a) Now, you want to add some nice resonant phosphor bronze strings to your instrument.
Phosphor bronze has a Young's modulus of 100 GPa, and a yield strength of 400 MPa.
You have 200 mm of string and the diameter of the long columnar shape of the string is
25 mm, but you need to apply load when you insert the string into the instrument and
tune it so it is at the correct pitch. The load that you apply is half of the yield strength.
How long is the string after you deform it to correctly tune it?
b) Turns out you need to remove some material from your string to make them easier to
pluck and to achieve the perfect pitch - you decide to use the turning operation.
Assuming that this is an electrolytic type of copper phosphor bronze, what is the motor
rating if you want your final string diameter to be 12 mm in a single pass, your feed is
0.002 in/rev, the cutting speed is 320 ft/min, and the machining efficiency is 75%? Please
give your answer in kW.
c) Turns out that the efficiency of the motor dropped dramatically after a practice run where
you got a string stuck in the gears, and instead of fixing the lathe, you decide to go ahead
and keep on machining. Instead of one pass to cut the diameter down to 12 mm, you can
do passes with the same depth of cut. How low of a motor efficiency can you have to
achieve this?
