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AP Physics 1 Videos 86 videos

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AP Physics 1: 3.4 Changes and Conservation Laws 6 Views


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AP Physics 1: 3.4 Changes and Conservation Laws. Which pair is closest to a cars speeds at the top and bottom of the loop?

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Transcript

00:00

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

00:05

brought to you by amusement parks where we go to

00:07

stuff our faces with junk food Then you get on

00:10

the rides that are basically designed to induce motion sickness

00:13

But we still have a blast And amusement park has

00:16

a roller coaster with a forty five meter hill followed

00:19

by a circular loop with a fifteen meter radius Assume

00:23

that there's no friction on the track and that a

00:25

roller coaster cars velocity is zero when it starts to

00:29

descend the first hill Well which pair is closest to

00:33

a car Speeds at the bottom and the top of

00:35

the loop respectively Alright here the potential answers and meters

00:39

per second Got it Okay well looking at this question

00:43

we see that it involved potential energy and kinetic energy

00:47

And well what does add up Tio that's right Funnel

00:49

cakes No wait Sorry Anytime we're dealing with amusement parks

00:53

are mined Just well Go straight to delicious fried dough

00:56

Kinetic energy plus potential energy equals mechanical energy And since

01:00

the total energy and a closed system can't change we

01:03

can use this equation to figure out all sorts of

01:05

stuff at the top of the track the coaster just

01:08

sits there full of potential energy with no kinetic energy

01:12

at all with kinetic energy it zero All we need

01:15

to do is figure out the maximum potential energy and

01:18

we can know the total energy in the system we'll

01:21

potential energy equals mass times height times gravity so we

01:24

can just plug the numbers in and well wait a

01:27

second We don't know the mass of the roller coaster

01:30

car I'll never mind folks Looks like we're stuck And

01:34

this question is a knowable it's hopeless there's no possible

01:37

way to well actually maybe we can figure it out

01:40

after all Let's take another look at the situation We

01:43

know what the top of the hill The coaster has

01:46

all potential energy and no kinetic energy It stands to

01:50

reason that if the bottom of the hill the coaster

01:52

has no potential energy and all kinetic energy kinetic energy

01:56

equals one half mass times the velocity squared But with

01:59

this in mind we know that the maximum potential energy

02:02

equals the maximum kinetic energy that means mass times gravity

02:06

times height equals one half mass times velocity squared and

02:10

with these equations balance like that mass cancels itself out

02:14

Well we knew he could do it the whole time

02:16

Using little algebra we can solve for velocity at the

02:18

bottom of the hill That velocity equals the square root

02:21

of two times gravity times height When we put in

02:25

the numbers we find that the velocity at the bottom

02:27

of the loop equals thirty meters per second Okay halfway

02:30

there We probably could have ridden this roller coaster three

02:33

times by now but it wouldn't be as much fun

02:35

is solving this problem right And we've knocked out half

02:38

of the answer's a and b you're definitely wrong So

02:41

least there's some progress Now think about the energy at

02:43

the top of the loop at this point With the

02:45

roller coaster above ground level and moving around the loop

02:50

we have both kinetic and potential energy going on the

02:54

equation Looks like of this right here This thing in

02:57

a potential energy equation the height is two times the

02:59

radius of the loop since that gives us our total

03:02

distance from the ground to the top Well this looks

03:05

trickier Remember the total energy and the system can't change

03:09

Knowing that we can use the same equation we used

03:12

before but just factor in the change in height So

03:15

the height in this equation will equal the starting height

03:17

minus the height of the loop Right there When we

03:20

put in the numbers we find the velocity at the

03:22

top of loop is seventeen meters per second So our

03:26

answer is d now considering our choices we really could

03:30

have ruled out see as soon as we figured out

03:32

the velocity at the bottom of loop that's because we

03:35

know that the top of the loop is lower than

03:37

the top of the hill and that means that the

03:39

potential energy at the top of the loop has to

03:41

be lower than it was at the top of the

03:43

hill And if the potential energy of the system is

03:46

lower than it was at the max then kinetic energy

03:49

has to be greater than zero for the mechanical energy

03:52

to be conserved There's no way The coasters velocity could

03:55

be a zero Plus what kind of roller coaster stops

03:58

at the top of the loop like no one would

04:00

want to ride that thing All right well now we're

04:02

going to go lay down All this physics and roller

04:03

coaster talk has our head spinning We need some grandma

04:06

me and about a pound of cotton candy Sounds good 00:04:08.995 --> [endTime] too Yeah

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