EXAM II, PHYSICS 1306



FINAL EXAM, PHYSICS 1403-001, May 5, 2008, 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!! PLEASE DO NOT write on the exam sheets, there will not be room!

2. PLEASE show all work, writing the essential steps in a problem solution. 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. The setup (PHYSICS) of a problem counts more heavily than the math of working it out.

4. 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 165 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!! THANKS!!

Three 8.5’’ x 11’’ pieces of paper with anything on them& a calculator are allowed. Problem 1 (Conceptual) IS REQUIRED! You MUST work EITHER Problem 2 OR Problem 3 (on fluids). Work three (3) of the remaining problems for five (5) problems total. Each problem is equally weighted & worth 20 points, for a total of 100 points.

1. MANDATORY QUESTIONS!! Answer in complete, grammatically correct sentences. Keep formulas to a minimum. Use WORDS! If you use a formula, DEFINE EVERY SYMBOL you use. (Note: Answers using ONLY symbols, without an explanation IN WORDS will receive NO credit!).

a. State Newton’s 1st Law. How many objects at a time does it apply to?

b. State Newton’s 3rd Law. How many objects at a time does it apply to?

c. State the Principle of Conservation of Mechanical Energy. What kinds of forces must be present in order for this principle to hold?

d. State the Law of Conservation of Linear Momentum. Under what conditions is momentum conserved?

e. State Newton’s 2nd Law for Rotational Motion. (The answer ∑F = ma will get ZERO credit!)

f. State Archimedes’ Principle (for the buoyant force on an object submerged in a static fluid).

g. State Bernoulli’s Principle (for a flowing fluid).

NOTE!!! Work EITHER Problem 2 OR Problem 3!

2. See figure. A balloon of volume V = 90 m3 floats statically in air. Air density ρa = 1.29

kg/m3. It is filled with enough gas of unknown density ρ that it will float statically (no motion!) with a load of mass M = 45 kg (not including the mass m of the gas). The free body diagram is shown. FB = buoyant force exerted by the air on balloon, w = mg = weight of gas in the balloon, & wload = Mg = load weight. Neglect the effect of atmospheric pressure. (NOTE! To solve this, you MUST use a COMBINATION of Archimedes’ Principle, Newton’s 2nd Law in the vertical direction, AND the definition of density in terms of mass & volume! Solution attempts using ONLY the definition of density in terms of mass & volume are worth ZERO credit!).

a. Calculate the buoyant force FB exerted by the air on the balloon. What Physical Principle did you use to do this calculation?

b. Write an equation resulting from applying Newton’s 2nd Law, in the vertical direction, to

the balloon.

c. Use the results of parts a & b to calculate the mass m of the gas inside the balloon.

d. Use the results of part c to calculate the density ρ of the gas inside the balloon.

NOTE!!! Work EITHER Problem 2 OR Problem 3!

3. See figure. A horizontal hypodermic syringe contains a fluid medicine

of density ρ = 1.8 ( 103 kg/m3. A force F = 1.5 N is exerted to the right on the plunger (left of figure), causing the fluid to move to the right with

velocity v1 = 0.6 m/s. This squirts the fluid from the needle (right of figure) with velocity v2. The

plunger & syringe have cross sectional area A1 = 3.8 ( 10-4 m2. The needle is narrower, with

cross sectional area A2 = 1.7 ( 10-4 m2. Neglect the effect of atmospheric pressure is the following. (Hint: “Horizontal” means y1 = y2!)

a. Calculate the volume flow rate (cubic meters of fluid per second passing a given point) in the syringe.

b. Calculate the velocity v2 of the medicine squirting out at the end of the needle.

c. Calculate the fluid pressure P1 in the left part of the syringe. (Hint: Use the definition of pressure in

terms of force!).

d. Calculate the fluid pressure P2 in the right part of the syringe. What Physical Principle did you

use to calculate this pressure?

NOTE: Work any three (3) of Problems 4, 5, 6 and 7!

4. See figures below. Use energy methods to solve this! A mass m = 30 kg is released from rest (Fig. 1) at the top of a frictionless inclined plane at height h above a frictionless horizontal surface. It slides down the incline onto the surface. The incline angle isn’t needed for the following. When it reaches bottom (Fig. 2), it is moving to the left at velocity v = 8.5 m/s. It continues to the left at the same speed towards an ideal spring of constant k = 2500 N/m (Fig. 3) attached to a wall. It continues left, makes contact with the spring & compresses it against the wall. When it is instantaneously at rest (v = 0) against the spring, the spring is compressed a distance x from it’s equilibrium position (Fig. 4).

a. Calculate the kinetic energy of the mass at the bottom of the plane (Fig. 2).

b. Calculate the gravitational potential energy of the mass at at the top of the plane (Fig. 1). Calculate

the initial height h where it started. What Physical Principle did you use to do these calculations?

c. Consider a point between the situations shown in Figs. 1 & 2, where the mass is at height y = 2.0

m above the bottom (y = 2.0 m is smaller than the height h you should have gotten in part c. However, it is

NOT simply half of h!). Calculate it’s gravitational potential energy, it’s kinetic energy, & it’s speed

at that point. (NOTE! Answers obtained by setting KE = PE at this point get ZERO credit! Such answers

show a complete lack of understanding of mechanical energy conservation!)

d. Calculate the spring potential energy and the spring compression distance x for the situation of

Fig. 4, where the spring is compressed it’s maximum amount & the mass is instantaneously at rest.

NOTE: Work any three (3) of Problems 4, 5, 6 and 7!

5. See figures. A helicopter, mass M = 7.5 ( 103 kg, moves up with acceleration a = 1.5 m/s2. It is lifting an object of mass m = 1.7 ( 103 kg, which is connected to it’s bottom by a massless cable. The upward force, FP, on the helicopter exerted by the air on the rotors is unknown. So is the tension in the cable, FT, which, of course, acts down on the helicopter & up on the object. The free body diagrams for the helicopter & object are in the figure. (Hints: The motion is vertical, but the acceleration is obviously NOT g down, but a up! 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!).

a. Apply Newton’s 2nd Law to the helicopter & to the object to find the two equations needed to calculate FP & FT. Writing these without substituting in numbers, will receive more credit than writing them with numbers substituted in!

b. Using the equations from part a, calculate FT & FP.

NOTE!! PROBLEM 5 CONTINUES ON NEXT PAGE!

PROBLEM 5 CONTINUED!!

Assume that all forces are constant, so that the acceleration a = 1.5 m/s2 is constant. Once the cable is tight, the upward velocity of the system is v0 = 8 m/s. Consider the system after it has moved up a distance y = 12 m.

c. Calculate the velocity v of the system at that point. (Hint: Use a kinematic equation from Ch. 2!)

d. Calculate 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-Kinetic Energy Principle!)

NOTE: Work any three (3) of Problems 4, 5, 6 and 7!

6. See figure. A mass m = 15 kg is pulled across a table by a massless cord, to which is applied a force FP = 70 N, as shown. The cord makes an angle of θ = 37º with the horizontal. The mass remains on the horizontal surface; there is no vertical motion. The coefficient of kinetic friction between the mass and the table is μk = 0.2. The free body diagram for the mass is shown.

a. Calculate the horizontal and vertical components of the applied force FP.

b. Calculate the normal force FN between the mass and the horizontal surface. Calculate the frictional force Ff between the mass & the table. (NOTE: Answers stating that FN is equal & opposite to the weight will receive ZERO credit! Such answers show a complete lack of understanding of Newton’s 2nd Law!! If you don’t know how to find FN, partial credit will be given if you explain, IN ENGLISH, why it can’t be equal & opposite to the weight!).

c. Write the Newton’s 2nd Law equation for the horizontal motion & use it to calculate the acceleration a of the mass.

Assume that the mass starts from rest (v0 = 0) & that all forces are constant, so the acceleration a is constant.

d. Calculate the work done by the pulling force FP after the mass has moved a distance x = 3 m across the table.

NOTE: Work any three (3) of Problems 4, 5, 6 and 7!

7. The figure is a compound wheel. The inner wheel radius is r1 = 0.35 m. The outer wheel radius is r2 = 0.67 m. (They are bolted together, so they can rotate rigidly together). Two equal forces, F1 = F2 = 60 N, are applied as shown. F1 is applied tangent to the inner wheel in the direction shown (down in figure). F2 is applied at the top of the outer wheel, at an angle of 60° with respect to the dashed vertical line in the figure (30° with respect to the tangent to the large wheel at that point). The moment of inertia of this compound wheel is I = 2.75 kg m2. (Hints: This means that I = (½)MR2 should NOT be used! To solve this problem, the wheel mass is NOT needed! The gravitational acceleration g, is irrelevant!)

a. Calculate the torque, τ1 due to F1 & the torque, τ2 due to F2. Be sure to include the signs of these in your answers. (Hint: Sign convention: A torque which, if it acted alone, would cause a counterclockwise rotation is considered positive & a torque which, if it acted alone, would cause a clockwise rotation is considered negative.) Calculate the net torque τnet on the compound wheel.

b. Calculate the wheel’s angular acceleration α. What physical principle did you use to do this? Calculate the tangential acceleration atan of a point on the outer rim (at r2).

c. The wheel starts from rest at time t = 0, calculate the angular velocity ω after t = 5 s.

d. Calculate the rotational kinetic energy and the angular momentum of the wheel at this same time.

8. BONUS!! During the semester, I did a few demonstrations. If you were present at any one of these, please write a few short, complete, grammatically correct English sentences telling about ONE of these demonstrations. BE SPECIFIC! Tell me what demonstration I did AND what physical principle I was trying to illustrate. If you do this, I will add five (5) points to your Final Exam grade as a small reward for attending class. If you missed class on demonstration days, you will (probably) not know what demonstrations I did and you will (probably) not be able to answer this. Have a good summer and good luck in the future!

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