# Calculating dA/dB ratio for horizontal log?

1. Apr 11, 2013

### rockchalk1312

In the figure, a 105 kg uniform log hangs by two steel wires, A and B, both of radius 1.25 mm. Initially, wire A was 2.50 m long and 1.80 mm shorter than wire B. The log is now horizontal. Young's modulus for steel is 2.00 × 1011 N/m2. What is the ratio dA/dB?

I'm honestly at a loss for how to even approach this problem. Any help is appreciated!

2. Apr 12, 2013

### SteamKing

Staff Emeritus
Draw a free body diagram of the log suspended by the two wires. Wire A was shorter than Wire B when no load was applied. Both wires are now the same length. Figure out the stresses and change in lengths of the two wires such that they both have equal length and the log is in static equilibrium. Then figure out the ratio of the deflection of wire A to the deflection of wire B.

3. Apr 12, 2013

### rockchalk1312

What exactly do you mean by deflection? Is it just asking for the ratio of the change in length of A to B?

B doesn't change in length so that would make the ratio invalid...

4. Apr 12, 2013

### SteamKing

Staff Emeritus
deflection = change of length of the wire.

Although the problem states the log is horizontal after being suspended, and this implies that the two wires are the same length after suspending the log, this does not mean that wire B, originally the longer wire, has not undergone some change in length. If wire B were the same length before and after the log was suspended, this would imply that there is no tension in wire B and that wire A thus is supporting the log all by itself.

5. Apr 12, 2013

### haruspex

Pls describe the figure. Are the wires vertical and attached at the same level at the top, or maybe attached at a common point?
I feel there must be something I'm missing. I don't see any reason, in the info given so far, that the wires would be subject to different loads, so it's hard to understand why the shorter one has undergone the greater extension. Maybe they're vertical but attached at different heights from the ground (specifically, B more than 1.8mm above A).