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Final Solutions

Final Solutions - Physics 1C Fall 2005 FINAL EXAM Dec 9th...

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Physics 1C Fall 2005 FINAL EXAM Dec 9th, 2005 Version A 1. The motion of a piston in an automobile engine is nearly simple harmonic. If the 1 kg piston travels back and forth over a total distance of 10.0 cm, what is its maximum velocity when the engine is running at 1500 rpm? (rpm means revolutions per minute, assume the piston makes one complete oscillation for each revolution of the engine) a. 31.4 m/s b. 15.7 m/s c. 7.85 m/s d. 3.93 m/s A = amplitude = 5 cm = 0.05m, ω = angular freq = 2 π f where f = (1500 rev/min)/(60 sec/min) = 25 Hz Speed v = ω A cos( ω t), max speed when cos( ω t) =1, max speed = ω A = 2 π fA = 7.85 m/s 2. A simple pendulum has a mass of 0.25 kg and a length of 1.0 m. It is displaced through an angle of 30 degrees and then released. After a time, the maximum angle of swing is only 10 degrees. How much energy has been lost to friction? Assume SHM. Use PE = mgh of pendulum bob measuring h from lowest point of swing, energy of pendulum is all PE when bob is at max amplitude and KE=0. At 30 o PE = mgL(1-cos30 o ) = 0.328J, at 10 o PE = mgL(1=cos10 o ) = 0.037J, loss of energy = (0.328 – 0.037)J = 0.29J 3. Transverse waves travel with a speed of 200 m/s along a taut copper wire that has a diameter of 2 mm. What is the tension in the wire? (The density of copper is 9 g/cm 3 .) a. 5.6 N b. 80 N c. 1130 N d. 2260 N Mass of 1m of the wire = density x vol = (9 g/cc).( π r 2 L) = (9g/cc) x 3.14 x (0.1cm) 2 x 100 cm = 28.3g Hence µ of wire is 2.8 x 10 -2 kg/m, Use v = sqrt(T/ µ ) to get T = v 2 µ = (200m/s) 2 x 2.83 x 10 -2 = 1130N 4. A wave is traveling in a string at 60 m/s. When the tension is then increased 20%, what will be the resulting wave speed: Use v = sqrt(T/ µ ) Because of the sqrt, if T increases by 20%, v increases by 10%, from 60 to 66 m/s 5. As a train starts from rest and then accelerates down the track, coming toward me faster and faster, the speed of the sound waves coming toward me will be: a. slower than the normal speed of sound in air. b. equal to the normal speed of sound in air. c. some constant speed faster than the normal speed of sound in air. d. faster and faster.
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