Engineering problem (uses stress, strain, Young's Modulus)

[twostep08]

Homework Statement

2. As engineers, we wish to use a metal bar as a support arm on a crane. The bar has a
Young’s Modulus of 3x106psi . Assuming the rod will need to be 3ft long. Answer the
following questions…
a)If the crane is designed so that the
maximum tensile force on the rod is predicted to be
160,000 lbs, what should the cross sectional area of the rod
be to have a strain less than 0.001? _________
b) There was an accident at the worksite and the crane needs to lift a
600,000 lbs boulder to rescue some workers. If the bar has an Ultimate Tensile Strength
of 6400psi and the bar supports all of the weight , how much can the
crane actually lift?
__________

Homework Equations

stress= force/ area (sq.in.)
UTS= weight where a rod breaks/cross sectional area
Strain=extension/original length
YM=stress applied/strain induced

The Attempt at a Solution

I tried everything seemling, but I can't figure out where to plug in everything to get an answer that makes sense. I would really appreciate it if someone can walk me through it (I'm really good at math, but I've never taken physics, and this is my first engineering class, so I am understandably a little lost)

thanks alot

 

[Valkarie]

. a) To have a strain below 0.001, the stress on the rod must be less than YMx0.001. So we need to solve for area using this equation:Area= force/ (YM x 0.001)Area= 160000/ (3x106 x 0.001) = 0.053sq.in. b) We can find the maximum weight the crane can lift by finding the cross sectional area of the rod when it reaches its UTS. This is found by solving for area using the following equation: Area= weight/UTS Area= 600000/6400 = 93.75 sq.in. Therefore, the crane can lift a maximum of 600000 lbs.