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Unformatted text preview: practice 12 – ALIBHAI, ZAHID 1 Latest unpenalized work: Apr 15 2007 Sunday 04:00 (after this date you can not make a perfect score). Work cutoff: Apr 15 2007, 4:00 am. Question 1 part 1 of 1 10 points Consider a car engine running at constant speed. That is, the crankshaft of the en gine rotates at constant angular velocity while each piston moves backandforth in its cylin der according to the rules of simple harmonic motion. 1740 rpm 10 . 9 cm Suppose the two extremal positions x max and x min of a piston are 10 . 9 cm from each other. When the crankshaft of the engine rotates at 1740 rpm (revolutions per minute), what is the maximal speed  v  max of the piston? Answer in units of m / s. Question 2 part 1 of 2 10 points Hint: Consider x as the projection of a counterclockwise uniform circular motion. Consider the oscillation of a massspring system, where x = A cos( ωt + φ ). At the time t = 0, the mass is at x = 0 and it is moving to the right with a speed v . k m v x = 0 x Find the phase angle φ . 1. φ = π 3 2. φ = 5 π 4 3. φ = 0 4. φ = 3 π 2 5. φ = π 4 6. φ = 2 π 7. φ = 3 π 4 8. φ = π 2 9. φ = 7 π 4 10. φ = π Question 3 part 2 of 2 10 points Denote the mass by m . Find the total energy of the oscillation at t = T 8 , where T is the period. 1. E = 3 2 mv 2 2. E = 1 4 mv 2 3. E = 3 mv 2 4. E = 5 2 mv 2 5. E = 5 4 mv 2 6. E = 1 2 mv 2 7. E = 4 mv 2 8. E = mv 2 9. E = 3 4 mv 2 10. E = 2 mv 2 Question 4 part 1 of 3 10 points practice 12 – ALIBHAI, ZAHID 2 A 2 . 2 kg object oscillates with an initial am plitude of 101 cm on a spring of force constant 98 . 8 N / m. Find the period. Answer in units of s. Question 5 part 2 of 3 10 points Find the total initial energy. Answer in units of J. Question 6 part 3 of 3 10 points If the energy decreases by 1 percent per period, find the damping constant b . Answer in units of kg / s. Question 7 part 1 of 1 10 points A simple 2.36 m long pendulum oscillates. The acceleration of gravity is 9 . 8 m / s 2 . How many complete oscilations does this pendulum make in 1.90 min? Question 8 part 1 of 2 10 points Consider a light rod of negligible mass and length L pivoted on a frictionless horizontal bearing at a point O . Attached to the end of the rod is a mass M 1 . Also, a second mass M 2 of equal size ( i.e. , M 1 = M 2 = M ) is attached to the rod parenleftbigg 6 9 L from the lower end parenrightbigg , as shown in the figure below. 6 9 L L M 2 M 1 O θ The moment of inertia I about O is given by 1. I = 5 4 M L 2 2. I = 65 49 M L 2 3. I = 58 49 M L 2 4. I = 74 49 M L 2 5. I = 29 25 M L 2 6. I = 17 16 M L 2 7. I = 25 16 M L 2 8. I = 13 9 M L 2 9. I = 89 64 M L 2 10. I = 10 9 M L 2 Question 9 part 2 of 2 10 points The period of this pendulum in the small angle approximation is given by 1. T = 2 π radicalBigg 29 35 L g practice 12 – ALIBHAI, ZAHID 3 2. T = 2 π radicalBigg 5 6 L g 3. T = 2 π radicalBigg 13 15 L g 4. T = 2 π radicalBigg...
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This note was uploaded on 10/13/2009 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner
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