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P221_2008_week13 - 1 A 30kg child is swinging on a swing...

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1. A 30kg child is swinging on a swing whose seat is a distance of 5.0m from the pivot point. Estimate the optimal time between “pumps” that the child should execute to increase her swinging amplitude. How does this time change for a 15.0 kg child? (11 got this right, 3 made a slight error, 13 didn’t answer and 12 didn’t know what to do). My best guess is to use the equation T= 2(pi)*square root of (I/mgL). However, we dont have the rotational inertia of the pendulum (I). However, it is apparent that if you change the mass, it will affect the time between ˜pumps˜. use equation T=2piesqrootI/mgh so I=mLsqrd and the optimal time T=4.48sec so the finally answer for a 15kg child changes to T=4.49s i was not for sure how to plug in this data especially for I (for someone who did not know what to, this is VERY GOOD!) T = 2*pi*(L/g)^(1/2) The time does not change. The estimate time is 4.5 s.
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Physical Pendulum I α = mghsin( θ ) but if θ <<1 then: α = (mgh/I) θ Be careful to distinguish the physical angle from the phase angle here!
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Chapter 15 Problems
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Chapter 15 problems
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Rotational Inertia for Selected objects and rotation axes: HR&W Table 10-2
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