Physics : Young's Modulus
posted by Rafi Tanzim .
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?
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.