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AP Physics 1 Videos 86 videos

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AP Physics 1: 2.3 Changes and Conservation Laws 203 Views


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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?


Transcript

00:00

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

00:05

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

00:08

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

00:11

how springs work in terms of comedy Well a sphere

00:15

with a massive forty five kilograms hangs on a vertical

00:17

spring With the spring constant k equals five thousand meters

00:22

at the bottom of its oscillations up announcing the sphere

00:26

barely touches the ground at the top It rises to

00:29

a height of three meters which of the following is

00:32

closest to the maximum speed of the oscillating sphere And

00:36

here the potential answers Anything that one all right well

00:41

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

00:43

on the idea that this spring is hanging from the

00:45

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

00:48

never mind Anyway it affects the equilibrium point But for

00:51

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

00:56

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

00:58

this system works Well when this spring is moving at

01:01

full speed all the energy and the system is kinetic

01:04

energy The equation for that is one half mass times

01:09

velocity squared Now at the moment of maximum displacement when

01:13

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

01:17

point the sphere is actually not moving just for a

01:20

blink of an eye The energy is all stored his

01:22

potential energy Then the spring gets back to spring it

01:25

again and the kinetic energy comes back into play Going

01:28

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

01:31

moving all of the energy and the system is elastic

01:34

potential energy Well to calculate that we find the product

01:39

of one half the spring constant jonas k in our

01:43

little equation here times the amplitude squared Well that equation

01:47

looks like this and you stands in for elastic potential

01:50

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

01:53

amplitude is the maximum displacement from the equilibrium point of

01:57

the spring In this case since the bottom of the

02:00

oscillation around level and the top of the oscillation is

02:03

three meters Will The amplitude is half of that or

02:06

one point five meters using advanced calculus Now we know

02:09

that in a system mechanical energy equals potential energy plus

02:13

kinetic energy And we also know that the total energy

02:17

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

02:20

it So the mechanical energy when all the energy is

02:23

potential is the same as when all of the energy

02:26

is kinetic Or to put it another way the maximum

02:30

kinetic energy of this system is equal to its maximum

02:33

potential energy Got it good And that means that the

02:38

two equations we looked at earlier have to equal each

02:40

other So you sometimes all this physics makes us feel

02:44

like our head is on a spring Now we can

02:46

plug in numbers and sol for velocity after we do

02:50

a little bit algebra With that we see that velocity

02:53

equals amplitude times the square root of a spring constant

02:57

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

03:01

root of five thousand newton meters divided by forty five

03:04

kilograms which is about the same as one point five

03:06

meters times the square root of one Hundred over one

03:10

second squared giving us an answer of fifteen meters per

03:14

second So the answer Isi This is another case where

03:19

understanding the relationship between kinetic energy potential energy and mechanical

03:23

energy is the key to finding the right answer So

03:25

we have to make sure to study these forms of

03:27

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

03:30

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

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