Final Exam, PHYSICS 1403, August 8, 2014, 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! 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 41 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) is REQUIRED! ALSO You MUST work EITHER Problem 2 (Momentum) OR Problem 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 are very large or very small numbers! PLEASE express such answers in scientific (power of 10) notation! Thanks! Note the BONUS questions on the last page!
1. MANDATORY CONCEPTUAL QUESTIONS!!! Answer briefly all parts in a few complete, grammatically correct English sentences. Give answers using mainly ENGLISH WORDS, NOT symbols or equations! If you insist on using symbols, DEFINE all 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, & c which do not mention forces will get ZERO CREDIT!
a. State Newton’s 1st Law of Motion. How many masses at a time does it apply to?
b. State Newton’s 2nd Law of Motion. How many masses at a time does it apply to?
c. State Newton’s 3rd Law of Motion. How many masses at a time does it apply to?
d. 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 get ZERO CREDIT! Your statement should give the mathematical form of the force with explanations of the symbols used.)
e. State the Work-Energy Theorem. (Note: This is NOT the same as the definition of the
work done by a constant force! Answers which give that definition will get ZERO
CREDIT!)
f. State the Principle of Conservation of Mechanical Energy. Which kinds of forces are required 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!)
g. 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!).
h. State the Principle of Conservation of Momentum. Under what conditions is
momentum conserved?
NOTE: Don’t forget to look at the BONUS questions (# 8 on the last page)!
NOTE: EITHER Problem 2 (Momentum) OR Problem 3 (Momentum) IS REQUIRED!!
2. See figures. A mass m1 = 9 kg, is on a horizontal, frictionless surface. In Fig. 1, it moves to the right at velocity v1 = 10 m/s. It collides with a mass m2 = 16 kg which is initially at rest. The collision is inelastic! They stick together, as in Fig. 2 & move right with velocity v´.
Calculate:
a. The momentum & the kinetic energy of mass m1 before the collision.
b. The momentum of the two stuck together masses & their velocity v´ after the collision.
What Physical Principle did you use to find these?
c. The impulse given to m2 by m1 due to this collision. Stated differently, calculate the
change in the momentum Δp2 for m2 due to the collision.
d. The average collision force that m1 exerts on m2 in this collision. Use the results of part c
and assume a collision time of Δt = 3.8 × 10-3 s. What Physical Principle did you use in
this calculation?
e. The kinetic energy of the 2 stuck together masses in Fig. 2. (Note: It’s physically
impossible for kinetic energy to increase in a collision! If the kinetic energy you get is
greater than the value you calculated in part a, you’ve done something wrong!) Is
kinetic energy conserved in this collision? (Is it an elastic collision?) Why or why not??
NOTE: EITHER Problem 2 (Momentum) OR Problem 3 (Momentum) IS REQUIRED!!
Don’t forget to look at the BONUS questions (# 8 on the last page)!
3. See figures. In a pool game, two balls undergo an elastic collision as one approaches the other from the rear. Fig. a shows them before the collision & Fig. b shows them after the collision. The masses are m1 = 0.5 kg m2 = 0.3 kg. The initial velocity of m1 is v1 = 5.2 m/s & that of m2 is v2 = 3.2 m/s. Both velocities are in the same direction as in Fig. a. After the collision, their velocities v1´ & v2´ are both still in the same direction, as in Fig. b.
Calculate:
a. The total momentum p1 + p2 and the total kinetic energy KE1 + KE2 of two balls before the collision.
b. The total momentum p1´+ p2´ and the total kinetic energy KE1´ + KE2´two balls after the collision. (Hint: The final velocities v1´ & v2´ are NOT needed to answer this part! Answer this by using conservation laws!) What physical principles did you use to find these results? Is kinetic energy conserved in this collision?
c. The velocities v1´ & v2´ of the balls after the collision.
d. The impulse that was delivered to m2 by m1. Stated another way, calculate the change in
momentum of m2 due to the collision.
e. The average collision force exerted by m1 on m2. Use the results of part d and asssume a
collision time of Δt = 8 ´ 10-3 s. What Physical Principle did you use in this calculation?
NOTE: WORK ANY THREE (3) OF PROBLEMS 4, 5, 6, or 7!!!!!c
Don’t forget to look at the BONUS questions (# 8 on the last page)!
4. See figure. Use energy methods to solve this!!! NO credit will be given for force methods! You don’t need to know force components or the incline angle θ to solve this! A mass m = 6 kg, is initially at rest (at C on the right of the figure) at the top of a frictionless inclined plane a height h above a horizontal, frictionless floor. It is released and moves down the incline to the floor below (at B near the middle of the figure), where it’s velocity is v = 8 m/s. It continues to move to the left until it encounters an ideal spring, of constant k = 850 N/m, attached to a vertical wall. After it makes contact with the spring, it continues to the left, compressing the spring and slowing down. It eventually comes instantaneously to rest (at A on the left of the figure) after
it compresses the spring a distance x.
Calculate:
a. The block’s kinetic energy at point B.
b. The block’s gravitational potential energy at the height h (point C) at which it started.
Find the height h. What Physical Principle did you use to do this calculation?
c. The block’s velocity when it is at height y = 1.9 m above the horizontal surface (not shown in the figure; above point B & below point C.) Note: Answers obtained by setting
the KE equal to the PE at this point will get ZERO credit!
d. The spring (elastic) potential energy of the mass-spring system when the block comes
instantaneously to rest at point A.
e. The distance x that the block has compressed the spring at point A. (Hint: The gravitational acceleration g is totally irrelevant to this part of this question as well as to
part d because gravitational potential energy doesn’t change as the block compresses the spring!)
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)!
5. See figure. A box, mass m = 25 kg, is placed on a flat, horizontal surface. The coefficient of kinetic friction between the box & the surface is μk = 0.25. The box is pulled a by a force FP = 70 N using a cord that makes an angle θ = 30º with the horizontal.
a. Sketch the free body diagram for the box, properly labeling all forces. Calculate the horizontal and vertical components of the force FP. (Note: If you do not make a sketch, you will lose points!)
b. Calculate the normal force FN between the box & the surface. Is this normal force equal (& oppositely directed) to the weight? Why or why not? Justify your answer using
Newton’s 2nd Law in the vertical direction. Also calculate the frictional force Ffr that the box experiences as it moves to the right.
c. Use Newton’s 2nd Law to find the acceleration experienced by the box. What forces cause this acceleration?
d. Calculate the WORK done by the force FP after the box has moved a distance d = 8 m across the surface. Calculate the work done by the friction force Ffr over that same distance. The work done by the weight mg and the work done by the normal force FN over distance d are both zero. WHY? Answer using English sentences, NOT equations!
e. Calculate the net work done by all forces on the box after it has moved the distance d = 8 m. If the box starts from rest, use the Work-Energy Principle (& not kinematic equations of Ch. 2) to calculate the box’s speed after it has moved the distance d.
NOTE: WORK ANY TWO (2) OF PROBLEMS 5, 6 or 7!!!!!
Don’t forget to look at the BONUS questions (# 8 on the last page!!)
6. See figures. Two masses (m1 = 25 kg & m2 = 15 kg) are placed in contact with each other on a frictionless, horizontal surface, as in Fig. a. A constant horizontal force F = 40 N is applied from the right to m1 as shown in Fig. a. The free body diagrams for masses m1 & m2 are shown in Fig. b & Fig. c, respectively. The force P21 in Fig. b is the contact force that m1 experiences because m2 is pushing to the left on it. Similarly, the force P21 in Fig. c is the contact force that m2 experiences because m1 is pushing to the right on it. The two mass system moves to the right with acceleration a. There are three unknowns in this problem: the acceleration a, the contact force P21 & the contact force P12.
a. Write an equation expressing a simple relationship between the contact
forces P21 & P12. Doing this reduces the number of unknowns in this
problem from three to two. Which Newton’s Law of Motion is used to
obtain this equation?
b. By applying Newton’s 2nd Law to m1 m2 separately, find the two equations needed to solve for the acceleration a & the contact force P21. Writing them in symbols, without substituting in numbers, will receive more credit than writing them with numbers substituted in! (That is, I DON’T want you to just write the abstract formula SF = ma for the masses m1 & m2! I want you to explicitly write out the left side of SF for m1 & m2 in terms of the forces in this problem which are relevant to m1 & m2.)
c. Using the two equations from part b, calculate a and P21 (in any order).
Assuming that this two mass system starts from rest, after a time t = 2.5 s,
Calculate:
d. The speed of the two masses.
e. The distance the two mass system has moved.
NOTE: WORK ANY TWO (2) OF PROBLEMS 5, 6 or 7!!!!!
Don’t forget to look at the BONUS questions (# 8 on the last page!!)
7. See figure. A roller coaster car, mass m = 3,000 kg, is shown a portion of a roller coaster ride. The height difference between points A and B is 45 m. The height difference between points B and C is 38 m. The car starts from rest at point A. Take the y = 0 point to be point B. For parts a., b., and c., assume that the roller coaster track is frictionless. NOTE: Some of the answers to the following are large numbers! PLEASE express your answers in scientific (powers of 10) notation for such numbers. Thanks!