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.

 

[kyle8921]

I would approach this problem by first identifying the relevant equations and variables. For the first part, we are looking for the mass of the largest steel ball that the wire can support, given its length, radius, and the ultimate strength of steel. We can use the equation for stress, which is force divided by area, to calculate the maximum force that the wire can withstand before breaking. Then, we can use the equation for weight, which is mass multiplied by acceleration due to gravity, to find the mass of the ball that would produce this maximum force when hung from the wire.

For the second part, we are asked to find the period of torsional oscillation of the system. This would involve using the equation for the period of a simple harmonic oscillator, which is dependent on the moment of inertia and the torsional constant. The moment of inertia can be calculated using the given formula, and the torsional constant can be found by using the equation for shear modulus and the cross-sectional area of the wire.

In summary, to solve both parts of this problem, we would need to apply relevant equations and use the given information to calculate the necessary variables. It is also important to pay attention to the units and make sure they are consistent throughout the calculations.