You are the Royal Engineer for the Kingdom of Grrrrx (pronounced as written). Each year in...

 

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You are the Royal Engineer for the Kingdom of Grrrrx (pronounced as written). Each year in the kingdom, on the last day of summer, a new Knightship of Grrrrrx is awarded to the winner of the Royal Singing-and-Hopping Race, in which participants (18 years of age and older) must hop and sing through three full laps of the castle perimeter, adhering to the strict regulations of the Royal Singing-and-Hopping Commission. The race begins when the King of Grrrrrx plucks a single note on the Royal Plucking Instrument, which consists of a single 1mm thick platinum wire stretched between two points on a solid gold frame, as shown in the picture. To achieve the proper note, the wire must be at a tension of 50.00N. On the morning of the race, you notice the temperature is a chilly 5 degrees Celcius but that the temperature is forecast to rise to 25 degrees Celcius by 2pm when the race starts. It is your duty as Royal Engineer to set the tension of the wire, so that it will play just the right note when plucked at 2pm. To what tension should you set it? (agold = 1.4 x 105K, aplatinum = 0.9 x 10 K, Yplatinum= 16x 1010 Pa) Hint: Assume that the expansion of the gold is unaffected by the presence of the wire. You do not need to know the length of the wire. You are the Royal Engineer for the Kingdom of Grrrrx (pronounced as written). Each year in the kingdom, on the last day of summer, a new Knightship of Grrrrrx is awarded to the winner of the Royal Singing-and-Hopping Race, in which participants (18 years of age and older) must hop and sing through three full laps of the castle perimeter, adhering to the strict regulations of the Royal Singing-and-Hopping Commission. The race begins when the King of Grrrrrx plucks a single note on the Royal Plucking Instrument, which consists of a single 1mm thick platinum wire stretched between two points on a solid gold frame, as shown in the picture. To achieve the proper note, the wire must be at a tension of 50.00N. On the morning of the race, you notice the temperature is a chilly 5 degrees Celcius but that the temperature is forecast to rise to 25 degrees Celcius by 2pm when the race starts. It is your duty as Royal Engineer to set the tension of the wire, so that it will play just the right note when plucked at 2pm. To what tension should you set it? (agold = 1.4 x 105K, aplatinum = 0.9 x 10 K, Yplatinum= 16x 1010 Pa) Hint: Assume that the expansion of the gold is unaffected by the presence of the wire. You do not need to know the length of the wire.

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