Calculating Mass of Steel Ball for Ultimate Strength

[aquabug918]

A solid steel ball is hung at the bottom of a steel wire length 2 meters and radius of 1mm. The ultimate strength of steel is 1.1 X 10^9 N/m^2. What is the mass of the biggest ball the wire can bare.

This seems like a pretty straight forward question. I am guessing the 2 meter radius doesn't matter. I am thinking that you need to find the area of a cross section of the 1mm wire. I am not sure what to do next.




2nd part ... what is the period of torsional oscillation of the system?
The shear modulus of steel = 8x10^10 N/m^2 and the interia is (2MR^2)/5.


Here I think you need to use the equation... T = 2pi * (I/c)^.5 where C is the shear modulus. I can't figure this part out. Do i need to worry about the cross sectional area here also?


Thank you very much everyone!

 

[Rozenwyn]

A solid steel ball is hung at the bottom of a steel wire length 2 meters and radius of 1mm. The ultimate strength of steel is 1.1 X 10^9 N/m^2. What is the mass of the biggest ball the wire can bare.

This seems like a pretty straight forward question. I am guessing the 2 meter radius doesn't matter. I am thinking that you need to find the area of a cross section of the 1mm wire. I am not sure what to do next.

Thank you very much everyone!

Let's say you found the area of the cross-section to be A. Well, if it is $$\frac{1.1 \times 10^9}{1m^2}$$, how much is it for $$\frac{x}{A}$$. And notice that this is not the final answer. It will give you the maximum force that that specific thickness of steel wire can resist.