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Thank you We sneak and here's your smoke du jour

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brought to you by springs it's Important understand how springs

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work in terms of physics it's also important to understand

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how springs work in terms of comedy Well a sphere

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with a massive forty five kilograms hangs on a vertical

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spring With the spring constant k equals five thousand meters

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at the bottom of its oscillations up announcing the sphere

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barely touches the ground at the top It rises to

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a height of three meters which of the following is

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closest to the maximum speed of the oscillating sphere And

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here the potential answers Anything that one all right well

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before we really get into this don't get hung up

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on the idea that this spring is hanging from the

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ceiling What we did there don't get hung up on

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never mind Anyway it affects the equilibrium point But for

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this question that doesn't come into play With that out

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of the way let's think about how the energy in

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this system works Well when this spring is moving at

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full speed all the energy and the system is kinetic

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energy The equation for that is one half mass times

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velocity squared Now at the moment of maximum displacement when

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the sphere is that it's very highest and very lowest

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point the sphere is actually not moving just for a

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blink of an eye The energy is all stored his

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potential energy Then the spring gets back to spring it

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again and the kinetic energy comes back into play Going

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going going So what That instant when the sphere isn't

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moving all of the energy and the system is elastic

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potential energy Well to calculate that we find the product

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of one half the spring constant jonas k in our

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little equation here times the amplitude squared Well that equation

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looks like this and you stands in for elastic potential

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energy Because it's just easier to type you know and

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amplitude is the maximum displacement from the equilibrium point of

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the spring In this case since the bottom of the

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oscillation around level and the top of the oscillation is

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three meters Will The amplitude is half of that or

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one point five meters using advanced calculus Now we know

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that in a system mechanical energy equals potential energy plus

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kinetic energy And we also know that the total energy

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in this system can't change unless something else acts on

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it So the mechanical energy when all the energy is

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potential is the same as when all of the energy

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is kinetic Or to put it another way the maximum

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kinetic energy of this system is equal to its maximum

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potential energy Got it good And that means that the

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two equations we looked at earlier have to equal each

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other So you sometimes all this physics makes us feel

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like our head is on a spring Now we can

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plug in numbers and sol for velocity after we do

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a little bit algebra With that we see that velocity

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equals amplitude times the square root of a spring constant

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over mass that's one point five meters times the square

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root of five thousand newton meters divided by forty five

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kilograms which is about the same as one point five

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meters times the square root of one Hundred over one

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second squared giving us an answer of fifteen meters per

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second So the answer Isi This is another case where

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understanding the relationship between kinetic energy potential energy and mechanical

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energy is the key to finding the right answer So

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we have to make sure to study these forms of

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energy And we know it's hard work studying so feel

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free to take a snack break anytime you want Want 00:03:32.373 --> [endTime] some jelly beans will you

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