Final Exam, vers Physics 1110 Fall 2011

Transcription

1 1 Final Exa, - Physics 1110 Fall 011 NAME Signature Student ID # TA s Nae(Circle one): Trais Autry, Judith Olson, Benjain Chapan, Brad Dinardo, Tyler Gorda, Oscar Henrisson, Qi Hu Starting tie of your Thurs recitation (write tie in box: 9a, 1p, etc) Please do not open the exa until you are told to. Your exa should hae 18 pages, nubered 1 thru 18. There is a blan sheet at the end for scratch. This exa consists of 4 questions, equally weighted. Fill in the bubble sheet with a # pencil. Please fill out your bubble sheet according to the following instructions or you ay be penalized. Chec each box as you coplete the instructions. Please circle your TA's nae and write the tie of your lab section aboe. Print and bubble in your nae on the bubble sheet. Print and bubble in your student Identification Nuber. Print and bubble in your Exa ersion, 0001 or 000, in the upper left of your bubble sheet in the area ared 134. On your bubble sheet, erase istaes thoroughly, and ae no extraneous ars As you tae the exa, show all your wor on the exa and circle the correct answers on your exa. Your circled exa answers and bubbled answers ust agree. I hae read and followed the instructions aboe. Signature Try to relax. All your neighbors also thin this is a long, difficult exa. Budget your tie. This is a.5 hour exa.

2 3P Possibly useful inforation: 1 P 1 g = 9.8 /s triangle triangle 1 Moents of inertia of circular or spherical objects with ass M and radius R about an axis coinciding with the axis of syetry: hoop or dis Hoop: I = M R Solid dis or cylinder: I = (1/) M R Sphere: I = (/5) M R Unifor rod or bar of length L and ass M with the axis perpendicular to its length: I 1 3 ML when the axis is at one end of the bar. I 1 ML when the axis is through the iddle of the bar. 1 IBaxisB IBCMB d total ass M Parallel Axis Theore: I axis = I CM + Md 0 o C = 73K 1 atosphere = 1.01 x 10 5 Pa 1 cal = J g = 9.8 /s density of water = 1.00 g/c 3 = 1000 g/ 3. Specific heat of liquid water = 1.00 cal/(g o C) Specific heat of ice = 0.50 cal/(g o C). Heat of fusion of water/ice = 80 cal/g Heat of aporization of water/stea = 539 cal/g = 539 cal/g.

3 3 1. The olue flow rate through a water hose is the olue of water per tie that flows out of the hose. Suppose water is flowing at a olue flow rate of 10 4 c 3 /s (10,000 cubic centieters per second). What is the olue flow rate in 3 /in (cubic eters per inute)? A) 0.6 B) 6000 C) 0.01 D) 60 E) 10. Two forces, F 1 and F, are exerted on an object of ass = 10.0 g. There are no other forces on the object. The coponents of the two forces are: (F 1x, F 1y ) = (1.0 N,.0 N), and (F x, F y ) = (3.0 N, 8.0 N). To two-place precision, what is the agnitude of the acceleration a of the object? A) 0.3 /s B) 5. /s C) 1.1 /s D) 0.7 /s E) None of these. 3. A ass 1 on an incline is attached by a assless string to a second ass hanging fro a pulley as shown. The incline has a rough surface so there is a frictional force of agnitude F fric on ass 1. Mass 1 is obsered to be sliding down the incline at constant speed. How does the agnitude of the tension F T in the string pulling on 1 copare to the agnitude of the force of friction F fric acting on the ass 1? Neglect any air resistance. A) F T > F fric B) F T < F fric C) F T = F fric D) Ipossible to answer based on the inforation gien = constantb FBfricB B1 B

4 4 4. Two cars, labeled A and B, are traeling along a long straight road. The road runs east and west. East is chosen as the positie direction; West is the negatie direction. The graphs of elocity s. tie for the two cars are shown in the graph. Consider the following stateents: During the tie period shown in the graph,.. I. both cars are always oing east. II. the distance between the cars does not change as they oe. III. both cars are speeding up all the tie. = 0, t = 0 A B t How any of the stateents ust be true, gien the inforation in the graph? A) exactly one stateent is true B) exactly stateents are true C) all 3 stateents are true D) None are true 5. A sall roc of ass is near a large planet of ass M. The force of graity on the roc fro the planet has agnitude F on roc. The force of graity on the planet fro the roc has agnitude F on planet. What is the ratio of the size of the forces Fon roc? F on planet A) /M B) M/ C) (/M) D) (M/) E) 1 (forces hae sae agnitude) M

5 5 6. A train oes along a straight trac. Its acceleration s. tie is shown in the graph. Which graph below ost accurately depicts the train's elocity s. tie? (A) (B) a t t t (C) (D) t t (E) t 7. Two stars are far out in intergalactic space. The only force on each star is the graitational force fro the other star. The stars are initially a distance R apart and are oing apart, each with an initial speed. Fill in the blans: While the stars are oing apart, the speed of each star, and the agnitude of the acceleration of each star. A) decreases, increases B) increases, decreases C) increases, increases D) decreases, decreases R E) decreases, reains constant.

6 6 8. The graph shows the graitational potential energy (in units of J) of a frictionless roller coaster of ass = 100 g as a function of horizontal position x (in eters). Notice that the units of the ertical axis are J (ilo-joules). When the roller coaster is a position x = 10 and oing to the right, its speed is = 1 /s. Will the roller coaster ae it oer the three hills to the right? A) The roller coaster will ae it oer all three hills. B) The roller coaster will not ae it oer any of the hills. C) The roller coaster will ae it oer the first hill, but not the second or third. D) The roller coaster will ae it oer the first and second hill, but not the third. PE (J) st hill nd hill 3 rd hill x (eters) 9. Three blocs are connected by assless strings, and assless frictionless pulleys, as shown. There is friction between the table and the iddle ass ( B ) and the iddle ass is obsered to be sliding to the left with constant speed. What are the correct relationships between the agnitudes of tensions and the agnitudes of the weights? A) A g > T 1, T > T 3, T 4 > C g B) A g = T 1, T = T 3, T 4 = C g C) A g = T 1, T > T 3, T 4 = C g D) A g > T 1, T = T 3, T 4 > C g E) A g > T 1, T < T 3, T 4 > C g T 1 A = constant T T 3 B K C T 4

7 7 10. A student sees the following CAPA proble: A ass is attached to a assless thread which is wrapped around a frictionless pulley of ass M and radius R. The oent-of-inertia of the dis-shaped pulley about its frictionless 1 axle is I MR. The CAPA proble ass for the agnitude of the tension in the thread. The student correctly writes down the following equations inoling the agnitude of tension F T in the thread and the angular acceleration of the pulley: 1 a g FT a, R FT I M R R What is the correct expression for the agnitude of the tension F T? M R a A) R g Mg B) Mg M Mg C) R g D) M R E) None of these 11. For this proble, assue g = 10 /s. At tie t = 0, a ball is thrown straight up fro the ground with an initial speed of 80 /s. Ten seconds after the ball is launched (t = 10 s), what is the speed of the ball? Assue no air resistance, and to eep the ath siple, assue g = 10 /s A) 180/s B) 0 /s C) 70 /s D) 10 /s E) None of these, the ball hits the ground, before 10 s has passed. 1. A car, oing at constant speed, traels through the botto of a alley, as shown. The alley is shaped lie part of a circle. At the instant that the car is at the nadir (the ery botto) of the alley, how does the agnitude of the noral force F N fro the road on the car copare to the agnitude of the weight g of the car? A) F N > g B) F N = g C) F N < g

8 8 13. A projectile of ass is fired straight upward fro the surface of airless planet X with an initial speed o, which is greater than the escape elocity. The radius of planet X is R and the ass of the planet is M. When the projectile is ery, ery far fro planet X (effectiely at r = ), what is the correct expression for inetic energy of the projectile? (Assue no other asses nearby.) A) 1 B) GM C) R 0 GM D) R 1 0 GM E) R An astronaut on the oon (where there is no air) hits a golf ball which flies along a parabolic trajectory. At two different ties, t 1 and t, when the ball has the sae height before and after the ball reaches its apex, the ball has elocities 1 and, respectiely. What is the direction of the change in elocity between these two ties, that is, what is the direction of? 1 A) to the right, along +x direction. B) straight down, along y direction C) soe direction to the upper right D) soe direction to the lower right E) None of these B y ) t t 1 C A D x ) 15. An object of ass is acted on by two constant forces, both with agnitude F, while it oes to the right a distance x. As shown in the diagra, one of the forces is perpendicular to the otion and the other is 45 o 0 fro the direction of otion. What is the total wor done by these two forces as the object oes the distance x? A) Fx 1 B) F x C) Fx D) 1 Fx F 45 o F E) None of these. x

9 9 16. Two asses of size and 4 are connected by a assless thread and are strung oer a frictionless pulley of radius R and oent-of-inertia I. The two asses are held otionless at the sae height and then released fro rest. After the ass 4 has fallen a distance L and the ass has risen the sae distance L, what is the total inetic energy of the entire syste? L I R A) 4gL B) gl C) 3gL 1 D) 4g L IR E) None of these 4 L 17. A boo of ass sits at rest on an inclined rap. The coefficient of static friction between the boo and the rap is s. If the rap is tilted to a critical angle of c = 47 o, the boo will start to slide down the rap. The angle is less that the critical angle of 47 o, so the boo reains at rest. What is the correct expression for the agnitude of force of friction F fric on the boo, when c? A) g B) g sin C) g cos D) s g cos E) s g sin s 18. A ass is pulled along the surface of a frictionless table by a constant external force of agnitude F ext at soe non-zero angle aboe the horizontal. The agnitude of the noral force exerted by the table on the ass is N. What is the agnitude of the net force on the ass? no friction direction of otion F ext A) F ext + N + g B) N g + F ext sin C) zero D)F ext sin E) None of these

10 Two balls, labeled 1 and, collide in D and stic together. The oentu of ball 1 before the collision and the final total oentu of both balls after the collision are shown in the graph. There are no forces on the balls, except the forces they exert on each other. The scale of the graph is such that 1 unit =1g /s. In units of g /s, what is the agnitude of the oentu of ball before the collision? A) B) C) 3 D) 4 E) 5 p 1i p FINAL 0. A structure consists of four identical point asses held together by ery light (assless) rods, and arranged in a square of edge length L, as shown. There are 3 different axes of rotation labeled A, B, and C, all in the plane of the figure. The oents of inertia about these 3 axes are I A, I B, and I B. Ran the oents of inertia fro largest to sallest. L L L A L B A) I A > I B > I C B) I A = I B = I C C) I A = I B > I C D) I C > I B > I A C E) I C > I A = I B 1. A person is standing near the center of a erry-go-round which is spinning at a constant rate of 6 rp (reolutions per inute). There is a otor on the erry-go-round which eeps the rotation rate constant. The person then oes fro near the center outward to the ri of the erry-go-round and hangs onto the ri. What happened to the person's speed and the agnitude of his (linear) acceleration a as a result of oing fro near-the-center to the ri? A) increased and a decreased B) both and a increased C) both and a decreased D) decreased and a increased E) increased and a reained constant

11 11. A unifor horizontal rod of length L and ass M has a frictionless priot at the left end and is held in place by a wire at the right end as shown. The wire aes an angle with the rod. What is the agnitude of the tension T in the wire? A) L M gsin D) M g sin B) M g cos E) Mg sin C) Mgsin M L T 3. Two sleds are each pushed across a frictionless ice rin a distance of 10. The ass of sled 1 is larger, M1>M. The sleds begin at rest, and each is pushed with identical, constant force, F, through a distance of 10. After each sled has traeled exactly 10 eters, which of the following two stateents is true? I. After each has oed 10, they hae the sae oentu. II. After each sled has oed 10, they hae the sae inetic energy. A) Only I is true. B) Only II is true. C) Both are true. D) Neither are true. E) Not enough inforation is gien to answer the question. Sled 1, M1 Sled, M F F 4. The elocity s. tie of a particle oing along the x-axis is shown. What is the agnitude of the displaceent of the object x x0 between t = s (when its elocity is = /s) and t = 5 s (when it s elocity is = 1 /s )? A) 1.0 B) 1.5 C).5 D) 8.5 E) None of these /s 1 /s 0-1 /s - /s 1 s s 3 s 5 s t

12 1 5. The ector A has coponents A x = 4, A y = 3. The ector B (not shown in the diagra) is such that the ector (A B) is parallel to the y-axis and points in the positie y-direction. Which of the following equations ust be correct? y A A) A y = B x B) A y = B y C) A x = B x D) A x = B x E) None of these x 6. A projectile is fired fro the origin at tie t=0 with an initial speed o at an angle aboe the horizontal, as shown. Assue no air resistance. Which of the following stateents about x- and y- coponents of the elocity ( x, y ) and the acceleration (a x, a y ) are true? I. Throughout the flight, a x = 0. II. Throughout the flight, a y = constant. III. Throughout the flight, x = constant. IV. Throughout the flight, y = constant. y o A) All are true B) None are true C) Only I and III are true. B) Only I and II are true. E) Only I, II, and III are true. x 7.Three different frictionless ass-spring systes are labeled I, II, and III. All three systes hae the sae ass. Syste I has a single spring of spring constant ; syste II has two springs, each with constant, connected in series; and syste III has two springs, each with constant, connected in parallel, as shown in the diagras. Ran the periods oscillation of the three systes fro longest to shortest period. A) T II > T I > T III I. II. B) T III > T I > T II C) T I > T II = T III D) T I = T II > T III E) T I > T II > T III III.

13 13 8. Consider this (highly siplified) scenario. A rocet is launched straight up, and the net force on the rocet as a function of tie is shown in this graph. The rocet traels straight up and the net force is straight up. Between t=1 in and 4 in, what happens to the speed of the rocet? A) The rocet is speeding up the whole tie B) The rocet is slowing down the whole tie. C) The rocet is oing with a constant speed the whole tie. D) The rocet is speeding up for awhile, and then it slows down. E) There is not enough inforation gien to decide. F net (ega newtons) t (in) 9. A spherical star of unifor ass density has ass M, an initial radius R i and initial rotational period of T i = 10 days. The star then undergoes a partial collapse, due to exhaustion of its nuclear fuel, and becoes a spherical star of ass M and unifor ass density with a final radius R f = R i /10 (one tenth its original radius). What is the final period T f of the star? A) 0.40 days B) day C) 1 day D) 0.10 days E) None of these 30. A unifor dis of ass M is rotating on a frictionless axis about its center with initial angular elocity 0. A non-rotating unifor dis of ass 3M is dropped directly on top the spinning ass M, as shown. Because of friction, the two asses quicly start spinning together and achiee the sae final angular elocity f. What is f? 0 A) 0 B) C) D) 4 0 E) M M

14 A ass is suspended fro a ertical spring with spring constant, and the spring is attached to the top of an eleator, as shown. The eleator is accelerating upward with constant acceleration of agnitude a, and the spring is obsered to be stretched (beyond its equilibriu length) by a constant distance d (d> 0). What is the correct expression for d in ters of the other ariables in the proble? d a A) g B) (a g) C) g D) (a g) E) None of these 3. An object of ass 1 = 10.0 g and oing right with speed 1 =.0 /s collides head-on with a second object of ass = 5.0 g which is oing left with speed = 1.0 /s. The two objects stic together. There are no external forces on the two objects. 1 = 10 g 1 = /s = 1 = 5 g What is the final speed of the stuc-together asses? A) 1.0 /s B).0 /s C) 3.0 /s D) 0.50 /s E) None of these. 33. A piece of plastic of olue V and density p would ordinarily float in water, but it is held under water by a string tied to the botto of bucet as shown. The density of water is w. Which is larger, the agnitude of the buoyant force F B or the agnitude of the tension in the cord F T? A) Buoyant force F B is larger. B) Tension F T is larger. C) The two forces hae equal agnitude, F B = F T. D) The answer depends on the olue of the piece of plastic. plastic

15 One ilogra of Aluinu (,700 g/^3) and one ilogra of Lead ( 13,000 g/^3) are dropped into a beaer of water (and sin.) Which object has the largest agnitude buoyant force on it? A) Aluinu. B) Lead. C) Sae buoyant force on both and the buoyant force is upwards. D) Sae buoyant force on both and the buoyant force is downwards. E) Sae buoyant force on both and the buoyant force is zero. 35. A subarine is 1000 feet under the ocean surface. The side of the subarine has two square windows. Window A is 0 c on a side; window B is 10 c on a side. How does the pressure p A on the outside of window A copare to the pressure p B on the outside of window B? A) p A = p B B) p A = 4 p B C) p A = (1/4) p B 0c A B 10c D) p A = (1/) p B E) p A = p B 36. The graph shows pressure ersus tie at the position of a listener's ear as a sinusoidal traeling sound wae passes by. The sinusoidal wae shown has period T and aplitude A. pressure A T tie If the source of the sound is altered so that the period T of the sinusoidal wae is increased, what happens? A) The pitch(frequency) and the speed of the wae both increase. B) The pitch(frequency) and the speed of the wae both decrease. C) The pitch(frequency) decreases and the speed of the wae increases. D) The pitch(frequency) decreases and the speed of the wae reains unchanged. E) The pitch(frequency) increases and the speed of the wae reains unchanged.

16 An iersion heater is placed in a cup of water. The heater produces 500 W of power. The cup contains 50 gras of water. To -place precision, what rate will the teperature of the water increase (in degrees Celsius per second)? Possibly useful inforation: 1 cal = J A).0 o C / s B) 0.48 o C / s C) 8.4 o C / s D) 84 o C / s E) 0.1 o C / s 38. Two ipulse waes on a stretched string are approaching each other, as shown. Which picture correctly shows the total wae when the two waes are passing through each other? A) B) C) D) E)

17 A bar of length L can rotate about a frictionless axle at its center. The bar is initially at rest and is then acted on by the three forces shown. What happens to the bar? F F/ axle F 30 o L L/ L A) it reains at rest B) it begins rotating clocwise C) it begins rotating counter-clocwise 40. Two etal objects labeled A and B hae exactly the sae ass but they are ade of different etals. Both A and B hae the sae initial teperature and 50 cal of heat is added to each object. After the heat is added, etal A has a higher teperature than B. Which etal has the higher specific heat? A) A B) B C) A and B hae the sae specific heat capacity D) Fro the inforation gien, it is ipossible to tell. 41. A bungy cord juper has juped off a bridge, reached the botto, and is now bouncing up and down with period T. We can odel the situation as a ass hanging fro a big ideal spring that obeys Hooe's law. Suppose the person's ass is, and the spring constant of the bungy is. If a second, heaier person with ass jups, what will heaier person's period of oscillation be? A) T B) T C) T/ D) T E) T/

18 18 4. Consider the following three situations I, II, and III. For which of these situations can we assue that the acceleration ector of the ass is constant during the otion, so that we can use the constant acceleration forulas of chapter [ = 0 + a t, = o + a(x x o ), etc ] I. A ass has just left a sling shot with an initial speed of 1 /s, at an angle of 45 o aboe the horizontal. It reaches a axiu height of y = 3.7 before falling bac to Earth. Neglect air resistance. II. A satellite of ass is in a circular orbit of radius R around a planet of ass M M R III. A ass is released fro rest at a point in space 3,000 aboe the surface of the Earth (3,000 is fie ties the radius of the Earth). It falls straight toward the center of the Earth and stries the surface after falling for.7 hours. The constant acceleration forulas fro Chapter apply for.. A) all three situations B) none of these situations C) only situations I and II D) only situations I and III E) only situation I earth END of EXAM Hae a pleasant holiday brea!

19 1A, D, 3C, 4D, 5E, 6B, 7D, 8A, 9C, 10B, 11B, 1A, 13B, 14B, 15A, 16C, 17D, 18E, 19A, 0E, 1B, E, 3B, 4B, 5C, 6E, 7A, 8B, 9D,30D, 31D, 3A, 33A, 34A, 35E, 36D, 37B, 38C, 39A, 40B, 41D, 4C