PY /005 Practice Test 1, 2004 Feb. 10

Transcription

1 PY /005 Practice Test 1, 2004 Feb. 10 Print nae Lab section I have neither given nor received unauthorized aid on this test. Sign ature: When you turn in the test (including forula page) you ust show an NCSU photo ID to identify yourself. Do not use other paper. If you need ore space, write on the back of a page and indicate that you did this. Read all probles carefully before attepting to solve the. You ust show all your work. Use correct vector notation. Your work ust be legible, and the organization ust be clear. Correct answers without adequate explanation will be counted wrong. Incorrect explanations ixed in with correct explanations will be counted wrong. Cross out anything you don t want us to read! Make explanations coplete but brief. Do not write a lot of prose. Include diagras where appropriate to explain your work. 3 6 ( 8 10 )( 5 10 ) 4 Show what goes into a calculation, not just the final nuber: = ( 2 10 )( 4 10 ) Give standard SI units with your results. Unless specifically asked to derive a result, you ay start fro the forulas given on the forula sheet. If you cannot do soe portion of a proble, invent a sybol for the quantity you can t calculate (explain that you re doing this), and do the rest of the proble. Proble Score 1 (25 pts): 2 (25 pts): 3 (25 pts): 4 (25 pts): 5 (5 pts): (bonus) Total (100 pts): 1

2 Proble 1 (25 pts) (a) (7 pts) An electron with a speed of 0.95c agnitude of the oentu of this electron? is eitted by a supernova, where c is the speed of light. What is the (b) (6 pts) A thin iron rod is suspended vertically. The diensions of the rod are 2.3 by 1.6 by 1.3. When you hang a ass of 37 kg fro the end of the rod, you find that the rod stretches 2 3 ( 2 10 ). What is Young s odulus for iron? (c) (12 pts) Here is a portion of the trajectories of two siilar asteroids that are oving away fro each other, with positions arked at ties t 1, t 2, and t 3. There are no other objects near the asteroids. At each of these positions, draw vectors of appropriate lengths and directions for the forces acting on the asteroids at that location, and label the F. Then at the sae locations draw vectors of appropriate lengths and directions for the oenta of the asteroids at those locations, and label the p. ( Appropriate lengths eans that larger agnitudes are represented by longer vectors.) t 1 t 2 t 3 t 3 t 2 t 1 2

3 Proble 2 (25 pts) A ping-pong ball is acted upon by the Earth, air resistance, and a strong wind. Here are the positions of the ball at several ties. Early tie interval: At t = s, the position was 3.17, 2.54, 9.38 At t = s, the position was 3.25, 2.50, 9.40 Late tie interval: At t = s, the position was 11.25, 1.50, At t = s, the position was 11.27, 1.86, (a) (6 pts) In the early tie interval, fro t = s to t = s, what was the average oentu of 3 the ball? The ass of the ping-pong ball is 2.7 gras ( kg ). (b) (6 pts) In the late tie interval, fro t = s to t = s, what was the average oentu of the ball? (c) (13 pts) In the tie interval fro t = s (the start of the early tie interval) to t = s (the start of the late tie interval), what was the average net force acting on the ball? 3

4 Proble 3 (25 pts) A ball of unknown ass is attached to a spring. In outer space, far fro other objects, you hold the other end of the spring and swing the ball around in a circle of radius 1.5 at constant speed. (a) (3 pts) You tie the otion and observe that going around 10 ties takes 6.88 seconds. What is the angular speed ω? (b) (3 pts) What is the speed of the ball? (c) (4 pts) Is the oentu of the ball changing or not? How can you tell? (d) (4 pts) If the oentu is changing, what interaction is causing it to change? If the oentu is not changing, why isn t it? (e) (4 pts) The relaxed length of the spring is 1.2, and its stiffness is 1000 N/. While you are swinging the ball, since the radius of the circle is 1.5, the length of the spring is also 1.5. What is the agnitude of the force that the spring exerts on the ball? (f) (7 pts) What is the ass of the ball? 4

5 Proble 4 (25 pts) Here is a portion of a progra to calculate and display the orbit of a planet around a star so assive copared to the planet that we can neglect the star s otion. Write or interpret progra stateents as specified. fro visual iport * fro future iport division G = 6.7e-11 deltat = 60*60*3 t = 0 star = sphere(pos=vector(0,4e11,0), radius=8e10, color=color.yellow) star.ass = 1.3e31 planet = sphere(pos=vector(9e11,0,0), radius=5e10, color=color.cyan) planet.ass = 8e25 planet.trail = curve(color=planet.color) The initial velocity of the planet is < 0, 3.5e4, 0 >. Write a stateent to set the initial oentu of the planet: planet.p = while t < 1e9: (a) (2 pts) Write a stateent to calculate the current vector that points fro the planet to the star: r = (b) (2 pts) Write a stateent to calculate the agnitude of the vector that points fro the planet to the star: rag = rhat = r/rag (c) (2 pts) Write a stateent to calculate the agnitude of the gravitational force acting on the planet: Fag = (d) (2 pts) Write a stateent to calculate the vector gravitational force acting on the planet: Fnet = (e) (3 pts) Write a stateent to update the planet s oentu: planet.p = (f) (2 pts) Write a stateent to update the planet s position: planet.pos = planet.trail.append(pos=planet.pos) t = t + deltat (continued on next page) 5

6 (g) (3 pts) What is the initial oentu of the planet, expressed as a vector? Give nuerical values. = <,, > p kg s (h) (2 pts) What is the tie step (tie between position updates), in hours? (i) (3 pts) The first stateent inside the loop calculates a vector r. What will the nuerical value of this vector be, the first tie the coputer calculates it? Show your work. r = <,, > (j) (2 pts) The calculation of the net force contains the quantity rhat. Explain briefly why this is needed. (k) (2 pts) Suppose you change the calculation of the vector r so that it represents a vector pointing fro the star to the planet.what other change or changes ust you ake in the progra? Why? 6

7 Proble 5 (5 pts) Since this proble is only worth 5 bonus points, don t attept it unless you have finished all the other probles and checked your work. There is no general analytical solution for the otion of a gravitational syste consisting of ore than two bodies. However, there do exist analytical solutions for very special initial conditions. Here are four stars, each of ass, which ove in the plane of the page along a circle of radius r. Calculate how long this syste takes to ake one coplete revolution. You can assue that v << c. r 7

8 FUNDAMENTAL PHYSICAL LAWS AND RELATIONSHIPS Principle of relativity: Physical laws work in the sae way for observers in unifor otion as for observers at rest. The superposition principle: the effective force on an object is the net force, the vector su of all forces acting on the object, each force unaffected by the presence of other interactions. The oentu principle, and the definition of oentu. (These ust be eorized.) The relationship aong position, velocity, and tie. (This ust be eorized.) EVALUATING SPECIFIC PHYSICAL QUANTITIES F gravitational G 1 2 = r 2 F gravitational g near the Earth s surface F spring = k s s, opposite the stretch Y F A = = L L k s, interatoic d atoic dp ω Circular otion at constant speed: dp = r, or ω for << c dt 1 v 2 c 2 dt 2 r v where ω dθ 2π = = v dt T 2π r = = ω r T CONSTANTS G = N 2 /kg 2 g = 9.8 N/kg c = /s M Earth = kg M Moon = kg 6 Radius of the Earth = Radius of the Moon = Distance fro Sun to Earth = Distance fro Earth to Moon = Avogadro s nuber = 6 10 Typical atoic radius r electron = 9 10 kg 27 proton neutron hydrogen ato = kg CONVERSION FACTORS 1 pound = 0.45 kilogra 1 kilogra = 2.2 pounds 1 ile = 1600 eters 1 inch = 2.54 centieters 1 hour = (60)(60) s = 3600 s 8