Final Exam, PHYSICS 1403, August 7, 2015, Dr. Charles W. Myles

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

  1. PLEASE put your name on every sheet of paper you use and write on one side of the paper only!! PLEASEDO NOT write on the exam sheets, there will not be room! This wastes paper, but it makes my grading easier!
  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 show n. Organized, logical, easy to follow work will receive more credit than disorganized work.
  3. The setup (PHYSICS) of a problem will count more than the math of working it out.
  4. PLEASE write neatly. Before handing in your solutions, PLEASE: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. NOTE!! The words “EXPLAIN”, “DISCUSS” & “DEFINE” below mean to answer mostly in ENGLISH, NOT math symbols!

I HAVE 43 EXAMS TO GRADE!! PLEASE HELP ME GRADE THEM EFFICIENTLY BY FOLLOWING THESE SIMPLE INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY RESULT IN A LOWER GRADE!! THANKS!

Up to three (3) 8.5’’ x 11’’ pieces of paper with anything written on them & a calculator are allowed.Problem 1 (Conceptual)isREQUIRED!ALSOYou MUST workEITHER Problem 2(Momentum)ORProblem 3(Momentum). Choose THREE (3) of the others for five(5) problems total. Each is equally weighted & worth 20 points, for a total of 100 points on this exam. NOTE: Some answers to the problems arevery large or very smallnumbers! PLEASEexpress such answers in scientific (power of 10) notation! Thanks!Note the BONUS questionson the last page!

1.MANDATORYCONCEPTUAL QUESTIONS!!!Answer brieflyall parts in a fewcomplete, grammatically correct English sentences. Give answers using mainly ENGLISH WORDS, NOTsymbols or equations! If you insist on using symbols, DEFINEall symbols! NO credit will be given for answers with ONLY symbols!If a part contains more than one question, please answer each one!Note: Newton’s Laws of Motion are about forces. Answers to parts a & b which do not mention forces will get ZERO CREDIT!

  1. State Newton’s 1st Law of Motion. How many masses at a time does it applyto?
  2. State Newton’s 3rd Law of Motion. How many masses at a time does it applyto?
  3. State Newton’s Universal Law of Gravitation. (Note: Saying only that two masses attract each other with a gravitational force is NOT a statement of this law! Answers stating only that will getZERO CREDIT! Your statement should give the mathematical form of the force with explanations of the symbols used.)
  4. State the Work-Energy Theorem. (Note: This isNOT the same as the definition of the

work done by a constant force! Answers which give that definition willget ZERO

CREDIT!)

  1. State the Principle of Conservation of Mechanical Energy. Which kinds offorces arerequired to be present in order for this principle to hold?(Note: Answers which quote the “Law of Conservation of Total Energy”are NOT correct and will get ZERO CREDIT!)
  2. State Newton’s 2nd Law in terms of Momentum. (Hint: This was Newton’s original form for his 2nd Law. It is also the most general form for it! It is NOT the definition of momentum, p = mv. Stating either p = mv or∑F = ma will get ZERO CREDIT!).
  3. State the Principle of Conservation of Momentum. Under what conditions is

momentum conserved?

NOTE: EITHERProblem2(Momentum) ORProblem 3(Momentum) IS REQUIRED!!

NOTE: Don’t forget to look at the BONUS questions (# 8 on the last page)!

  1. See Fig 1.A bullet, mass m = 0.08 kg, traveling at an unknown velocityv strikes & becomes embedded in a block of wood, mass M =5.2 kg, initially at rest on a horizontal surface. The block-bullet combination then moves to the right. After the collision, their velocity is V = 7.9 m/s. Note that, since the bullet & the block move together after the collision, It is NOT an elastic collision! Calculate the following:
  1. The momentum and the kinetic energy of the bullet-block combination just after the collision.
  2. The momentum of the bullet and it’s velocity v just before the collision. What Physical Principle did you use to answer this?
  3. The bullet’s kinetic energy just before the collision. Was kinetic energy conserved in the collision? Explain (with brief, complete,grammaticallycorrect English sentences!) Hint:PleaseTHINK before answering! Compare the kinetic energy found here with that in part a! It is Physically Impossibleto GAIN kinetic energy in a collision!
  4. The impulse Δp delivered to the block by the bullet. Stated another way, calculate the momentum change of the block in the collision.
  5. The average force exerted by the bullet on the block if the collision time was Δt = 1.9 10-3 s. What Physical Principle did you use to answer this question?

NOTE: EITHERProblem 2(Momentum) ORProblem 3 (Momentum) IS REQUIRED!!

Don’t forget to look at the BONUS questions (# 8on the last page)!

  1. See Fig 2. Two bumper cars in an amusement park have an elastic collision as one approaches the other from the rear. Their masses are m1 = 420 kg and m2 = 540 kg. The initial velocities are both in the same direction (Fig. a) & are (for m1) v1 = 5.3 m/s & (for m2) v2 = 4.3 m/s. After the collision, the velocities v1´v2´ are still in the same direction (Fig. b). Calculate the following:

a.The total momentum p1 + p2and the total kinetic energy KE1 + KE2 of the two cars before the collision.

b.The total momentum p1´+ p2´ and the total kinetic energy KE1´ + KE2´of the two cars after the collision. (Hint: Do this using only the results of part a, along with physical principles! You DON’T need to know the answers to partc before answering this!) What physical principles did you use to answer this? Is kinetic energy conserved in this collision?

c.The velocities v1´v2´ of the cars after the collision. (Note: To solve this you MUST solve two algebraic equations in two unknowns! Attempts to find the answers without doing this algebra will not be successful and will be given ZERO credit!)

d.The impulse that was delivered to m2 by m1. Stated another way, calculate the momentum change Δp2of m2due its collision with m1.

e.The average force exerted by m1 on m2if the collision time was Δt = 3.2 10-3 s. What Physical Principle did you use to answer this question?

NOTE: WORK ANY THREE (3) OF PROBLEMS 4, 5, 6, or 7!!!!!

Don’t forget to look at the BONUS questions (# 8 on the last page)!

  1. See Fig 3. A mass m = 8.1 kg slides with initial velocity v = 3.5 m/s across a horizontal, frictionless surface until it encounters a spring with constant k= 285 N/m. It comes instantaneously to rest after compressing the spring a distance x. (Hints: In the following, PLEASE try to take square roots properly! The gravitational potential energy of the mass, as well as the gravitational acceleration gare not relevant to any part of this problem, because the mass never changes its vertical position. Answers which attempt to use the gravitational potential energy will be given ZERO credit!)
  1. Calculate the initial kinetic energy of the mass (left hand figure).
  2. Calculate the elastic potential energy of the spring-mass system at the point where the mass is instantaneously at rest (right hand figure). Also, calculate the distance x the spring is compressed there. What physical principle did you use to find these?
  3. Calculate the elastic potential energy of the spring-mass system & the distance the spring has been compressed when the mass’s speed has slowed down to 1.9 m/s. (This is not shown in the figures! This occurs after the mass touches the spring, but before it has come to rest in as in the right hand figure!)
  4. The mass in the left hand figure was given its initial velocity by sliding it from rest down a frictionless inclined plane from a height h. (This is not shown in the figures! This happened sometime before the situation shown in the left hand figure!) Calculate the potential energy the mass had at the top of the inclined plane & the height h from which the mass started. What physical principle did you use to find these results?
  5. Calculate the FORCE (magnitude & direction) the spring exerts on the mass at the final position (right hand figure) where the mass has stopped moving.NOTE: I’m asking for the force the spring exerts on the mass. A force is NOT the same thing as a potential energy! Answers which just repeat the potential energy calculation of part b will be given ZERO credit!

NOTE: WORK ANY THREE (3) OF PROBLEMS 4, 5, 6, or 7!!!!!

Don’t forget to look at the BONUS questions (# 8 on the last page!!)

  1. Fig 4 is the free body diagram for a crate, mass

m = 20 kg, which is pulled a distance x = 40 m across a flat, horizontal floor. It is being pulled by a constant force FP = 95 N, making an angle θ = 37° with the horizontal as shown. There is NO vertical motion. There is a friction force Ffr = 20 N between the crate & the floor. Use the x-y coordinate system shown.

Calculate the following:

  1. The horizontal and vertical components, FPx and FPy of the pulling force FP.
  2. The normal force FNbetween the box and the floor. (Note: Answers stating that FN = mg for the crate will get ZERO credit! Why is this not true for this problem?)
  3. The coefficient of kinetic friction, μk between the crate and the floor.
  4. The acceleration a of the crate across the floor.
  5. The work done by the pulling force FP and by the friction force Ffrin this process.
  6. The work done by the normal force FN and by the weight mg in this process.
  7. The net work done by all forces in the process. If the crate starts from rest, USE ENERGY METHODS to calculate it’s kinetic energy & speed after it has gone x = 40 m.

NOTE: WORK ANY THREE (3) OF PROBLEMS 4, 5, 6, or 7!!!!!

Don’t forget to look at the BONUS questions (# 8 on the last page!!)

  1. See Fig 5. A helicopter,mass M = 7.3 103 kg, moves UPan acceleration a. It lifts an object of mass m = 2.1 103 kg, which is connected to its bottom by a massless cable. The upward forceon the helicopter exerted by the air on the rotors isFP =1.25  105N. The tension in the cable is FT. Of course FT acts down on the helicopter & up on the object. The free body diagrams for the helicopter & object are in the figure. The two unknowns in this problem are the upward acceleration a and the tension in the cable FT. (Hints: The motion is vertical, but the acceleration is obviously NOTg down, but aup! If it were g downward, the object would be in free fall & FT would be zero! Also, FT can’t possibly be = mg, or a would be zero!).
  1. Write the equations resulting from applying Newton’s 2nd Law separately to the helicopter & to the object. These are thetwo equationsneeded to solve for aFT. (Note: I don’t mean to just write them abstractly as ∑F = ma. I mean to write the explicit equationswhich result when Newton’s 2nd Law is APPLIED to this problem! For each, I want to see which forces are on the left side of ∑F = ma!) You will receive more credit by writing these in terms ofsymbols, without numbers substituted in, than you will by writing them with numberssubstituted in!
  2. Using the equations from part a, calculate aFT.

Assume that all forces are constant, so that the upward acceleration a, found in parts ab is constant. You are given that, once the cable is tight (time t = 0), the upward velocity of the system is v0 = 5 m/s. Consider the system after it has moved up a distance y = 12 m.

  1. Calculate the upward velocity v of the system at that point. (Hints: Use a kinematic

equation! Remember that this is NOT a free fall problem, so the acceleration is aNOT g!)

  1. Calculate the initial kinetic energy of the system (when v0 = 5 m/s) & it’s final kinetic

Energy (when it is moving with the velocity v found in part c).

  1. Calculate the Net Work done in this process (Hint: Rather than calculate the work done due to each force separately & adding them, it’s easier to use the Work-Energy Theorem! Use the results of part d!).

NOTE: WORK ANY THREE (3) OF PROBLEMS 4, 5, 6, or 7!!!!!

Don’t forget to look at the BONUS questions (# 8 on the last page!!)

  1. See Fig 6.Two masses (m1 = 20 kg, m2 = 30 kg) are connected by a massless cord & placed on a horizontal, frictionless surface. The mass system is accelerated to the right by a force FP = 50 N using a cord attached to m1 that makes an angle  = 30º with the horizontal. There is no vertical motion.
  1. Let the tension in the cord connecting the two masses be FT, & sketch the free body diagrams for the two masses, properly labeling all forces. (Note: If you don’t make sketches, you will losepoints!!)
  2. Calculate the horizontal & vertical components of FP.
  3. Write the equations resulting from applying Newton’s 2nd Law to both m1m2 in both

the horizontal (x) & the vertical (y) directions. (Note: I don’t mean to just write them

abstractly as ∑F = ma. I mean to write the explicit equationswhich result when

Newton’s 2nd Law is APPLIED to this problem! For each, I want to see which forces are

on the left side of ∑F = ma!) You will receive more credit by writing these in terms of

symbols, without numbers substituted in, than you will by writing them with numbers

substituted in!

  1. Calculate the normal force between mass m1& the horizontal surface. Is this normal

force equal(and oppositely directed) to the weight m1g? If so, why? If not why not? Justify your answer usingthe appropriate Newton’s 2nd Law equation from part c.

  1. Using the appropriate Newton’s 2nd Law equations from part c., calculate the acceleration a of the system & the tension FT in the cord connecting the two masses. (Note: To solve this you MUST solve two algebraic equations in two unknowns! Attempts to find the answers without doing this algebra will not be successful and will be given ZERO credit!)
  1. BONUS QUESTIONS! (10 bonus points total!) Answer briefly, in a few complete, grammatically correct English sentences. You may supplement these sentences with equations, but keep these to a minimumand EXPLAINwhat the symbols mean! I want most of the answer to be in WORDS! (Note: Answers with ONLY symbols, with no explanation about what they mean, will receive NO credit!).
  1. See figure. A box of mass m is sliding at constant velocity v across a flat, horizontal, frictionless surface. Sketch the free body diagram for the box. (Note: Answers which do not include a sketch will receive ZERO credit!) Is there a force in the direction of the motion (parallel to the velocity)? WHYor WHY NOT? Explain (in English!)your answer using Newton’s Laws! (Hint: Is there a force in the direction of the box’s motion?) To answer correctly, you need to think like Newton (300+ years ago) NOT like Aristotle (3,000+ years ago)!
  2. See Fig. !Suppose that you are riding in a convertible with the top down. It is moving to the right (x-direction) at constant velocity v0x. You throw a ball

straight up (from your viewpoint) with initial velocity v0y while the car moves forward at v0x. Neglect air resistance. Will the ball land behind the car, in front of the car, or in the car? WHY?Explain (briefly!) your answer. Use what you know about projectiles! Make a sketch of the situation to illustrate your explanation. NOTE! If you don’t make a sketch, you will lose points!

  1. (2 points) A box of mass m sits statically (not moving!) on a flat horizontal table. The figure is the box’s free body diagram when the only forces acting on it are the normal force FN upward & it’s weight mg downward. Is the normal force FN in this case equal in size & opposite in direction to the box’s weight mg? Which Newton’sLaw of Motion did you use to answer this?
  2. Briefly state THE THEME OF THE COURSE. (Note: I’ve stated this several times in class, beginning at our first meeting! It’s also on the webpage & in some downloadable lectures!)
  3. See figure. Two water slides are shaped differently, but start atthe same height,h. Two riders, Paul & Kathleen, start from rest at the same time & at the same heighth but on different slides. (The figure shows them at different heights because it shows them AFTER they’ve started down!) The slides are frictionless. Who is traveling faster at the bottom? What Physical Principle did you use to answer this? Who gets to the bottom first? Why? (Answer in words!!)