FINAL EXAM, PHYSICS 1403

August 6, 2004

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! Yes, this wastes paper, but it makes my grading easier!
  2. PLEASE show all work, writing the essential steps in the solutions. Write appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided that essential work is shown. Organized, logical, easy to follow work will receive more credit than disorganized work.
  3. For answers which are very small or very large numbers PLEASE use scientific (power of 10) notation!
  4. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
  5. PLEASE write neatly. Before handing in your solutions, PLEASE:a) number the pages and put the pages in numerical order, b) put the problem solutions in numerical order, and 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.

NOTE: I HAVE 50 EXAMS TO GRADE!!! PLEASE HELP ME GRADE THEM EFFICIENTLY BY FOLLOWING THE ABOVE SIMPLE INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY RESULT IN A LOWER GRADE!! THANK YOU!!

Three 8.5’’ x 11’’ pieces of paper with anything written on them and a calculator are allowed. Problem 1 (Conceptual Questions) IS REQUIRED! Work any 4 of the remaining problems for five (5) problems total. Each problem is equally weighted and worth 20 points, for a total of 100 points.

  1. THIS QUESTION IS MANDATORY!!! Answer briefly, in complete,

grammatically correct English sentences. Supplement answers with equations, but

keep these to a minimum and EXPLAIN WHAT THE SYMBOLS MEAN!!

  1. State Newton’s 3 Laws of Motion.
  2. State the Principle of Conservation of Mechanical Energy and the Principle of Conservation of Momentum.
  3. State Newton’s 2nd Law for Rotational Motion. (∑F = ma will get ZEROcredit!)
  4. In the Figure, the round objects are rolling without slipping down an inclined plane. The box is sliding without friction down the slope. All round objects all have radius R andmass M (which is the box mass). Moments of inertia:Hoop: I = MR2, Cylinder: I = (½)MR2, Sphere: I = (2MR2)/5. The objects are released, one at a time, from the same height H. Which one arrives at the bottom with the greatest (linear) speed V? Why? Which arrives with the smallest V? Why? What physical principle did you use to arrive at these conclusions? (Note: You may write an equation, but explainthe meaning of the symbols. I want most of the answer in WORDS!)

e.5 Point Bonus!!During class discussion about rotational motion, I did a demonstration to try to illustrate the answer to part e. Briefly describe this demonstration. (If you were in class the day I did this demonstration, likely will be able to answer this. If you “cut” class that day, as several of you have habitually done this session, you probably won’t be able to answer it!)

NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!

  1. Note: Parts a, b, c are independent of parts de.

For a, b,c, see Figures to right. A crown is weighed in air & the scale

reads w = mg = 145 N(left figure). It is then submerged in water & weighed.

The scale now reads w′ = m′g = 129 N(right figure).Water density: ρw

= 1.0  103kg/m3.(Hint: To answer these, you must use both Archimedes’

Principle andNewton’s 2nd Law in the vertical direction with a = 0!). Answers using

ONLY the definition of density in terms of mass & volume will getZERO credit!).

  1. Compute the buoyant force FB, that the water exerts on the crown.
  2. Compute the crown volume V.
  3. Compute the crown density ρc. Density of gold: 1.93  104 kg/m3.

Is the crown made of gold?

For parts d & e, see Figureto right. Gasoline at street level flows at a velocity

v1 = 3 m/s through a circular pipe, radius r1 = 0.25 m. The pipe bends up & empties into a storage tank a height h = 30 m above the street. Before it empties into the tank, the pipe narrows to a radius of 0.15 m. The gasoline pressure is P2 = 6 x 105 N/m2 when it empties into the tank. The gasoline density is ρ = 700 kg/m3.

  1. Compute the volume flow rate of gasoline in the pipe and the velocity v2

of the gasoline at as it empties into the tank.

  1. Compute the gasoline pressure, P1, at street level. What Physical

Principle (or whose principle) did you use to do this calculation?

  1. See Figure. A hoop of radius R = 0.5 mmass M = 6.0 kg starts from rest at the top of an inclined plane. Initially, it’s height is H = 8.0 m above the bottom of the plane. The hoop’s moment of inertia is I = MR2. (NOTE: The object in the figure may look like a sphere, but it IS a HOOP!).

Before After

  1. Compute the gravitational potential energy of the hoop at its initial position.
  2. Calculate the linear speed V of the center of mass and the angular speed ω of the hoop when it reaches the bottom.
  3. Compute the translational kinetic energy of the center of mass of the hoop when it reaches the bottom.
  4. Compute the rotational kinetic energy & angular momentum (about an axis through the center of mass) of the hoop when it reaches the bottom.
  5. Suppose that the constant angular acceleration on the hoop as it moves from its highest point to its lowest point is 9 rad/s2. Compute the net torque on the hoop during its motion. What Physical Principle did you use to do this last calculation?

NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!

  1. See figuresbelow. A mass m = 15 kg is released from rest at the top of a frictionless inclined plane a height h above a frictionless horizontal surface (left figure). It slides down the incline onto the surface, where it has a velocity v = 7 m/s (middle figure). The incline angle is 25º with respect to the horizontal. The mass moved to the left at v = 7 m/s until it collides with a second mass m′ = 20 kg, initially at rest. The two masses STICK TOGETHER (the collision is inelastic) and move off to the left with velocity V(right figure).
  1. Compute the kinetic energy and the momentum of the first mass after it gets to the

bottom of the incline (middle figure).

  1. Compute the gravitational potential energy and the height h at the starting point of

the first mass at the top of the incline (left figure).

  1. Compute the velocity v1 the first mass had when it was a height y = 0.25 m above

the bottom of the incline (part of the way between the left and middle figures).

  1. Compute the momentum of the two masses after they collide and stick together

(right figure). Compute their velocity V and their kinetic energy. Was kinetic

energy conserved in this collision? Explain (in complete, grammatically correct

English sentences!)

  1. Compute the normal force between the first mass and the incline as the mass

slides down the incline (NOTE: Answers which state that the normal force is

equal & opposite to the weight will receive ZERO credit!)

  1. See figure. It takes 15 J of work to stretch an ideal spring a distance 0.75 m from its equilibrium position.
  1. Determine the spring constant k of the spring. (Hint:The

above statement is about work or ENERGY, notabout

force! You can’t use a force relationto compute k!)

A mass m = 2.0 kg is attached to the same spring, pulled a distance 1.8 m from its

equilibrium position and released from rest. Neglect friction. Determine:

  1. The amplitude, the period, and the frequency of the motion.
  2. The maximum speed and the total mechanical energy
  3. The maximum force on the mass and the maximum acceleration it experiences.
  4. The mass’s speed, the force on it, and the potential energy when x = 1.2 m.
  5. Write an expression for x as a function of time (x(t)). (Note: Answers which use a kinematic equation from Ch. 2 will receive ZERO credit!)

NOTE: Work any four (4) of Problems 2.,3.,4., 5., and 6.!

  1. See Figure. A box, mass m = 25 kg, is given a shove across a horizontal surface. It is released at the origin with an initial velocity of v0 = 18 m/s in

the +x-direction. After it is released, the only horizontal force on the box

is friction between the box and the surface, which causes it to slow down

and eventually come to rest. The coefficient of kinetic friction between the

box and the surface is μk = 0.16. (Note: How the box was shoved and the

force used in shoving it are NOT part of this problem! The problem begins

when the box is alreadyreleased and is moving to the right with velocity v0!)

  1. Draw the free body diagram for the box, properly labeling all forces. Is there aforce in the direction of the motion (parallel to the velocity)? (Hint: The velocity v0is NOT a force and does not belong in a free body diagram!)
  2. Compute the weight of the box and the normal force between it and the surface.
  3. Compute the frictional force the box experiences as it slides across the surface.What is the direction of this force?
  4. Compute the acceleration (magnitude and direction) experienced by the box as itslows down. What force causes this acceleration? What Physical Principle did you use to find this acceleration?
  5. How far from its release point will the box go before coming to rest? How longwill it take to stop?
  1. BONUS!!!If you were present at the movie shown on Wed., Aug. 4, please write a few short, complete, grammatically correctEnglish sentences telling me what the movie was about. If you do this, I will add five (5) points to your Final Exam grade. If you missed class that day (as many of you habitually have done this session) or if you left class before the movie was shown, you will (probably) not know what the movie was about and you will (probably) not be able to answer this. Have a good rest of the summer and good luck in the future!