Two steel wires are connected together, end to end, and attached to a wall as sh
ID: 1908039 • Letter: T
Question
Two steel wires are connected together, end to end, and attached to a wall as shown below. The two wires have the same length and elastic modulus, but the ratio of the radius of the first wire to the radius of the second wire is 5 : 2. As the wires are initially the same length, the midpoint of the combination coincides with the connection point. An applied force then stretches the combination by 4.900 mm while the two wires stay connected together. After the wires are stretched, what is ?, the distance from the midpoint to the connection point?
Explanation / Answer
L1 = FL/A1*E = FL/(*r1^2*E)
L2 = FL/A2*E = FL/(*r2^2*E)
L1/L2 = (r2/r1)^2 = (2/5)^2 = 0.16
L1 = 0.16*L2
L1 + L2 = 4.9
0.16*L2 + L2 = 4.9
L2 = 4.224 mm
L1 = 0.16*4.224 = 0.6759 mm
Total final length = 2L + 4.9
Final Mid-point from left end = (2L + 4.9)/2 = L + 2.45
Distance of connection point from left end = L + L1 = L + 0.6759 mm
= (L + 2.45) - (L + 0.6759) = 1.7741 mm
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