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Practice Homework 12

Practice Homework 12 - practice 12 ALIBHAI ZAHID Latest...

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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 back-and-forth 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 counter-clockwise uniform circular motion. Consider the oscillation of a mass-spring 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 0 . k m v 0 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 m v 2 0 2. E = 1 4 m v 2 0 3. E = 3 m v 2 0 4. E = 5 2 m v 2 0 5. E = 5 4 m v 2 0 6. E = 1 2 m v 2 0 7. E = 4 m v 2 0 8. E = m v 2 0 9. E = 3 4 m v 2 0 10. E = 2 m v 2 0 Question 4 part 1 of 3 10 points

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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 41 45 L g 5. T = 2 π radicalBigg 25 28 L g 6. T = 2 π radicalBigg 53 63 L g 7. T = 2 π radicalBigg 17 20 L g 8. T = 2 π radicalBigg 85 99 L g 9. T = 2 π radicalBigg 65 72 L g 10. T = 2 π radicalBigg 73 88 L g Question 10

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