Two steel wires of the same length, one with radius r and the other with radius
ID: 2152545 • Letter: T
Question
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 = 1.6 mm. How far does the point where the two wires meet move?
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 = 1.6 mm. How far does the point where the two wires meet move?Explanation / Answer
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.pr²) Wire 1: E = Fl/(e2.p(3r)²) The Young's modulus (E) and lengths(l) are the same for both wires so Fl/(e1.pr²) = Fl/(e2.p(3r)²) Cancel out common factors e1 = 9e2. e1+ e2=1.6 9e2 + e2 = 1.6 e2 = 0.16mm e1 = 1.44mm If the thinner wire is attached to the wall, the point move 1.44mm If the thicker wire is attached to the wall, the point move 0.16mm