- #1
AJKing
- 104
- 2
Vibrations and Waves, A.P. French, questions 3-9
Please /do not/ provide full solutions. Just suggestions.
A solid steel ball is hung at the bottom of a steel wire of length 2m and radius 1mm, the ultimate strength of steel is 1.1E9 N/m2. What are the radius and mass of the biggest ball the wire can bear?
[itex]Y = \frac{\sigma}{\epsilon}[/itex] (line)
[itex]U = \frac{\sigma_u}{\epsilon_u}[/itex] (point below line)
[itex]m = \frac{4}{3}\pi*r^3 \rho[/itex]
[itex]\rho \approx 7850 Kg/m^3[/itex] (Internet)
For the sake of sanity, I arrange eq.2 by knowns and unknowns.
[itex]\frac{U*A}{g*l_0} = \frac{m}{\Delta l} [/itex]
I must find Δ l
I consider two points on the Y line:
[itex]Y = \frac{\sigma_u}{\epsilon_1}[/itex]
[itex]Y = \frac{\sigma_2}{\epsilon_u}[/itex]
both can be written as
[itex]Y = C\frac{\sigma_u}{\epsilon_u} = C U[/itex]
[itex]C = Y/U[/itex]
Then I stop and think about how this will lead me in circles.
------
I have a suspicion that the solution to my problem requires differential equations. Anyone second that notion?
Please /do not/ provide full solutions. Just suggestions.
Homework Statement
A solid steel ball is hung at the bottom of a steel wire of length 2m and radius 1mm, the ultimate strength of steel is 1.1E9 N/m2. What are the radius and mass of the biggest ball the wire can bear?
Homework Equations
[itex]Y = \frac{\sigma}{\epsilon}[/itex] (line)
[itex]U = \frac{\sigma_u}{\epsilon_u}[/itex] (point below line)
[itex]m = \frac{4}{3}\pi*r^3 \rho[/itex]
[itex]\rho \approx 7850 Kg/m^3[/itex] (Internet)
The Attempt at a Solution
For the sake of sanity, I arrange eq.2 by knowns and unknowns.
[itex]\frac{U*A}{g*l_0} = \frac{m}{\Delta l} [/itex]
I must find Δ l
I consider two points on the Y line:
[itex]Y = \frac{\sigma_u}{\epsilon_1}[/itex]
[itex]Y = \frac{\sigma_2}{\epsilon_u}[/itex]
both can be written as
[itex]Y = C\frac{\sigma_u}{\epsilon_u} = C U[/itex]
[itex]C = Y/U[/itex]
Then I stop and think about how this will lead me in circles.
------
I have a suspicion that the solution to my problem requires differential equations. Anyone second that notion?
Last edited: