PHYS 107 Practice Final Test Fall 2018

Transcription

1 The actual test contains 10 ultiple choice questions and 2 probles. However, for extra exercise, this practice test includes 20 questions and 5 probles. Questions: N.B. Make sure that you justify your answers explicitly on the space provided on this page in order to qualify for partial credit even when your choice is wrong. Q1: [4] The adjacent diagra shows the positions at equal tie intervals of four identical particles oving horizontally with zero or constant acceleration. Which of the four particles is acted by a larger net force? a) A b) B c) C d) D A B C D Q2: [4] Two identical particles are launched siultaneously with equal initial velocities v 0, and race between the sae initial and final positions along differently shaped frictionless rails, as in the figure. Which of the particles wins the race? a) A b) B c) The particles will reach the end at the sae tie. d) It depends on the depth of the seicircular pit. A B v 0 v 0 Q3: [4] A cannon ounted on a cart slides down on a frictionless rap. The cannon fires a projectile vertically upward. Where does the projectile fall? a) Behind the cart. b) Right back in the cart. c) In front of the cart. d) It depends on the angle of inclination. Q4: [4] Throughout this seester we used an Attwood achine as a deo prop to introduce various concepts, including conservation of echanical energy. How any forces do work in this arrangeent? a) None overall, because the syste is conservative. b) 2 c) 4 d) 6 e) It depends on how fast it oves 1 2 Q5: [4] Two particles a heavy one and a light one are pressed against identical ideal springs by the sae copression and launched on a flat frictionless surface. Which of the particles reaches a higher speed when the springs relax copletely? a) The heavier particle. b) The lighter particle. c) Both particles have the sae speed. d) The particles won t ove since they are inertial fraes. 1 >

2 Q6: [4] A constant force is applied to a box, contributing to a certain displaceent on the floor. If the angle between the force and displaceent is 135, the work done by this force is a) energy gained by the box. b) energy lost by the box. c) energy gained by the floor. d) energy lost by the floor. e) Both (b) and (c) above are true. Force (N) Q7: [4] The adjacent graph represents the net horizontal force acting on an object as it oves in a straight line along x-axis. What is the net work done by this force in the shown interval? a) 0 b) 20 J c) 10 J d) 20 J e) Insufficient inforation x () Q8: [4] The adjacent graph represents a vertical ap with the paths of two balls rolling fro rest down two frictionless slopes with the indicated profile. Knowing that ball A is twice as heavy as B, which ball will ove faster at the botto of its hill, and what will be its speed? a) Ball A will ove faster, v A = 19.8 /s. b) Ball A will ove faster, v A = 390 /s. c) Ball B will ove faster, v B = 19.8 /s. d) Ball B will ove faster, but the inforation is insufficient to find the speed. e) Both will ove with the sae speed, v A = v B =19.8 /s y () A B x () Q9: [4] The elastic constant k 1 of spring is twice the constant k 2 of spring. The spring is copressed by x 1, and the spring is stretched by x 2. The copression x 1 is also twice the stretch x 2. Then the ratio PE 1 / PE 2 between the elastic potential energies of the two springs is a) 2 b) -2 c) 4 d) 8 Q10: [4] Two objects, one heavier than the other, have the sae kinetic energy. Which has the sallest linear oentu? a) The light object b) The heavy object c) Both have the sae oentu. d) It depends on the potential energy e) It depends of the speed. 2

3 Q11: [4] A ball with ass = 0.5 kg oves with a speed v i = 4.0 /s perpendicularly onto a wall, collides inelastically with the wall and bounces back along the sae line with speed v f = 2.0 /s. If the ball was in contact with the wall for 10-2 s, how large was the force exerted by the wall on the ball? a) 100 N b) 300 N p i c) 0 N p f d) 9.8 N Q12: [4] Scrat, the conspicuous Ice Age squirrel, sits on a sled of ass M = 5.0 kg, holding tightly on his beloved acorn. Scrat s ass is 1 = 1.0 kg and acorn s ass is 2 = 30 g. The sled is at rest when Scrat throws out the acorn horizontally with a speed v 2 = 24 /s. As a result, the sled oves with a speed a) v 1 = 0 /s b) v 1 = 24 /s c) v 1 = 0.12 /s d) v 1 = 120 /s e) Nonsense! Scrat would never throw away his acorn. Before After Q13: [4] Consider two colliding objects. Each of the adjacent diagras attepts to represent their oenta before and after the collision using unpried and pried sybols respectively. Which of the diagras cannot be correct? a) None of the is correct. b) All of the are actually correct c) A and D d) B and C e) D only A B C D Q14: [4] The weight of a certain sleeping bear is unusually close in agnitude (for an earthly creature) to the noral force acted by the flat surface it lays on. What is the ost likely color of the bear? a) An ineffable nuance of blue. b) Brown. c) Black. d) White. e) Pink Q15: [4] In a rare separateness, And a peculiar quietness, Thing One and Thing Two Lie at rest, relative to the ground And their wacky hairdo. If Thing One freezes in Morrisville, New York, Whereas Thing Two toasts in Key West, Florida, Which Thing oves with a larger angular speed Merrily adorned in his crison thneed? a) Thing One. b) Thing Two. c) Both Things have the sae angular speed. d) Insufficient inforation. 3

4 The next three questions refer to the following situation: Mary spins a arry-go-round of ass M = 100 kg and radius R = 1.5. The syste starts fro rest as the child applies a force of constant agnitude F = 15 N but changing direction, always tangent to the edge of the errygo round. The friction is negligible. R Mary Q16: [4] Considering the erry-go-round as a thin cylinder, what is the agnitude of its angular acceleration? a) 9.80 rad/s 2 b) rad/s 2 c) 0.15 rad/s 2 d) 0.20 rad/s 2 M Q17: [4] Considering that Mary oves close to the edge of the erry-go-round, what is the angular velocity in rotations per inute, rp of the erry-go-round after Mary runs 15 eters in a circle? a) 2.4 rp b) 4.0 rp c) 9.5 rp d) 19 rp Q18: [4] What is Mary s centripetal acceleration after she travels 15 eters in a circle? a) Mary is a lady, sir! She ain t got no darn centerpeetal asseleration! b) Insufficient inforation, because Mary s speed cannot be found. c) Insufficient inforation, because Mary s ass is not given. d) 6.0 /s 2 e) 0.15 /s 2 Q19: [4] A DVD with oent of inertia of about kg 2 rotates with unifor angular acceleration 200 rad/s 2. Starting fro rest it reaches its noinal angular speed in about 2.4 seconds. What is the iniu energy spent in order to bring the disk to its noinal angular speed? a) 2.7 J b) J c) J d) 3.1 J Q20: [4] A 70-c stick with ass 1.4 kg is ounted on a pivot as in the figure. What is the agnitude of the net torque acting on the stick with respect to the pivot? a) 1.6 N b) 3.6 N c) 0.69 N d) 0 4

5 Probles: In order to qualify for partial credit you have to provide at least a logical start toward a solution, even if it ay be flawed. Do not flood the space with obviously useless inforation. P1: A box with ass = 5.0 kg is launched in point with speed v 1 = 5.1 /s. It oves a distance d = 0.60 along a rough horizontal surface, with coefficient of kinetic friction μ k = In point, the box starts to clib up a frictionless rap. Eventually, the box stops on the rap in point, at height h with respect to the flat surface. a) [5] Calculate the echanical energy E 1 of the box in point. v 1 d v 2 h b) [10] Sketch the force diagra for the box in an arbitrary position between points and. Then calculate the work W fr done by the friction between these two points. v c) [10] Use the conservation of energy to calculate the echanical energy of the box in point. Then use the result to copute the speed v 2 of the box in point. d) [5] Write out a sybolical expression for the echanical energy E 3 in point. Then use conservation of energy to copute the axiu altitude h reached by the box up the rap. 5

6 P2: A wooden block of ass M = 1.98 kg is initially at rest when it is hit horizontally by a bullet of ass = 20.0 g with speed v = 30 /s. The bullet is ibedded in the wood and subsequently the bullet-block syste copresses a spring with elastic constant k = 200 N/ along a frictionless surface. v M k a) [5] Denote p bullet, p wood the respective oenta before the collision, and p bullet, p wood after the collision. Write out the oentu conservation during the collision, and use it to calculate the speed of the syste bullet-box iediately after the collision. x b) [5] What is the echanical energy of the syste before and after the collision? c) [5] Calculate the percent of energy lost during the collision. What happened with the issing energy? d) [5] Use conservation of echanical energy to calculate the axiu copression x of the spring. e) [10] Knowing that the axiu copression is achieved in a tie Δt = 0.20 s, what is the average power of the spring? Also, use the Ipulse-Moentu Theore to calculate the average force exerted on the syste block-bullet by the spring in this interval. 6

7 P3: The adjacent figure shows a crankshaft echanis acted by a piston applying a force to the crankpin via the connecting rod. To illustrate the applicability of what we learned in class about rotational dynaics, let us perfor soe siple calculations of forces, torque and ensuing otion. a) [6] At the instant shown, the connecting rod akes an angle θ p = 30 relative to the piston axis. Assuing that the piston applies an axial force F p = 500 N alost constant for ost of the piston s range in the cylinder, how strong is the force F transitted along the rod to the crankpin? F ω Crankpin journal θ r Cylinder connecting rod Main journal F p θ p Piston Cylinder Gas b) [6] The crankpin is at a distance r = 0.11 fro the center of the ain journal. If in the figure the angle between the rod and r is θ = 52, calculate the instantaneous torque applied to the crank by the piston. c) [6] Is this the axiu torque applied to the crank by the piston in the gas expansion regie? Circle one and provide a brief explanation. If no, specify when the torque is axiu and calculate it. 1. Yes 2. No 3. No way to know d) [6] Assuing that the oent of inertia of the spinning echanis about the ain journal axis is I = kg 2, calculate the instantaneous angular acceleration of the syste at the oent represent in the figure, if one were to assue that only the torque described above acted on it. e) [6] A naïve reading of this physical situation would lead to unrealistic conclusions: for instance, note that the crankshaft sees to be accelerated ost of the tie, which would ean that its angular speed ω would increase indefinitely as long as the piston works obviously, this is not consistent with the fact that you reach constant rp values on your tachoeter when the crankshaft is used to keep a car in otion. Use the logic of siple dynaics introduced in our course to explain briefly why. 7

8 P4: A rigid body is coposed of a central sphere of ass = 3.0 kg and radius r = 0.34, and three identical point-like particles of equal asses /5. The particles are connected by coplanar spokes of length 3r to the center of the sphere, as in the figure. The ass of the spokes is negligible. The syste is initially at rest, ω 0 = 0, then it starts to rotate about an axis of rotation perpendicular on the page. It rotates with unifor angular acceleration through an angle at the center Δθ = 14π, until it achieves an angular speed ω = 21 rad/s. a) [6] Calculate the net oent of inertia of the syste. 3r r ω point-like asses, not spheres! b) [6] Calculate the angular acceleration of the syste. c) [6] Calculate the tie t that the syste needs to achieve the given angular speed ω. d) [6] Calculate the net torque applied to the syste. e) [6] Say that the net torque calculated above is due to three equal forces, each applied to one of the three particles under an angle β = 30 with respect to the respective spoke, as shown on the adjacent figure. Calculate the agnitude of the three forces. F β ω β F F β 8

9 P5: A block of ass M and a sall ball of ass = 2.5 kg, are connected to each other by a light string passed through a hole in a horizontal table. The block is at all ties at rest on the rough surface of the table with coefficient of static friction μ s = The ball hangs under the table and rotates uniforly in a horizontal circle of radius R = 0.25 with the string aking an angle θ = 35 with the vertical, as shown on the figure. (We say that ass oves as a conical pendulu.) a) [6] On the figure below, sketch the free body force diagras for asses and M. Consider the portion of the string between the ass M and the hole parallel with the tabletop, as represented. Label the forces eaningfully. R θ M rough table M y x θ R y r b) [7] Write Newton s 2 nd law sybolically for asses and M along the directions indicated for each object. The expressions for the ass should contain the angle θ fro the coponents of the tension. Mass M: Fx Mass : Fy F F y r c) [7] Use one of the equations for ass in part (b) to calculate the tension in the string. Then substitute the tension in the other equation to calculate the speed v of the ball. d) [7] Use the results of parts (b) and (c) to calculate the static friction keeping the ass M fro oving. What is the iniu ass M that will prevent the block fro sliding on the table? e) [3] If the string is cut at the oent shown in the figure fro part (a), how will the ball ove? Circle one: out of the page to the left downward (free fall) 9