# AP Physics 1: 2.3 Changes and Conservation Laws

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AP Physics 1: 2.3 Changes and Conservation Laws. Which of the following is closest to the maximum speed of the oscillating sphere?

AP Physics 1 | Changes and Conservation Laws |

Science Practice 2 | Using math appropriately |

### Transcript

spring With the spring constant k equals five thousand meters

at the bottom of its oscillations up announcing the sphere

barely touches the ground at the top It rises to

a height of three meters which of the following is

closest to the maximum speed of the oscillating sphere And

here the potential answers Anything that one all right well

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

on the idea that this spring is hanging from the

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

never mind Anyway it affects the equilibrium point But for

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

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

this system works Well when this spring is moving at

full speed all the energy and the system is kinetic

energy The equation for that is one half mass times

velocity squared Now at the moment of maximum displacement when

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

point the sphere is actually not moving just for a

blink of an eye The energy is all stored his

potential energy Then the spring gets back to spring it

again and the kinetic energy comes back into play Going

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

moving all of the energy and the system is elastic

potential energy Well to calculate that we find the product

of one half the spring constant jonas k in our

little equation here times the amplitude squared Well that equation

looks like this and you stands in for elastic potential

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

amplitude is the maximum displacement from the equilibrium point of

the spring In this case since the bottom of the

oscillation around level and the top of the oscillation is

three meters Will The amplitude is half of that or

one point five meters using advanced calculus Now we know

that in a system mechanical energy equals potential energy plus

kinetic energy And we also know that the total energy

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

it So the mechanical energy when all the energy is

potential is the same as when all of the energy

is kinetic Or to put it another way the maximum

kinetic energy of this system is equal to its maximum

potential energy Got it good And that means that the

two equations we looked at earlier have to equal each

other So you sometimes all this physics makes us feel

like our head is on a spring Now we can

plug in numbers and sol for velocity after we do

a little bit algebra With that we see that velocity

equals amplitude times the square root of a spring constant

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

root of five thousand newton meters divided by forty five

kilograms which is about the same as one point five

meters times the square root of one Hundred over one

second squared giving us an answer of fifteen meters per

second So the answer Isi This is another case where

understanding the relationship between kinetic energy potential energy and mechanical

energy is the key to finding the right answer So

we have to make sure to study these forms of

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

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