# Does hooks law appy to leaf springs?

1. Jul 30, 2014

### hlock

Does hooks law apply to a bent hockey stick. How does one measure the potential energy? Do I start by clamping one end weighing down the other and noting weight and deflection of the tip?

I realise hooks law is an approximation, and can picture its relevance to an extension/compression and even a torsion spring but does it also apply to a bent "leaf" spring? to what accuracy assuming the tip deflection is proportional to pressure applied.

2. Jul 30, 2014

### hlock

I think the right question is, is the measurement of the force constant the same or a leaf spring the same as an extension spring?

Does measuring the distance of extension of a spring = measuring the flex of the tip of a leaf spring when calculating spring force constant?

3. Jul 30, 2014

### sophiecentaur

Hi and welcome to PF.

Good question. I found this delightful link - which doesn't answer you question but it is worth looking at. In it, there is the assumption of Hooke's Law. Leaf springs go back a long way, apparently!

I think the leaf spring is, at least ideally, the equivalent of a set of linear springs, 'connected in parallel'. For two coil springs, sharing a load, the deflections will be equal and the force on each will be kd so the total force should be simply proportional to the (common) displacement times (k1 + k2) - so it behaves as a linear spring, following Hooke's Law. This linearity only breaks down if there is an end stop on one of the springs, when all the extension will be confined to one spring and the total k will be less.
For a leaf spring, where the leaves are not constrained, the same thing basically applies, I think. The deflection of each will be according to the share of the force (torque?) it gets. I realise that the intuitive reaction is that the leaf spring would get stiffer and stiffer as it deflects more but all the leaves are operating all the time. That makes one ask why we use leaves and not a single bar. More deflection for a given load, perhaps (softer springing).

4. Jul 30, 2014

### 256bits

A leaf spring is just a beam supported at the ends and a load applied in the middle.
Deflection is proportional to force applied, so the same thing as a coil spring, whether one notes the deflection at the end as in a cantiliever ( half of the end supported beam ) or the deflection of the ends wrt the middle of the fully ( end ) supported beam.

Multiple leaf springs are designed to approach a beam of triangular cross section, where the bending stress is constant throughout the length of the beam. Leafs are easy to make, and you just stack them together to get your leaf spring, and something resembling the ideal.

Downhill skies, at least the ones of earlier years if you ever see one, are of the same principle - thicker in the middle than the ends, and made as a whole unit from composites. Even much older ones, cross country included, were made from a single piece of wood with the shape refined by working on the wood.

See
http://roymech.co.uk/Useful_Tables/Springs/Springs_Leaf.html

Note than there is no difference in the equations for the cantilever or the fully supported. You might think so by looking at them, but substitute the L and P from the cantilever as L/2 and 2P for the fully supported and the equations become equivilant.