PHYS 154 Practice Final Test Spring 2018

Size: px

Start display at page:

Download "PHYS 154 Practice Final Test Spring 2018"

Jody Clark
5 years ago
Views:

1 The actual test contains 10 ultiple choice questions and 2 probles. However, for extra exercise and enjoyent, this practice test includes18 questions and 4 probles. Questions: N.. ake 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) b) c) C d) 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) b) c) The particles will reach the end at the sae tie. d) It depends on the depth of the seicircular pit. C D v 0 v 0 Q3: [4] Two boxes of asses 1 and 2 such that 1 > 2 lay in contact with one another on a frictionless surface. One can apply a horizontal force F either fro the left (on 1 ) or fro the right (on 2 ). When F is applied, the contact force between the asses is a) larger when F is applied fro the left b) larger when F is applied fro the right c) the sae in either case d) Q4: [4] cannon ounted on a cart slides down on a frictionless rap. The cannon fires a projectile vertically upward. Where does the projectile fall? a) ehind the cart. b) ight back in the cart. c) In front of the cart. d) It depends on the angle of inclination. Q5: [4] Throughout this seester we used an ttwood 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 Q6: [4] Planet Earth has radius = How long should be a day in order to ake the objects on the Equator levitate? a) s b) 3600 s c) 5100 s d) s 1

Q7: [4] particle of ass is connected to one end of a string of length and rotated vertically, as in the figure When the string akes an angle θ with respect to the vertical direction, the tension in

2 Q7: [4] particle of ass is connected to one end of a string of length and rotated vertically, as in the figure When the string akes an angle θ with respect to the vertical direction, the tension in the string is T and the speed v of the ass is: a) v T v T g cos v T g cos b) v T g sin c) d) Q8: [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) oth particles have the sae speed. d) The particles won t ove since they are inertial fraes. efore θ v 1 > 2 fter 1 2 Q9: [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) ll of the are actually correct c) and D d) and C e) D only C D Q10: [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) n ineffable nuance of blue. b) rown. c) lack. d) White. e) Pink Q11: [4] In a rare separateness, nd a peculiar quietness, Thing One and Thing Two Lie at rest, relative to the ground nd their wacky hairdo. If Thing One freezes in orrisville, New York, Whereas Thing Two toasts in Key West, Florida, Which Thing oves with a larger angular speed errily adorned in his crison thneed? a) Thing One. b) Thing Two. c) oth Things have the sae angular speed. d) Insufficient inforation. 2

3 The next three questions refer to the following situation: arry spins a arry-go-round of ass = 100 kg and radius = 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 erry-go round. The friction is negligible. arry Q12: [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 Q13: [4] Considering that arry 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 arry runs 15 eters in a circle? a) 2.4 rp b) 4.0 rp c) 9.5 rp d) 19 rp Q14: [4] What is ary s centripetal acceleration after she travels 15 eters in a circle? a) arry is a lady, sir! She ain t got no darn centerpeetal asseleration! b) Insufficient inforation, because arry s speed cannot be found. c) Insufficient inforation, because arry s ass is not given. d) 6.0 /s 2 e) 0.15 /s 2 Q15: [4] 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 Q16: [4] 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 3

Q17: [4] heavy sphere and a light sphere have the sae radius and the sae kinetic energy. Which has the greatest angular oentu?

acorn which is stuck in the center of an ice disk with radius = 2.0 and ass = 20 kg, rotating with angular speed ω = 11 rad/s. Scrat s ass is 1 = 1.

Considering Scrat and his acorn as pointlike asses, what is the angular speed of the syste when Scrat reaches the edge? a) 11 rad/s b) 10 rad/s c) 9.

4 Q17: [4] heavy sphere and a light sphere have the sae radius and the sae kinetic energy. Which has the greatest angular oentu? a) The light sphere b) The heavy sphere c) The angular oenta are equal d) It depends on the angular potential energy ω Q18: [4] Scrat sits on top of his acorn which is stuck in the center of an ice disk with radius = 2.0 and ass = 20 kg, rotating with angular speed ω = 11 rad/s. Scrat s ass is 1 = 1.0 kg and acorn s ass is 2 = 30 g. Scrat leaves his acorn in the center, and walks radially to the edge of the disk. Considering Scrat and his acorn as pointlike asses, what is the angular speed of the syste when Scrat reaches the edge? a) 11 rad/s b) 10 rad/s c) 9.97 rad/s d) 2.7 rad/s 1 2 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. 4

5 P1: block of ass 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 = 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. Consider the portion of the string between the ass and the hole parallel with the tabletop, as represented. Label the forces eaningfully. θ rough table y x θ y r b) [7] Write Newton s 2 nd law sybolically for asses and along the directions indicated for each object. The expressions for the ass should contain the angle θ fro the coponents of the tension. ass : Fx ass : 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 fro oving. What is the iniu ass 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) 5

6 P2: sall box of ass = 1.7 kg is released fro rest in position down a frictionless rap with a quarter-circle profile of radius = 1.2. esides the usual forces, an external force acts on the box. The force is given in ters of the angle θ ade by the radius and the x-axis (as shown on the figure) by: F 0, sin, where = 10 N is a positive constant. a) [4] The box is represented on the figure for an arbitrary θ. Sketch the vector force diagra for the box in that position. b) [6] Sketch the vector position r of the box. Provide sybolical expressions (in ters of and θ) for r, and for the respective eleentary displaceent dr. y 0 θ x c) [10] Calculate the work done by each of the forces acting on the box as it slides fro point to point. Then calculate the net work. d) [5] Use the Work-Energy Theore to calculate the speed v of the box in point. e) [5] Suppose that in the shown position θ = 30. y what aount does the force F contribute to the centripetal force acting on the box in that position? Circle one: 2.5 N 4.3 N 5.0 N 6

7 P3: 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 7

8 P4: cable is wrapped around a pulley P 1 of ass = 5.0 kg and radius = The cable is then passed over a pulley dubbed P 2 with the sae ass, but radius 2, and connected to a dangling box of ass = 10 kg, as shown in the figure. The box is released at level fro rest. Subsequently, it falls a distance h = 0.20 to the level rotating the pulleys. Consider the pulleys as cylinders. 2 P 2 a) [10] Choose the ground at level. Then write out sybolical expressions for the echanical energy of the syste at levels and then in ters of known quantities, the speed v of the box, and the angular speeds of the pulleys ω 1 and ω 2 at level.. echanical energy E of the syste at level : E P 1 h. echanical energy E of the syste at level : E b) [5] The angular speeds of the two pulleys are not the sae, ω 1 ω 2. Notice that the cable rotating the two pulleys ove with the speed v of the box, and express ω 1 and ω 2 in ters of the speed v and the respective radii and 2. Then indicate the direction of the respective angular velocity on each pulley in the figure (use sybols and for directions out and into the page). c) [10] Substitute ω 1 and ω 2 in the equations fro part (a), and use the conservation of echanical energy to calculate the speed v of the box at level. Then calculate ω 1 and ω 2 nuerically. d) [5] Calculate the angular displaceent and the angular acceleration of pulley P 2 in the interval -. 8

PHYS 107 Practice Final Test Fall 2018

PHYS 107 Practice Final Test Fall 2018 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