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Solutions to Conceptual Questions from Homework 1

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 **to**tal 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 **to**tal 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 **to**tal 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, Pis**to**ns 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 in**to** 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