Two steel wires of the same length, one with radius r and the other with radius 3r, are connected together, end to end, and tied to a wall. An applied force stretches the combination by d = 1.8 mm. How far does the point where the two wires meet move?
___mm
___mm
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I assume only one end of one wire is tied to the wall and the far end of the other wire is is pulled.
E = Fl/(eA)
Wire 1: E = Fl/(e1.πr²)
Wire 1: E = Fl/(e2.π(3r)²)
The Young's modulus (E) and lengths(l) are the same for both wires so
Fl/(e1.πr²) = Fl/(e2.π(3r)²)
Cancel out common factors
e1 = 9e2.
e1+ e2=1.8
9e2 + e2 = 1.8
e2 = 0.18mm
e1 = 1.62mm
If the thinner wire is attached to the wall, the point move 1.62mm
If the thicker wire is attached to the wall, the point move 0.18mm
E = Fl/(eA)
Wire 1: E = Fl/(e1.πr²)
Wire 1: E = Fl/(e2.π(3r)²)
The Young's modulus (E) and lengths(l) are the same for both wires so
Fl/(e1.πr²) = Fl/(e2.π(3r)²)
Cancel out common factors
e1 = 9e2.
e1+ e2=1.8
9e2 + e2 = 1.8
e2 = 0.18mm
e1 = 1.62mm
If the thinner wire is attached to the wall, the point move 1.62mm
If the thicker wire is attached to the wall, the point move 0.18mm