# AP Physics 1: 3.4 Changes and Conservation Laws

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?

AP Physics 1 | Changes and Conservation Laws |

Language | English Language |

Science Practice 2 | Using math appropriately |

### Transcript

a roller coaster with a forty five meter hill followed

by a circular loop with a fifteen meter radius Assume

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

roller coaster cars velocity is zero when it starts to

descend the first hill Well which pair is closest to

a car Speeds at the bottom and the top of

the loop respectively Alright here the potential answers and meters

per second Got it Okay well looking at this question

we see that it involved potential energy and kinetic energy

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

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

are mined Just well Go straight to delicious fried dough

Kinetic energy plus potential energy equals mechanical energy And since

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

can use this equation to figure out all sorts of

stuff at the top of the track the coaster just

sits there full of potential energy with no kinetic energy

at all with kinetic energy it zero All we need

to do is figure out the maximum potential energy and

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

potential energy equals mass times height times gravity so we

can just plug the numbers in and well wait a

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

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

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

way to well actually maybe we can figure it out

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

know what the top of the hill The coaster has

all potential energy and no kinetic energy It stands to

reason that if the bottom of the hill the coaster

has no potential energy and all kinetic energy kinetic energy

equals one half mass times the velocity squared But with

this in mind we know that the maximum potential energy

equals the maximum kinetic energy that means mass times gravity

times height equals one half mass times velocity squared and

with these equations balance like that mass cancels itself out

Well we knew he could do it the whole time

Using little algebra we can solve for velocity at the

bottom of the hill That velocity equals the square root

of two times gravity times height When we put in

the numbers we find that the velocity at the bottom

of the loop equals thirty meters per second Okay halfway

there We probably could have ridden this roller coaster three

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

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

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

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

the top of the loop at this point With the

roller coaster above ground level and moving around the loop

we have both kinetic and potential energy going on the

equation Looks like of this right here This thing in

a potential energy equation the height is two times the

radius of the loop since that gives us our total

distance from the ground to the top Well this looks

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

Knowing that we can use the same equation we used

before but just factor in the change in height So

the height in this equation will equal the starting height

minus the height of the loop Right there When we

put in the numbers we find the velocity at the

top of loop is seventeen meters per second So our

answer is d now considering our choices we really could

have ruled out see as soon as we figured out

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

know that the top of the loop is lower than

the top of the hill and that means that the

potential energy at the top of the loop has to

be lower than it was at the top of the

hill And if the potential energy of the system is

lower than it was at the max then kinetic energy

has to be greater than zero for the mechanical energy

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

be a zero Plus what kind of roller coaster stops

at the top of the loop like no one would

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

going to go lay down All this physics and roller

coaster talk has our head spinning We need some grandma

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