# Homework Help: A few questions on Hooke's Law

1. Sep 13, 2006

### OVB

I think im getting some concepts confused, so i need help clarifying the answers to the following questions:

1. can you use a rubber band instead of a steel spring in a scale to measure weight?
- I said no, because it would break
2. Should the wires supporting a suspension bridge be elastic or inelastic?
- I said elastic so that it can return to its original position, but I dont know how to expand on this...

3. How is a steel wire "very elastic" if it does not stretch much with large forces?

And k is independent of gravity right? (i.e., if you have a force and a displacement on earth, would those be in the same proportion on the moon? I'm thinking F/x = k equals a direct proportion but I might be breaking smoe rules).

I spent a good hour before and that is the progress I have made.

Last edited: Sep 13, 2006
2. Sep 13, 2006

### OVB

does anyone know?

3. Sep 13, 2006

### OVB

I explained rather well what I knew and what I didn't. Am I being ignored for something I left out or does no one know?

4. Sep 13, 2006

### Astronuc

Staff Emeritus
1. can you use a rubber band instead of a steel spring in a scale to measure weight?
- I said no, because it would break

Well, no is the right answer, but the reasoning is not correct.

1. In order to measure weight, the deflection must be linearly proportional to the weight - that is the point of Hooke's law. Only this way can one obtain a uniformly graduated scale. Steel spring could also be overloaded into the inelastic region, in which case it would be permanently deformed.

A rubber band is non-linear. The cross-section changes as it stretches. One might try and experiment with a suitable rubber band. Load it up with gram weights e.g. 1g, 2g, 3g, . . . and see if the deflection is a constant multiple of the mass.

The spring constant is a property of the metal and independent of gravity. The weight of something is a measure of the gravitational force on the mass - W = mg.

2. If a metal is stressed into the inelastic range, there will be permanent deformation. Structures are designed such the materials in the components operate well below the yield strength, i.e. well within the elastic range. When a structure is loaded then unloaded, as happens when a vehicle crosses a bridge, then the structure must return to its original unloaded form. Bridges are designed to deflect under load, but not by much. Many (or most) structures tend to be very stiff - i.e. resist displacement.

3. If a metal is highly loaded, and still does not stretch (which I take to mean 'permanently deform'), then it has a 'large elastic' range.

When metals are deformed, they are worked beyond the elastic range (yield strength) and they are plastically deformed.

Last edited: Sep 13, 2006