Question

279 WORKED AND GUIDED PROBLEMS pendulum's period on Earth: 9.8m/S -25. The period of a 0.50-m lunar pendulum is therefore EVALUATE RESULT The longer period on the Moon n accelerations to sense because, as we found in part a, the gravitational accele TE gM 0.50 rn 1.6 m 3.5 s. = (b) We can use the general expression ixth that on Earth. get the desired ratio of periods without having to calculate the on the Moon, 1.6 m/s', is about ote Guided Problem 15.4 In sync A block of mass m is hung from a vertical spring, stretching the DEVISE PLAN spring a distance h beyond its relaxed length. The block is pulled 4. What general expressions give you the periods of the tvo knowledge of the lunar and earthly fon for period and our removed from the spring and used as the bob on a 5. What unknown quantities must you determine before setting uantities? For example, how can you calculate the systems? down a bit and released, resulting in a vertical oscillation. The the two periods equal? What information can help you deter spring constant k? Does calculating this constant help period of the oscilating pendulum is the same as the period of the oscillating block-spring system, what is mine these q the length of the pendulum? 0GETTING STARTED 1. How are the motions of the spring and pendulum analogous 6. Work through the algebra and solve for the pendulum lengti 3 EXECUTE PLAN to each other? EVALUATE RESULT 7. Is the answer plausible, that is, does your expression behave 2. Sketch both oscillating systems at an arbitrary instant, labeling as you expect it to with variation s in m and h? assumptions do you need to make in order to solve this Worked Problem 15.5 A very tall grandfather clock ta pendulum consisting of a very long Because this is a hypothetical ("Suppose you could...") problem long) and a bob that swings just above we assume that practical considerations of pendulum construction Earth's surface with an amplitude that is small compared to Earth's diameter. What would the period of its oscillation be? and air drag should be ignored 2 DEVISE PLAN Because the pendulum's motion is nearly linear that in Principles Example 15.8 O GETTING STARTED The problem statement describes a sp we wil use an analysis similar to that in Principles Example 153, we know that the pe- to derive the angular frequency, beginning with pendulum. From Worked riod of a pendulum increases with the square root of its tengtn; law, SF mia, and casting it in a form that looks like T 2mVeg This relationship implies that the period of our very oscillator equation (Eq. 15.9): ong pendulum should be really long, increasing without limit to infinity as the length increases. So, what is at issue? Why do we bother with this problem if the solution is that easy? To answe this question, we need to derive an expression for the period. I us start with a sketch showing how this infinite pendulum mig differ from a normal pendulum (Figure WG15.3). ns secono (1 near variable lly straight-lin e are taking ou Figure WG15.3 ositio (st ob al on UTE PLAN Fr at two forc Eb gr e note that an infinite e pendu