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Physics 2A -Sec B - Final Exam (winter 2012) Instructor: Benjamin Grinstein Name: ___________________________________ 3-digit personal No: _____________ Date: ______________ Write your name, and code number above and on your scantron over the line labeled "NAME". Bubble in your code number in the scantron in the space labeled "EXAM NUMBER" (always use a No 2 pencil. on the scnatron). Bubble in the version of your test (a letter, A-D), found at the botton of this page, on your scantron in the space labeled "TEST FORM." Unless otherwise instructed, use g = 9.8 m/s 2 Rotational Inertia about an axis through com: Hoop about axis(radius=R, mass=M) : MR 2 Hoop about diameter (radius=R, mass=M): 1/2MR 2 Disk/solid cyllinder about central axis(radius=R, mass=M, length=L): 1/2MR 2 Disk/solid cyllinder about axis perpendicular to length, that is, central diameter (radius=R, mass= M, length=L): 1/4MR 2 +1/12ML 2 Thin rod about axis perpendicular to length (mass=M, length = L): 1/12ML 2 Solid sphere about diameter (radius=R, mass=M): 2/5MR 2 Thin spherical shell about diameter (radius=R, mass=M): 2/3MR 2 Rectangular slab about perpendicular axis (mass=M, sides: a, b): 1/12M(a 2 +b 2 ) Solve the following problems. Enter the answers in your scantron (always use a No 2 pencil. on the scnatron). 1. A block of mass m is pulled along a rough horizontal floor by an applied force as shown. The vertical component of the force exerted on the block by the floor is: A) mg B) mg T cos θ C) mg + T cos θ D) mg T sin θ E) mg + T sin θ Page 1

Physics 2A -Sec B - Final Exam (winter 2012)physics.ucsd.edu/students/courses/winter2012/physics2a/solutions/... · Physics 2A -Sec B - Final Exam (winter 2012) ... at the geometric

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Page 1: Physics 2A -Sec B - Final Exam (winter 2012)physics.ucsd.edu/students/courses/winter2012/physics2a/solutions/... · Physics 2A -Sec B - Final Exam (winter 2012) ... at the geometric

Physics 2A -Sec B - Final Exam (winter 2012)Instructor: Benjamin Grinstein

Name: ___________________________________ 3-digit personal No: _____________ Date: ______________Write your name, and code number above and on your scantron over the line labeled "NAME". Bubble in your code number in the scantron in the space labeled "EXAM NUMBER" (always use a No 2 pencil. on the scnatron).Bubble in the version of your test (a letter, A-D), found at the botton of this page, on your scantron in the space labeled "TEST FORM."

Unless otherwise instructed, use g = 9.8 m/s2

Rotational Inertia about an axis through com:Hoop about axis(radius=R, mass=M) : MR2

Hoop about diameter (radius=R, mass=M): 1/2MR2

Disk/solid cyllinder about central axis(radius=R, mass=M, length=L): 1/2MR2

Disk/solid cyllinder about axis perpendicular to length, that is, central diameter (radius=R, mass=M, length=L): 1/4MR2+1/12ML2

Thin rod about axis perpendicular to length (mass=M, length = L): 1/12ML2

Solid sphere about diameter (radius=R, mass=M): 2/5MR2

Thin spherical shell about diameter (radius=R, mass=M): 2/3MR2

Rectangular slab about perpendicular axis (mass=M, sides: a, b): 1/12M(a2+b2)

Solve the following problems. Enter the answers in your scantron (always use a No 2 pencil. on the scnatron).

1. A block of mass m is pulled along a rough horizontal floor by an applied force as shown. The vertical component of the force exerted on the block by the floor is:

A) mg B) mg – T cos θ C) mg + T cos θ D) mg – T sin θ E) mg + T sin θ

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2. Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true? I. The horizontal distance traveled by the bullet is greater for the Moon. II. The flight time is less for the bullet on the Earth. III. The velocities of the bullets the moment just before they hit the ground are the same.

A) III only B) I and II only C) I and III only D) II and III only E) I, II, III

3. A girl wishes to swim across a river to a point directly opposite as shown. She can swim at 2 m/s in still water and the river is flowing at 1 m/s. At what angle θ with respect to the line joining the starting and finishing points should she swim?

! A) 30° B) 45° C) 60° D) 63° E) 90°

4. A wheel starts from rest and spins with a constant angular acceleration. Its axis is fixed, that is, it is not moving. As time goes on the acceleration vector for a point on the rim:

A) decreases in magnitude and becomes more nearly tangent to the rim B) decreases in magnitude and becomes more nearly radial C) increases in magnitude and becomes more nearly tangent to the rim D) increases in magnitude and becomes more nearly radial E) increases in magnitude but retains the same angle with the tangent to the rim

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5. A 1-N pendulum bob is held at an angle θ from the vertical by a 2-N horizontal force F as shown. The tension in the string supporting the pendulum bob (in newtons) is:

A) cos θ B) 2/cos θ C) D) 1 E) none of these

6. Two objects interact with each other and with no other objects. Initially object A has a speed of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude:

A) the potential energy changed from the beginning to the end of the trip B) mechanical energy was increased by nonconservative forces C) mechanical energy was decreased by nonconservative forces D) mechanical energy was increased by conservative forces E) mechanical energy was decreased by conservative forces

7. As a particle moves along the x axis it is acted by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the force, least to greatest.

A) AB, BC, CD B) AB, CD, BC C) BC, CD, AB D) BC, AB, CD E) CD, BC, AB

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8. When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2, where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:

A) axL + bx2L B) aL + 2bL2

C) a + 2bL D) bL E) aL2/2 + bL3/3

9. A block is released from rest at point P and slides along the frictionless track shown. At point Q, its speed is:

A) B) 2g(h1 – h2) C) (h1 – h2)/2g

D)

E) (h1 – h2)2/2g

10. The center of mass of the system consisting of Earth, the Sun, and the planet Mars is: A) closer to the Earth than to either of the other bodies B) closer to the Sun than to either of the other bodies C) closer to Mars than to either of the other bodies D) at the geometric center of the triangle formed by the three bodies E) at the center of the line joining the Earth and Mars

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11. A thick uniform wire is bent into the shape of the letter "U" as shown. Which point best indicates the location of the center of mass of this wire?

A) A B) B C) C D) D E) E

12. A 75-kg man is riding in a 30-kg cart at 2.0 m/s. He jumps off in such a way as to land on the ground with no horizontal velocity. The resulting speed of the cart is:

A) zero B) 2.0 m/s C) 3.0 m/s D) 7.0 m/s E) 5.0 m/s

13. A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest the heavier object moves downward and the lighter object moves upward with the same magnitude acceleration. Which of the following statements is true for the system consisting of the two objects?

A) The center of mass remains at rest. B) The net external force is zero. C) The velocity of the center of mass is a constant. D) The acceleration of the center of mass is g, downward. E) None of the above statements are true.

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14. A ball hits a wall and rebounds with the same speed, as diagrammed below. The changes in the components of the momentum of the ball are:

A) Δpx > 0, Δpy > 0 B) Δpx < 0, Δpy > 0 C) Δpx = 0, Δpy > 0 D) Δpx = 0, Δpy < 0 E) Δpx > 0, Δpy < 0

15. Four identical particles, each with mass m, are arranged in the x, y plane as shown. They are connected by light sticks to form a rigid body. If m = 2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis is:

A) 4.0 kg ⋅ m2

B) 12 kg ⋅ m2

C) 9.6 kg ⋅ m2

D) 4.8 kg ⋅ m2

E) none of these

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16. A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of A about the common axis XX' is:

A) 2 B) 4 C) 8 D) 16 E) 32

17. To increase the rotational inertia of a solid disk about its axis without changing its mass: A) drill holes near the rim and put the material near the axis B) drill holes near the axis and put the material near the rim C) drill holes at points on a circle near the rim and put the material at points between the

holes D) drill holes at points on a circle near the axis and put the material at points between the

holes E) do none of the above (the rotational inertia cannot be changed without changing the

mass)

18. A heavy steel ball B is suspended by a cord from a block of wood W. The entire system is dropped through the air. Neglecting air resistance, the tension in the cord is:

A) zero B) the difference in the masses of B and W C) the difference in the weights of B and W D) the weight of B E) none of these

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19. A uniform disk, a thin hoop, and a uniform spherical shell, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according the their angular velocities after a given time t, least to greatest.

A) disk, hoop, sphere B) hoop, disk, sphere C) hoop, sphere, disk D) sphere, disk, hoop E) sphere, hoop, disk

20. A small disk of radius R1 is fastened coaxially to a larger disk of radius R2. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead veiw below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force as shown. The tension in the string pulling the block is:

A) R1F/R2

B) mR1R2F/(I – mR22)

C) mR1R2F/(I + mR22) D) mR1R2F/(I – mR1R 2) E) mR1R2F/(I + mR1R 2)

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21. A disk starts from rest and rotates about a fixed axis, subject to a constant net torque. The work done by the torque during the second revolution is ______ as the work done during the first revolution.

A) the same B) twice as much C) half as much D) four times as much E) one fourth as much

22. A solid cyllinder rolls without sliding along the floor. The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass) is:

A) 2 B) 1 C) 3 D) 1/2 E) 1/3

23. A solid wheel with mass M, radius R, and rotational inertia MR2/2, rolls without sliding on a horizontial surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

A) F = Ma, f = 0 B) F = Ma, f = Ma/2 C) F = 2Ma, f = Ma D) F = 2Ma, f = Ma/2 E) F = 3Ma/2, f = Ma/2

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24. A wheel, with rotational inertia I, mounted on a vertical shaft with negligible ratational inertia, is rotating with angular speed ω 0. A nonrotation wheel with rotational inertia 2I is suddenly dropped onto the same shaft as shown.. The resultant combination of the two wheels and shaft will rotate at:

A) ω 0 /2 B) 2ω 0 C) ω 0 /3 D) 3ω 0 E) ω 0 /4

25. Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods. Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod?

A) Only 1 B) Only 2 C) Only 3 D) Only 1 and 2 E) All three

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26. A 960-N block is suspended as shown. The beam AB is weightless and is hinged to the wall at A. The tension force of the cable BC has magnitude:

A) 720 N B) 1200 N C) 1280 N D) 1600 N E) none of these

27. A particle moves back and forth along the x axis from x = –xm to x = +xm, in simple harmonic motion with period T. At time t = 0 it is at x = +xm. When t = 0.75T:

A) it is at x = 0 and is traveling toward x = +xm

B) it is at x = 0 and is traveling toward x = –xm

C) it is at x = +xm and is at rest D) it is between x = 0 and x = +xm and is traveling toward x = –xm

E) it is between x = 0 and x = –xm and is traveling toward x = –xm

28. The displacement of an object oscillating on a spring is given by x(t) = xmcos(ω t + φ ). If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant φ is between:

A) 0 and π/2 radians B) π/2 and π radians C) π and 3π/2 radians D) 3π/2 and 2π radians E) none of the above (φ is exactly 0, π/2, π, or 3π/2 radians)

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29. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. At one point in its motion its kinetic energy is K = 5J and its potential energy (measured with U = 0 at x = 0) is U = 3J. When it is at x = xm, the kinetic and potential energies are:

A) K = 5J and U = 3J B) K = 5J and U = –3J C) K = 8J and U = 0 D) K = 0 and U = 8J E) K = 0 and U = –8J

30. Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass m are given below. Which leads to the smallest rate of loss of mechanical energy?

A) k = 100N/m, m = 50g, b = 8g/s B) k = 150N/m, m = 50g, b = 5g/s C) k = 150N/m, m = 10g, b = 8g/s D) k = 200N/m, m = 8g, b = 6g/s E) k = 100N/m, m = 2g, b = 4g/s

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Answer Key - final-secB

1. D 2. B 3. A 4. D 5. C 6. C 7. D 8. E 9. D 10. B 11. B 12. D 13. E 14. C 15. B 16. E 17. B 18. A 19. C 20. C 21. A 22. A 23. E 24. C 25. C 26. D 27. A 28. B 29. D 30. B

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