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Solutions to Conceptual Questions from Homework 1

Solutions to Conceptual Questions from Homework 1

Solutions to Conceptual Questions from Homework

Physics 224 Homework 1 (solutions) (2006 Spr) Solutions to Conceptual Questions from Homework 1 Young, Q13.1: An object is moving in SHM of amplitude A on the end of a spring. If the amplitude is doubled, what happens to the total distance the object travels in one period? What happens to the period? What happens to the maximum speed of the object? Discuss how these answers are related. A Brief Answer: From the definition of Amplitude, the body will travel a total distance of 4A in one period (eg. from +A to –A then back to ++A). In SHM, the period is independent of Amplitude, thus the period remains the same. From considering the equation describing energy conservation in each case separately, one can easily show that the total energy E in the second system is 4 times that in the first. Thus the max. velocity (when the potential energy U=zero and hence E=1/2 kv 2 ) is 2 times the max. velocity of the first system. Basically the distance traveled doubles, but the speed at all points in the cycle doubles such that the time taken for 1 cycle remains the same. Young, Q13.2: Think of several examples in everyday life of motions that are at least, approximately simple harmonic. In what respect does each differ from SHM? A Brief Answer: Swings, Pistons in a car engine, pendulums in grandfather clocks, watch springs, rocking horses, water in a U-tube, etc etc Young, Q13.8: You are captured by aliens, taken into their ship, drugged. You awake some time later and find yourself looked in a small room with no windows. All they have left you with is your digital watch, your school ring, and your long silver necklace. Explain how you can determine whether or not you are still on Earth, or if you have been transported to Mars, A Brief Answer: Using your necklace and ring, you can make a pendulum. You can then set this pendulum swinging with SHM (ie. With small amplitude), and use your digital watch to measure the period T n of the oscillations. (Measuring the time for (say) 10 oscillations, then dividing by 10 will increae the accuracy of the measurement of course.) You can also estimate the length L n of the pendulum to a fair degree of accuracy. If you are still on Earth, then you expect where Hopefully it will also have occurred to you that you should also check whether you really can distinguish between the period expected on Earth versus that expected on Mars…. (cont) 1

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