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--------------------------------------------------------------------------------------------------------------------- 29:011 Summer 2011 Exam 3 Practice Problems --------------------------------------------------------------------------------------------------------------------- (The exam will have 15 questions.) 1. A long thin rod of length 2L rotates with a constant angular acceleration of 10 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the tangential acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4 2. A 3.0-kg ball and a 1.0-kg ball are placed at opposite ends of a massless beam so that the system is in equilibrium as shown. Note: The drawing is not drawn to scale. What is the ratio of the lengths, b/a? A) 2.0 B) 2.5 C) 3.0 D) 4.0 E) 5.0 3. What happens when a spinning ice skater draws in her outstretched arms?

A) Her angular momentum decreases. B) Her angular momentum increases. C) Her moment of inertia decreases causing her to speed up. D) Her moment of inertia decreases causing her to slow down. E) The torque that she exerts increases her moment of inertia. 4. A simple pendulum consists of a ball of mass m suspended from the ceiling using a string of length L. The ball is displaced from its equilibrium position by an angle θ. What is the magnitude of the restoring force that moves the ball toward its equilibrium position and produces simple harmonic motion? A) kx B) mg C) mg (cos θ) D) mg (sin θ) E) mgL(sin θ) 5. Using the value of atmospheric pressure at sea level, 1 × 105 Pa, estimate the total mass of the earth's atmosphere above a 5-m2 area. A) 5 × 104 kg B) 9 × 102 kg C) 2 × 10−4 kg D) 4 × 10−2 kg E) 3 × 105 kg 6. A spinning disc rotating at 130 rev/min slows and stops 31 s later. How many revolutions did the disc make during this time? A) 34 B) 67 C) 8.4 D) 17 E) 4.2

ab

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7. One end of a rope is tied to the handle of a horizontally-oriented and uniform door. A force F is applied to the other end of the rope as shown in the drawing. The door has a weight of 145 N and is hinged on the right. What is the maximum magnitude of F for which the door will remain at rest? A) 145 N B) 265 N C) 381 N D) 424 N E) 530 N 8. A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M easily slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time from the top of their inclined planes, A) the cylinder will reach the bottom first. B) the block will reach the bottom first. C) the block will reach the bottom with the greater kinetic energy. D) the cylinder will reach the bottom with the greater kinetic energy. E) both the block and the cylinder will reach the bottom at the same time. 9. A string is wrapped around a pulley of radius 0.20 m and moment of inertia 0.40 kg ⋅ m2. The string is pulled with a force of 28 N. What is the magnitude of the resulting angular acceleration of the pulley? A) 22 rad/s2 B) 14 rad/s2 C) 68 rad/s2 D) 0.55 rad/s2 E) 8.0 rad/s2 10. The position of a simple harmonic oscillator is given by

( ) (0.50m)cos3

x t tπ =

,

where t is in seconds. What is the period of the oscillator? A) 0.17 s B) 0.67 s C) 1.5 s D) 3.0 s E) 6.0 s 11. In a certain clock, a pendulum of length L1 has a period T1 = 0.95 s. The length of the pendulum is adjusted to a new value L2 such that T2 = 1.0 s. What is the ratio L2/L1? A) 0.90 B) 0.95 C) 1.0 D) 1.1 E) 1.3 12. An object weighs 15 N in air and 13 N when submerged in mineral spirits, which has a density of 788 kg/m3. Determine the density of the object. A) 330 kg/m3 B) 500 kg/m3 C) 1.2 × 103 kg/m3 D) 5.9 × 103 kg/m3 E) 7.5 × 103 kg/m3

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Answers 1. C 2. D 3. C 4. D 5. A 6. A 7. B 8. B 9. B 10. E 11. D 12. D