(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is a 104kg uniform log hung on two steel wires, A and B, both of radius 1.00mm. Initially, wire A was 2.70m long and 2.00mm shorter than wire B. The log is now horizontal. Note that the centre of gravity (com) is not necessarily centered between the wires and the modulus of steel is 20x10^{10}Pa.

a) What is the magnitude of the force on the log from wire B?

b) What is the ratio of distance from wire A to com/distance from wire B to com?

2. Relevant equations

[tex]modulus = \frac{stress}{strain}[/tex]

[tex]modulus_B = \frac{F_B~/~m^{2}}{Δl~/~l_{o}}[/tex]

[tex]F_B = \frac{(Δl)(area)(modulus)}{l_{o}}[/tex]

3. The attempt at a solution

I'm assuming the left wire is wire A

length of A = 2.70 m

length of B = 2.702 m

area of wire = [itex]\pi d^2 ÷ 4[/itex]

let x = change in length of B

so that x+0.002 = change in length of A

[itex]F_A[/itex] = force of wire A

[itex]F_B[/itex] = force of wire B

total weight of block = (104kg)(9.81) = 1020.24N

[itex]F_A + F_B[/itex] = 1020.24 N

distance from wire A = d_A

distance from wire B = d_B

a)

[tex]F_B = \frac{(Δl)(area)(modulus)}{l_{o}}[/tex]

[tex]F_B = \frac{(x)(7.85398*10^{-7}m^{2})(20*10^{10}Pa}{2.702m}[/tex]

[tex]F_B = 58134.579x[/tex]

[tex]F_A = \frac{(Δl)(area)(modulus)}{l_{o}}[/tex]

[tex]F_A = \frac{(x+0.002)(7.85398*10^{-7}m^{2})(20*10^{10}Pa}{2.70m}[/tex]

[tex]F_A = 58177.64x + 116.355[/tex]

[tex]F_A + F_B = 1020.24 N[/tex]

[tex](58177.64x)+(58130x)+(116.355)=1020.24 N[/tex]

[tex]x(58177.64+58130)=1020.24-116.355[/tex]

[tex]x=7.77*10^{-3} m[/tex]

[tex]F_{B}=(area)(modulus)(strain)[/tex]

[tex]F_{B}=(7.85398*10^{-7})(20*10^{10})(X ÷ 2.702) = 4.51775*10^{2} N[/tex]

[tex]F_{A}=5.6846*10^{2} N[/tex]

b)

[tex]\sum\tau=0[/tex]

[tex](d_A)(F_A)-(d_B)(F_B)=0[/tex]

[tex]\frac{d_A}{d_B} = \frac{F_B}{F_A}[/tex]

[tex]\frac{d_A}{d_B} = \frac{4.51775*10^2}{5.6846*10^2}[/tex]

[tex]\frac{d_A}{d_B} = 1.25829 = 1.26[/tex]

Unfortunately, the website said that my answers for a) and b) are wrong. I know that since a) is wrong, that automatically makes b) wrong. Any help would be appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Stress, strain and modulus - log hung from 2 wires

**Physics Forums | Science Articles, Homework Help, Discussion**