Question

classic yet interesting question about roller coaster :
find the minimum height from which the car needs to fall so as to complete the loop safely. The diameter of loop is 100m and the mass of car is 1000kg.

Answer 1

EWWWW I might have this problem on my test!

Answer 2

\[\sum F_y = ma_{cp} = F_{N} + F_{g} = N + mg=\frac{mv^2}{r}\]

Answer 3

Well that's technically a little wrong because the vector for the normal force should be longer than the force of gravity, but still....

Answer 4

I think it's more wrong because your bottom circle is elliptical and thus does not obey rules of circular motion ;)

Answer 5

haha, vertical circle

looks like you've fallen in the trap that physics is :)

Answer 6

Try to prove that the minimum velocity at the bottom is \(v_{min} = \sqrt{5gR}\) and thus the minimum kinetic energy is \(\frac{5}{2}mgR\) which can be equated to the initial potential energy to find the minimum height.

Answer 7

in the course of a few years parth has learned like 4 times as much physics as me.

Answer 8

\[N = \frac{mv^2}{r} -mg\]um... at the top of the roller coaster the normal force is neither more than the gravitational force, and nt less, but equal to it, therefore \(N=0\) \[mg = \frac{mv^2}{r}\]

Answer 9

why do we need to know the mass :-)

Answer 10

I wasnt there yet haha

Answer 11

Exactly, no need to know the mass. Jhanny is almost there. To be precise, \(N \ge 0\) to complete the vertical circle. At the minimum value of \(N\), we also get the minimum value of \(v\) at the top.

Answer 12

anyway the answer is \(h_{min} = 5R/2\)

Answer 13

that looks really nice and simpler!
i think mass is given so that we can assume that newton mechanics works just fine
but it is amazing how mass disappears after the calculations in most of these problems!

Answer 14

yeah, Galileo and Neil Armstrong!!

Answer 15

is that tesla in ur dp

Answer 16

yes

if anyone loads up an Edison avatar, there's gonna be blood!!

Answer 17

no this is a dog

Answer 18

lol!

Answer 19

so a naive q, do roller coasters really work like this?
without any chains hooked to the tracks?

Answer 20

\[g=\frac{v^2}{r} \implies v^2 = gr\] Yeah the mass is relevant when we're finding the change in work done, but this is where I get a little lost every time. :( \[U_i +K_i = U_f + K_f\]

Answer 21

Just from the back of my mind, i think Walter Lewin did this in one of the 8.01 lectures on MIT OCW

Answer 22

been a couple years since watching those

Answer 23

they had removed all his lectures from MIT after some controversy

Answer 24

in ideal conditions, they can work like that

Answer 25

:-O, well good thing i dl them all, hehe

Answer 26

yeah, he harassed a young female student on one of his MOOCs

it's still a shame, because he did know his physics pretty well

Answer 27

hell yes, his lectures and feynman spiked my interest

Answer 28

watching top 5 rolller coaster accidents
https://www.youtube.com/watch?v=mM0HE7DKTvg

Answer 29

i am pretty sure the acceleration at the top of the circle is zero for one instant to 'just' make it over... maybe not

Answer 30

https://www.youtube.com/watch?v=HN8nv4tVFuA

Answer 31

maybe a way to do it with just energy conservations