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A professor’s badge ID Reel is made of a hairspring with one end connected to a

ID: 1333431 • Letter: A

Question

A professor’s badge ID Reel is made of a hairspring with one end connected to a string. As the string is pulled out of the ID reel it causes the hairspring to unwind. Hairsprings are functionally identical to linear springs that we have talked about in class, except that their force increases based on angle the spring is stretched, not the distance. (Fs=k?)

A)The diameter of the hairspring is 34 mm, the string is pulled out 25 cm and the force of tension on the string is measured to be 95 N. What is the stiffness of this spring?

Explanation / Answer

a)

Fs=k

95 = k (25/17) ( theta = x/R)

k = 64.6 N-rad-1

b) once elastic limit of wire crossed it can't come back to normal position.....it's k changes after that and F is not directly propotional to theta....

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