Find the elongation in the wire

[Jahnavi]

Homework Statement

Homework Equations

∆l = Fl/YA

The Attempt at a Solution

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The net acceleration of the system is F/2M .

Force at the right end of the wire will be F towards right .

Force at the left end of the wire will be F/2 towards left .

Now how should I take the two forces into account ?

 

[PumpkinCougar95]

1) Consider an infinitesimal element at a distance $x$ from the end with the box.
2) Make force diagram for that element.
3) Would the tension in the rod be same everywhere?

 

[Jahnavi]

1) Consider an infinitesimal element at a distance $x$ from the end with the box.
2) Make force diagram for that element.
3) Would the tension in the rod be same everywhere?

No . Tension in the rod will not be same everywhere .

I can find the tension at any point . But please explain how will I find the total elongation ?

 

[PumpkinCougar95]

Find the elongation of an element $dx$. You can use: $$ d \delta l = \frac {T dx} {A Y} $$ where $\delta l$ is the total elongation. Then just integrate.

 

[Jahnavi]

Thanks !