# Springback of a Ruler

1. Nov 17, 2007

### serco

1. The problem statement, all variables and given/known data
Hello everyone,

I am currently working on a lab report investigating the spring back of a stainless steel ruler. I am trying to determine a relationship between the distance/angle that the ruler is bent (without warping it) and the amount of force exerted by the ruler.

Here are some pictures of the lab:

I've measured the x and y components of the ruler when bent (and the angle can be calculated) with various amounts of mass attached to the end.

2. Relevant equations
Well, im trying to find the force exerted by the ruler against the bending force (gravity).

-The very basic equation is the force Fg=(mass of attached object) x gravity

-Since when the ruler is bent (with masses attached to the end), the Fnet of the mass is Zero.

3. The attempt at a solution

Using Fg=mg
I was thinking, if an object is at rest on a table, the Fg=mg, and F normal= -mg. Bringing this idea to this ruler situation, if Fnet of mass=0, then F exerted by ruler is like F normal, and therefore is -mg.

But would the bending of the ruler play a factor in the force exerted by the ruler? Then using the angles and distances the ruler is bent, can an equation be found? I just want to know if i got the idea right.

And btw, any suggestions on a good graphing program?

regards,
steven

Last edited: Nov 17, 2007
2. Nov 17, 2007

### PhanthomJay

I'm not sure what you're looking for, but this seems to be a problem in engineering mechanics. There is a net upward force of mg exerted by the table/clamp on the ruler, and also a moment 'couple' of mgL counterclockwise. In accordance with newton 3, the ruler exerts a force of mg downward on the table, and a moment of mgL clockwise. Is that what you are looking for? In regard to the angles fomed, these are determined from calculus and depend on the elastic modulus and geometrc properties of the ruler. The deflection increases linearly with the mass, but increases proportional to the cube of the length (i.e, double the length, and the deflection increases by 8, assuming no yielding/warping of the steel).

3. Nov 17, 2007

### serco

I think i see wut ur saying here. So the normal Force is not just exerted by the ruler but by the clamp/table system and ruler as a whole. Also, u mentioned deflection increases linearly with mass. Wut do u mean by deflection? -The angle the ruler is bent or distance the ruler moves on the y-component?
What im trying to find is the force exerted by the ruler when it is bent to a certain angle.

4. Nov 17, 2007

### PhanthomJay

No, the table/clamp exerts a normal upward force and a ccw moment on the ruler. The ruler exerts a normal downward force and cw moment on the clamp/table.
by deflection I meant the vertical downward y distance the ruler moves. If you measure 5cm deflection at the end of the ruler under a mass of m, then when you double the mass, you should measure a 10cm deflection at the end.
I'm unsure what you mean. As the angle increases under inceasing applied weight at the end, the moment increases, and the internal stresses in the ruler increase. The normal force always equals the weight of the applied mass (applied slowly). (We are neglecting the weight of the ruler itself).

5. Nov 17, 2007

### serco

That seemed to clear up my misunderstanding, i have a rough idea of wut to write now.

Thanks,
I really appreciate all the help :)

6. Nov 18, 2007

### LOLECSS

are you from ECSS? I think I see the chair I sit on.

7. Nov 19, 2007

### serco

lol arrvin. imma kill Alan

8. Mar 14, 2010

### inutard

Hmm. Where did you learn this? It seems interesting. Can you recommend some source where I can learn more?

9. Mar 14, 2010

### PhanthomJay

You might want to do a google search...it takes a course in engineering mechanics to fully understand the calculus behind the deflection equations....essentially the deflection curves are cubic in nature...for example, a cantilever ruler of constant section and uniform material, under an applied force P at the far end, has a deflection at that end of PL^3/3EI, where EI is a property of the beam's material and cross section.

Last edited: Mar 14, 2010
10. Mar 14, 2010

### inutard

I see. Thank you!