Finding the Stretch in a Spring for a 2D Equilibrium Problem

[Oblivion77]

Homework Statement

Here is the problem

Homework Equations

Sum of the forces in x, y and moments

The Attempt at a Solution

I am having troubles drawing a good FBD.

 

[Doc Al]

What forces act on the rod?

Hint: Find the spring stretch as a function of angle.

 

[Oblivion77]

What forces act on the rod?

Hint: Find the spring stretch as a function of angle.

I know there are 2 normals that act on the bar (from the collars) but which way are the normals acting?

 

[Doc Al]

Which way do "normals" usually act?

 

[Oblivion77]

Which way do "normals" usually act?

perpendicular, so the normal at the bottom is vertical and the normal at the top is horizontal?

 

[Doc Al]

perpendicular, so the normal at the bottom is vertical and the normal at the top is horizontal?

Exactly.

 

[Oblivion77]

Ok, so where does the force in the spring come along in the FBD?

 

[Doc Al]

Ok, so where does the force in the spring come along in the FBD?

You tell me. How is the spring oriented? Which way does it push?

 

[Oblivion77]

Would the force in the spring be tension going straight up?

 

[Doc Al]

Would the force in the spring be tension going straight up?

Yep. You should have a good handle on that FBD now.

 

[Oblivion77]

Yep. You should have a good handle on that FBD now.

Thanks for the help!

 

[Oblivion77]

I am having some trouble seeing the stretched and un-stretched lengths of the spring. When the bar is vertical it looks like the un-stretched length is 0.

 

[Doc Al]

I am having some trouble seeing the stretched and un-stretched lengths of the spring. When the bar is vertical it looks like the un-stretched length is 0.

The unstretched length of the spring is unknown and unneeded. What you do need is how much the spring is stretched when the bar is at an angle. When the bar is vertical the spring is unstretched, thus the the amount of stretch is zero.

Hint: When the bar is at some angle α, how far down has the end of the bar pulled the spring compared to when the bar was vertical?

 

[Oblivion77]

Is it something like 5sinα?

 

[Doc Al]

Is it something like 5sinα?

Something like that--but not that.

Locate the right triangle whose hypotenuse is the bar. What's the height of that triangle? That's the height of the right end of the bar. Compare that to its height when vertical. That will tell you the amount the spring has been stretched.

 

[Oblivion77]

Ok, the hypotenuse is 5. So the adjacent side(vertical) is 5Cosα and opposite(horizontal) is 5Sinα. So is 5Cosα the stretched?

 

[Doc Al]

So is 5Cosα the stretched?

No, it's the height of the spring end measured from the horizontal fixed bar. Compare that to where the spring was when the angled bar was vertical (and the spring unstretched). The difference in height will tell you the amount the spring was stretched.

 

[Oblivion77]

I still can't see what is happening. I am not good at spring questions. I know F=k(L-Lo). but earlier you said the un-stretched length was not needed.

 

[Doc Al]

I know F=k(L-Lo). but earlier you said the un-stretched length was not needed.

You need L-Lo, but not Lo.

Do this. Find the height of spring end above the fixed horizontal bar when the 5m bar is vertical. (That should be easy!) Then find its height when the 5m bar is at an angle. (You've already done that.) The difference between those two heights is the amount of stretch in the spring (which is all that L-Lo is) when the bar moves from vertical to some angle.

 

[Oblivion77]

You need L-Lo, but not Lo.

Do this. Find the height of spring end above the fixed horizontal bar when the 5m bar is vertical. (That should be easy!) Then find its height when the 5m bar is at an angle. (You've already done that.) The difference between those two heights is the amount of stretch in the spring (which is all that L-Lo is) when the bar moves from vertical to some angle.

Thanks for all the help! I solved it now.