Final Exam, vers Physics Fall, 2012

Transcription

1 1 Final Exa, - Physics Fall, 01 NAME Signature Student ID # TA s Nae(Circle one): Clarissa Briner, Effie Fine, Mathis Habich, Ada Keith, Willia Lewis, John Papaioannou, WeisenShen, JiayiXie, Jian Yao, Xiao Yin Circle start tie of your recitation: 8a 9a 10a 11a Noon 1p p 3p 4p Please do not open the exa until you are told to. Your exa should have 17 pages, nubered 1 thru 17. The last sheet is for scratch paper. This exa consists of 4 questions, weighted equally. Fill in the bubble sheet with a # pencil. Please fill out your bubble sheet according to the following instructions or you ay be penalized. Check each box as you coplete the instructions. Please circle your TA's nae and the tie of your lab section above. Print and bubble in your nae on the bubble sheet. Print and bubble in your student Identification Nuber. Print and bubble in your Exa version, 0001 or 000 in the upper left of your bubble sheet in the area arked 134. On your bubble sheet, erase istakes thoroughly, and ake no extraneous arks As you take the exa, show all your work on the exa and circle the correct answers on your exa. Your circled exa answers and bubbled answers ust agree. I have read and followed the instructions above. I give y word that I have neither given nor received unauthorized assistance on this exa. Signature BUGET YOUR TIME. THIS is a.5 HOUR EXAM.

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 disk Hoop: I = M R Solid disk 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 kg/ 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 vaporization of water/stea = 539 cal/g = 539 kcal/kg.

3 3 1. The ass per area of a certain type of tile is 1 g/c (gras per square centieter). What is the ass per area of this tile in units of kg/ (kilogras per square eter)? A) 1.0 B) 10 C) 100 D) 10 5 E) none of these. Here are four atheatical expressions that involve 3 vectors, the cross-product operation( ), and the dot product operation ( ) : A B C A B C A B C A B C Each of these expressions ight be a nuber, a vector, or ake no sense at all. How any of these 4 expressions ake no sense at all? A) Zero (all of the are valid expressions) B) 4 (none of the are valid expressions) C) 1 D) E) 3 v 3. Two cars, labeled A and B, are traveling along a long straight road. The road runs east and west. East is chosen as the positive direction; West is the negative direction. The curves of velocity vs. tie for the two cars are shown in the graph. Consider the following stateents: During the tie period shown in the graph,.. v = 0, t = 0 I. one car is always oving East and the other car is always oving West. II. the net force on each car is constant and nonzero. III. one car is slowing down and the other car is speeding up. A B t How any of the stateents ust be true, given 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

4 4 4. A rock is dropped fro rest. How long will it take to fall a distance h? Ignore air resistance. A) g h B) g h C) h g D) h g E) None of these. 5. By applying a constant horizontal force of agnitude F, a student pushes a heavy box of ass M along the kitchen floor at a constant speed v. The coefficient of kinetic friction between the floor and the box is K, and the coefficient of static friction is S (where S > K ). Now the student halves the size of the applied force, so the agnitude of the constant horizontal force which she applies is F/. What can you say about the otion of the box after the force F/ is applied? A) The box slows to a stop with constant acceleration of agnitude F/(M). B) The box slows to a stop with constant acceleration of agnitude 3F/(M). C) The box has a constant speed of v/. D) The box has a constant speed between v/ and v. E) The box slows down, and the speed asyptotically approaches zero (the box goes slower and slower all the tie, but never stops). 6. Two non-zero vectors A and B both lie in the xy-plane. The only thing that you know about these vectors is that vector su A B is in the +x direction. What can you say for certain about the coponents of these vectors? (Hint: draw a vector diagra) A) A x = B x B) A x = B x C) Ay B y D) Ay B y E) Ax B y 7. A toy car coasts up and then back down a straight inclined track. Neglect any effects of friction. How does the agnitude of the toy's acceleration vector vary with tie? A) It decreases while the toy oves up the rap, and increases on the way down. B) It increases while the toy oves up the rap, and decreases on the way down. C) It is constant (not zero) at all ties except the very top, where it becoes zero for an instant. D) It is constant at all ties, with value zero. E) It is constant at all ties, with a value different fro zero.

5 5 8. A box of ass = 10.0 kg is initially sitting stationary on a flat rough floor where the coefficient of static friction is S = 0.5 and the coefficient of kinetic friction is K = 0.4. A horizontal force of agnitude F = 15.0 N is then applied to the box. What then is the agnitude of the force of friction on the box? [g = 9.8 /s ] A) 0 N B) 49.0N C) 39. N D) 15.0 N E) None of these. 9. A train oves along a straight track and its velocity vs. tie is shown. Which graph below correctly depicts the train's acceleration vs. tie? v a (A) a (B) t t t a (C) a (D) t t a (E) t

6 6 10. The velocity of an object that is oving with constant acceleration is shown at two different ties: v 1 is the velocity at an earlier tie and v is the velocity at a later tie. What is the direction of the acceleration of the object? v 1 v A B C E D A) straight up B) upper right C) straight right D) lower right E) lower left 11. A ass is held by two identical springs, each of spring constant k, as shown. When there is no gravity, both springs are relaxed, and have their unstretched lengths. When there is noral gravity present, the equilibriu position of the ass is a distance x below its position when there is no gravity. What is the correct expression for the distance x? A) g k E) None of these B) g k C) g k D) k g k ) ) k ) No gravity x ) g Gravity 1. A box of ass is held stationary against a vertical frictionless wall by a force of agnitude F at an angle of about 50 0 to the horizontal, as shown. Which is larger, the agnitude of the weight g or the agnitude of the force F? no friction A) F > g B) F < g C) F = g D) ipossible to tell without ore inforation. F

7 7 13. A block slides down a rough incline and then part way up an equally steep incline, as shown. The coefficient of kinetic friction between the block and the surface is the sae on both inclines. How does the agnitude of the block's acceleration while it is sliding down (a down ) copare to the agnitude of its acceleration while it is sliding up (a up )? (Hint: Free-body diagras!) a down a up A) a down > a up B) a down < a up C) a down = a up D) Ipossible to say without ore inforation 14.A block of ass slides down a frictionless rap into roundbottoed ditch as shown. When the block is at the botto of the ditch, how does the agnitude of the net force F net copare to the agnitude of the noral force N? A) F net > N B) F net < N (but F net 0) C) F net = N D) F net = 0 E) F net could be greater than, less than, or equal to N, depending on the speed of the ass. 15. An object with ass = 1 kg is acted on by the 3 force shown in the diagra. No other forces are present. What is the agnitude of the acceleration a of the object? A) 1 /s B) /s C) /s D) 5 /s F 1 F 3 E) None of these F 1 N 1 N

8 vb0b 8 16.Two blocks of ass M and are both being pushed along a frictionless surface by a horizontal external force F, as shown. What is the agnitude of the contact force F C which the little block (ass ) exerts on the big block (ass M)? F M M A) M F B) M F C) F M D) M F E) None of these is correct. 17. A clay block of ass oving to the right with speed v o has a head-on collision a second block of ass oving to the left with speed v 0. The two clay blocks stick together after the collision. There are no outside forces acting on the blocks. How uch kinetic energy was lost in this inelastic collision? A) v o B) 3 v o C) (3/) v o D) (/3) v o vb0 E) None of these 18. A rock of ass is released fro rest a distance 3R fro the center of an airless planet of ass M and radius R (the rock's initial position is R above the surface of the planet). The rock falls straight down and strikes the planet's surface. What is the final speed of the rock when it reaches the planet s surface (at the instant just before it hits)? (A) GM R (B) 3GM 4R (C) 4GM 3R (D) 3 GM R (E) None of these.

9 9 19. A frictionless sliding hockey puck and two rolling objects, a hoop and a cylinder, all start fro rest at the sae initial height on an incline. All three objects have the sae ass M; the two rolling objects have the sae radius R, and roll without slipping. Assue no air resistance. The objects descend down into a valley and up onto the hillside on the right as shown. Consider the following two stateents. I. All 3 objects take the sae tie to reach the axiu height on the right side of the valley. II. All 3 objects attain the sae axiu height on the right side of the valley sliding puck rolling hoop rolling cylinder Which of these stateents is true? A) I only B) II only C) Both I and II are true. D) Neither are true. 0. A rock of ass suspended on a string is being lowered, but it is slowing down with a constant acceleration of agnitude a. What is the agnitude of the tension T in the string? Hint: Draw the freebody diagra. A) (a g) B) a C) g D) (a + g) E) (g a) oving down, and slowing 1. A box of ass is given a brief, strong shove, so that its initial speed along a horizontal floor is v. Because of friction, the box slows and stops in a distance d. The coefficient of kinetic friction between the floor and the box is K. What is the agnitude of the acceleration of the box, while it is slowing? K A) vd g B) g K g K C) Kg D) d E) None of these.

10 10. Two sleds are being pulled across a frictionless ice rink by two otors. The ass of sled is twice as large as the ass of sled 1. The sleds start at rest and each is pulled with the sae constant force F for the sae distance d. M F d otor 1 M F d otor Consider the following two stateents: I. After the sleds have each traveled the sae distance d, they have the sae kinetic energy. II. After the sleds have each traveled the sae distance d, they have the sae speed. Which stateents are true? (Hint: Consider the work done) A) Neither are true. B) Both are true. C) Only I is true. D) Only II is true. 3. A projectile of ass is fired straight up fro an initial height h 0 with an initial speed v 0. The projectile rises to a axiu height of h ax and falls straight back down to the ground at zero height. What is the total work done by the force of gravity during this trajectory? A) + gh ax B) +gh 0 C) zero D) g(h ax h 0 ) E) +g(h ax h 0 ) h 0 v 0 h ax 4. A sailboat is being pushed along the surface of a lake at constant velocity by a strong wind. What is the direction of the net force on the sailboat? A) left B) right C) up D) down E) no direction because the net force is zero

11 11 5.A ass is suspended by two strings as shown. T 1 and T are the (unknown) tensions in the strings. One of the strings is horizontal and the other akes an angle with the horizontal ceiling, as shown. What is the vertical coponent of the tension T? That is, what is T y? (Note: The question asks for the coponent T y, not T ) A) g cos B) g sin g D) cos E) None of these. C) g sin T 1 y T x 6.A ass is sitting on a rotating erry-go-round that is rotating with constant angular velocity. The ass is not sliding. At the oent when the ass is at the far right (as shown in the diagra), which free-body ost accurately represents the forces on the ass? ass A) B) C) platfor D) E) 7. An object consists of 5 point asses, each of ass, connected by assless rods as shown. The four short rods have length L and the long rod has length L. Although the diagra shows the asses as sall spheres, assue they are points. What is the oent of inertia about an axis perpendicular to the diagra (out of the page) and through the ass labeled x (the one on the lower right of the square). L L L L x A) 3L B) 6L C) 5L D) 8L E) 9L L

12 1 8. Ball 1 strikes Ball in a collision. The figure shows the oentu of both Ball 1 and Ball before the collision and the oentu of Ball 1 after the collision. There are no forces on the balls except the collision forces. As a result of the collision, did Ball speed up, slow down, or keep the sae speed? Ball.. A) speeds up. B) slows down. C) has the sae speed after the collision. D) Ipossible to tell without knowing the asses of the balls E) ipossible to tell without knowing whether the collision was elastic or inelastic. p 1i p i p 1F 9. A toy car with ass oves along a assless wooden plank lying horizontally over two support posts, as shown. The car is rolling across the bridge fro point P to point P3, ( i.e. fro left to right). As the car oves fro P to P3, what can you say about the agnitude of the net torque about the point P1 at the far left of the plank? The net torque is P1 P P3 (A) increasing. (B) decreasing. (C) constant and zero (D) constant and non-zero. (E) Not enough inforation is given to answer. 30. A projectile of ass is fired at an angle above the horizontal with an initial speed v o, as shown. Assue no air resistance. Just before the projectile hits the ground at final height h, as shown, what is its final speed v? A) vo gh B) gh C) v cos E) None of these o D) vo gh v o v =? h

13 I P = 0 kg f =? Initially, a person is sitting stationary on stool that can rotate on a frictionless pivot, and the person is holding a spinning wheel with its axis vertical as shown. The oent-of-inertia of the person+stool about the stool's axis is I P = 0 kg. The wheel has oent-of-inertia I W = 5 kg about it axis and it is initially spinning at f w = 4 revs/s. The person then reaches up and slows the wheel so she can hold the wheel by the ri while keeping its axis vertical. What is the final rotation rate of the person while she is holding the wheel by the ri? I W = 5 kg f W = 4 rev/s Initial A) zero B) 1 rev/s C) 6 rev/s 5 D) 4 rev/s 5 Final E) 3 rev/s 3. In the proble above, coparing the final total (rotational) kinetic energy of the syste (person+stool+wheel) to the initial kinetic energy of the syste, did the KE of the syste increase, decrease, or reain constant when the person grabbed the wheel? A) KE reained constant B) KE decreased C) KE increased.

14 A siple haronic oscillator consists of a ass attached to a assless spring with spring constant k, on a frictionless table. The spring is initially stretched a distance D to the right and the ass is given an initial speed v 0 to the left, as shown. What is the aplitude A of the subsequent otion of the ass? A) D B) D v0 k C) D v D) k o k 0 D v 0 k D v o E) None of these x 34. A lead ball and two identical plastic balls all have the sae volue V. All three are placed in a bucket of water. The lead ball sinks to the botto. One of the plastic balls floats on the surface with part of its volue above the water, and the other plastic ball is held below water with a string. Which object experiences the largest agnitude buoyant force? lead plastic plastic A) the lead ball B) the floating plastic ball C) the plastic ball tied under water D) the two plastic balls have the sae buoyant force which is larger than the buoyant force on the lead ball. E) the lead ball and the tied plastic ball have the sae buoyant force which is larger than the buoyant force on the floating plastic ball. 35. Marine biologists wish to videotape fish at the botto of a lake. A heavy sealed box with caeras inside and two square windows is placed at the botto of a lake. Inside the box is air at one atosphere of pressure. Both windows are on the top side of the box. Window A is 5 c on a side, Window B is 10 c on a side. How does the pressure p A on window A copare to the pressure p B on window B? A) p A = p B B) p A = (1/) p B C) p A = (1/4) p B D) p A = 4 p B E) p A = p B A 5 c 10 c B

15 This graph shows pressure versus tie at the position of a listener's ear as a sinusoidal sound wave passes by. The wave has period T and aplitude A. pressure A T If the period T of the sinusoidal sound wave is decreased, what happens to the speed of this sound wave? A) Speed increases B) Speed decreases C) Speed stays the sae. tie 37. A transverse sinusoidal traveling y wave with aplitude A is oving to the right along a horizontal stretched string. A point on the string is arked with a A vbwaveb spot of paint. The graph shows the paint spot displaceent of the string fro equilibriu at a particular instant of tie. At this instant, the paint spot is at y = -A. At this instant, what is the direction of the velocity of the paint spot? x A) up B) down C) right D) left E) no direction, the velocity is zero. 38. A horizontal plank with a frictionless axis of rotation at its center has a large ass at one end and a sall ass at the other end. It is held stationary and then released. As the plank rotates (and before one end hits the ground), the agnitude of the net torque on the plank about the center (increases/decreases/or reains constant) and the agnitude of the angular acceleration (increases/decreases/or reains constant)? increases and decreases A) net B) net decreases and increases C) net reains constant and decreases D) net decreases and decreases E) net reains constant and reains constant

16 A pair of objects, with asses 3 and, are connected by a hook and have an ideal assless copressed spring between the. Initially, the objects are at rest. Then the hook unlatches, the spring expands to its relaxed length, and the asses have final velocities, as shown. Assue no friction and no theral energy generated anywhere, and no outside forces acting on the asses. 3 rest BEFORE 3 v1 AFTER Which of the following three quantities are conserved in this process: total oentu p tot, total kinetic energy KE, total echanical energy (E ech = KE+PE) A) p tot and KE are conserved, but not E ech B) Only E ech is conserved C) Only p tot is conserved D) p tot and E ech are conserved, but not KE E) All three (p tot, KE, and E ech ) are conserved. v 40. Two solid objects, labeled A and B, both with the sae ass, are placed in a icrowave oven which is turned on. Both objects absorb energy fro the icrowaves at the sae rate [sae power P (joules per second)]. It is found that the teperature of object A rises 4 ties faster than object B. Which object has the larger specific heat capacity? A) object A B) object B C) both objects have the sae specific heat D) ipossible to tell without ore inforation 41. A sall block of ass oving to the right collides with a large block of ass 10 oving left. During the collision, the sall block exerts a force of agnitude F S on the large block, and the large block exerts a force of agnitude F L on the sall block. How do the agnitudes of the forces copare? A) F S = (0.1) F L (F S is 10 ties saller than F L ) B) F S = 10 F L (F S is 10 ties bigger than F L ) C) F S = F L D) The answer depends on the speeds of the blocks. E) Answer depends on the duration of the collision. 10 BEFORE BANG! DURING

17 17 4. The 3 scenarios shown have initial states on the left and final states on the right. The three scenarios above show initial states on the left and final states on the right. In scenario I, a rocket of ass M carries 50 L of fuel with ass. The rocket accelerates in outer space to speed v by expelling the fuel with speed v Exhaust. In scenario II, a car of ass and a truck of ass M are initially oving towards each other. The car and truck collide on an icy road, stick together, and both then ove to the left with speed v iediately after the collision. In scenario III, a car of ass M carries a passenger of ass. The passenger pushes down on the accelerator pedal and the car/passenger syste accelerates to a speed v. For which scenario(s) is the total oentu of the two asses conserved; that is, for which scenario(s) is ptot pm p = constant? A) Scenario I only. B) Scenario II only. C) Scenario III only. D) Scenarios I and II. E) Scenarios I and III. End. Have a pleasant Break!