Posted by **Rafi Tanzim** on Thursday, May 23, 2013 at 4:50am.

A mass m is attached to a weightless string of

length L, cross section S, and tensile strength ( the

maximum tension it can withstand ) T . The mass

is suddenly released from a point near the fixed

end of the string. What condition should be on the

value of Young's modulus Y so that the string

does not break?

- Physics : Young's Modulus -
**drwls**, Thursday, May 23, 2013 at 7:47am
The effective spring constant of the string is

k = Y*S/L Newtons/meter

When the mass m is dropped from the fixed end, the string will stretch a maximum amount dL, so that

m g L = (1/2) k *dL^2 = (1/2)Y*S/L*dL^2

dL^2 = 2 m g L^2/(Y*S)

dL/L = sqrt[2 m g/(Y*S)]

If the string is about to break at maximum stretch, the tensile stress will then be

sigma = T = Y*(dL/L)

T = sqrt[2 m g Y/S]

Solve for Y. A larger value of Y will cause the string to break.

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