. For the case of part c., calculate the kinetic energy & the speed of the block at the bottom of the incline. What Physical Principle did you use to do this calculation?

Consider the case of parts c & d where there is friction acting up the plane. As the block slides down the plane, after it leaves it’s initial height y = h = 3.5 m & before it gets to the floor at y = 0, it obviously moves down to different heights y & it gains speed & kinetic energy as it goes.

  1. 2 POINT BONUS! Calculate the work done by gravity in moving it from y = h = 3.5 m down to a lower height y1 = 2.5 m.
  2. 3 POINT BONUS! Calculate the kinetic energy & the speed of the block when it reaches the lower height y1 = 2.5 m. What Physical Principle did you use to do this calculation?
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