in today's video we're going to look at the two equations you need to know about elasticity the first F equals ke links the force that you apply to an object - how much it extends by when you apply that force with K being a spring constant which is specific to each object and as a measure of how firm or elastic the object is a lowest spring constant means that the object is more elastic and so easier to stretch while a higher spring constant means that the object is more stiff and so harder to stretch the other equation is the elastic potential energy equals 1/2 ke squared where K and E are the spring constant and extension again and importantly it's only the extension as being squared not the whole thing you can think of elastic potential energy as the energy transferred to an object as its stretched so if you used 100 joules of energy to stretch a spring then the 100 joules would be transferred to the springs elastic potential energy store and then when you let it go and it springs back it would transfer that 100 joules back out to a different form light kinetic energy you to see how these equations work let's try a couple of examples imagine this spring has a natural length of 0.6 meters but when we apply a force of 14 Newtons it stretches to 0.8 meters what's the spring constant of the spring well first we need to figure out what's going on as the spring has stretched from 0.6 to 0.8 meters we can find this extension by subtracting 0.6 from 0.8 which gives us zero point 2 meters so we now know the force and the extension and we want to find the spring constant if we look at our two equations we can see that we would have to use F equals K E and then rearrange it to get F over e equals K which if we plug in 14 divided by 0.2 gives us 17 Newton's per meter at our spring constant you now using the same scenario what would the elastic potential energy of the spring now be this time we're gonna have to use the other equation so elastic potential energy equals 1/2 ke squared and it's a bit simpler because we've already worked out the spring constant and extension so all we have to do is plug the values into the equation so we get 1/2 or 0.5 times 70 times 0.2 squared which gives us one point four joules the last thing we want to point out is that if you have a graph of force against extension like this one then as long as we only look at the straight part of the line the gradient of the line will be the spring constant and the area under the curve is equal to the energy transferred to the spring so the elastic potential energy and just to recap remember that this point here is known as the elastic limit or the limit of proportionality and it's when the object stopped to obeying Hookes law you anyway that's everything for this video so hope you found it useful if you did then give us a like and subscribe and I'll see you next time