Does hooks law appy to leaf springs?

[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 realize 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.

 

[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?

 

[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 realize 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).

 

[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.

 

[PJC01]

I can provide a response to your questions regarding the application of Hook's law to different objects and the measurement of potential energy.

Firstly, Hook's law states that the force applied to an elastic material is directly proportional to the amount of deformation or stretch of the material. This law applies to a wide range of materials, including springs, rubber bands, and even solid materials like metals.

Regarding the application of Hook's law to leaf springs, the answer is yes. Leaf springs are commonly used in vehicles and are designed to flex and absorb shock during movement. They work on the principle of Hook's law, where the force applied to the spring is directly proportional to the amount of deflection or bending of the spring.

Similarly, a bent hockey stick can also be considered as an elastic material, and thus, Hook's law can be applied to it. The force applied to the stick is directly proportional to the amount of bending or deflection of the stick.

Now, let's discuss how one can measure the potential energy of an object. The potential energy of an object is the energy stored within the object due to its position or configuration. In the case of a bent hockey stick or a leaf spring, the potential energy is stored in the form of elastic potential energy.

To measure the potential energy, one can use the formula for elastic potential energy, which is given by PE = 1/2 * k * x^2, where PE is the potential energy, k is the spring constant, and x is the displacement or deflection of the object.

To measure the deflection, as you mentioned, one can clamp one end of the object and apply a known weight to the other end, noting the weight and deflection of the tip. By varying the weight and measuring the corresponding deflection, one can determine the spring constant (k) and calculate the potential energy.

It is important to note that Hook's law is an approximation and may not accurately predict the behavior of all materials. However, it is a useful tool in understanding the behavior of elastic materials and can provide a good approximation in many cases.