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## Physics library

### Course: Physics library>Unit 5

Lesson 2: Springs and Hooke's law

# Intro to springs and Hooke's law

Discover the phenomena of springs and Hooke's Law. Explore how force applied to a spring results in compression or elongation, and how this relationship is linear. Uncover the concept of restorative force and how it counteracts applied force, keeping our spring in equilibrium. Created by Sal Khan.

## Want to join the conversation?

• I have a simple question: On a microscopic level, what force(s) makes the spring want to restore itself to its original position?
• The equilibrium position of the string minimizes the potential energy of the metal atoms from which the spring is constructed. I don't know how much inorganic chemistry you know, but what it basically comes down to is that chemical bonds have a sort of "best distance of separation." Atoms consist of subatomic constituents that carry electric charges (nuclei are positively charged due to protons and the space around the exterior of the atom has a negative charge due to the electrons). Bring two nuclei too close together and their positive like charges will repel--this is the case with spring compression. Separate the bound atoms by too great a distance and the "electron glue" that holds them together will create tension that draws the atoms back together--this is stretching the spring. Keep in mind that this is a very very simplified explanation of what really happens, to truly understand the nature of this elastic energy you must study the wave-nature of subatomic particles and quantum mechanics.
• What does the constant K of the spring determine ? Does it vary from spring to spring depending on the material it's made of ? If not , then what ?
• K is a constant that represents the elasticity of a spring (and therefore stiffness). It varies between spring to spring, depending on what it is made of, the shape of the spring, and the width of the wire.
• What are elastomers ?
• Elastomers are polymers that are designed to be highly elastic (they can stretch far without breaking). For example, yoga pants, running tights, nylons, and the rubber bands are all composed of elastomers.
The concept was first discovered with the sap of the rubber tree, which was distilled into highly flexible material. Today, manufacturing companies can artificially design/construct their own materials.
• As Sal explained in the video that the restoring for is ' F = -kx", he also take the restoring force to be equal to the force applied by Newton's 3rd Law. But how is it necessary to be the same. If k has big value, we will have to apply large force for very small displacement in that case restoring force will be lesser because of very small value of 'x'.
So how can Sal take it to be equal to the force applied?
• Sal is right. If k has a big value, you will have to apply a huge force to cause a small displacement. But that also means (k having a big value) that for a small displacement the restoring force will be huge.
In the end everything is balanced and Newton's 3rd law still holds :D
• well what does x stand for?
• x is the displacement of the spring's end from its equilibrium point - how much the spring is stretched (or, in the other direction, compressed)
• I have a query regarding springs in a series combination.
Say, there's a thread attached to the ceiling, connecting three springs vertically and a block of mass 'M' connected at the bottom.
It is said that the force is same for all springs in series (=Mg in this case). How is this possible if we have mass-full springs?
Or is it applicable solely for 'mass-less' springs?
• great point.

yes, usually we have 'mass-less' springs... ie their mass is very very small compared to the mass being suspended by the springs.

OR

we may be given the 'mass per unit length' of each spring and therefore able to figure out the extension due to the mass of the springs, but this is probably an unlikely situaiton (though not impossible in some courses)

ok??
• k is always positive so it cant be -2 at
F=-kx <->-2 = -kx <-> -2=-k <-> k=2; is the correct equation
• I saw F= k*x^2/2 what is that different from Hooke's law?