Heinz Doofenshmirtz captures Agent P and attaches him to an oscillating spring i

Question

Heinz Doofenshmirtz captures Agent P and attaches him to an oscillating spring in order to tell his backstory about springs and watch-making in Drusselstein. Agent P has a mass of 2.10 kg and the period of oscillation when he is attached to the spring is 1.50 s. Find the spring constant, and if the total energy of the spring-Agent P system is 4.55 J, find the amplitude of the oscillations. Luke Skywalker emerges through a blast door with Princess Leia only to find that in an inexplicable example of Empire architecture he's standing on a small platform over an open pit. He throws his grappling hook (who wouldn't carry a grappling hook on an interstellar adventure?) onto a convenient bar on the center of the ceiling so that he and Leia can swing like a pendulum to the blast door on the opposite side. If the length of the grappling hook line is 5.0 m, Luke and Leia have a combined mass of 120 kg, and the Death Star has g = 10.0 m/s^2, will they successfully make it across and through the blast door on the opposite side if it will close in 3.0 seconds? (Serway & Vuille, C13, #28) The position of an object connected to a spring varies with time according to the expression x = (5.2 cm) sin(8.07 pi t). Find the period of this motion, the frequency of the motion, the amplitude of the motion, and the first time after t = 0 that the object reaches the position x = 2.6 cm. Ender Wiggin finds himself on an unknown planet and wants to determine its value of g for battle strategy purposes. There is a 1.0 kg mass hanging from a thin wire with a length of 5.0 m. Ender plucks the wire and sees that the resulting wave takes 0.5 s to travel the length. If he assumes the wire itself has a mass of 100 grams (so he can, ahem, compute its mass per unit length), what value of g will he determine? One of the coldest game temperatures for an NFL game occurred in the NFC Championship game in 2008 (Packers vs. Giants, in Green Bay). The temperature was -20.0 degree C. If you were at the game and sitting 150 m from the field where the referee blew his whistle, how long would it take before you heard the whistle? Compare this to how long it would take if the radio broadcast instantly transmitted the signal and it had to travel 750 miles to a medium Earth orbit communications satellite and back (so 1500 miles total, at the speed of light which is 3.00 Times 10^8 m/s).

Explanation / Answer

speed of sound, for any temperature T is given as

v=331+0.6*T

so at -20 degree celcius, speed of sound=331-20*0.6=331-12=319 m/s

then time taken to hear the whistle sound=distance to travel for the sound wave/speed of the sound wave=150/319=0.47022 seconds

distance to travel for the radio wave to reach the listner=1500 miles=2414016 m

then time taken=distance/speed of light=2414016/(3*10^8)=8.0467 ms

hence time taken by the radio wave is significantly lesser than the time taken for the sound wave to reach you.

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