Finding the minimum speed of a loop the loop and finding the height of the hill

Click For Summary

Homework Help Overview

The discussion revolves around a physics problem involving a roller coaster cart navigating a loop-the-loop. The problem includes determining the minimum speed required for the cart to remain on the track and calculating the height of the hill from which the cart descends. The loop has a radius of 10 meters, and the scenario assumes no friction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the minimum speed needed at the top of the loop and question whether the calculated speed ensures the cart stays on the track. There are discussions about kinetic and potential energy at different points in the loop, as well as the forces acting on the cart.

Discussion Status

Participants are actively engaging with the problem, raising questions about the calculations and the physical principles involved. Some guidance has been offered regarding the relationship between kinetic energy at the bottom of the loop and potential energy at the top of the hill, but no consensus has been reached on the specific values or methods to use.

Contextual Notes

There is a mention of a rider in the cart, and participants express uncertainty about the implications of the diameter provided in the problem. The discussion includes a focus on the necessary calculations and assumptions required to solve for the height of the hill.

SherBear
Messages
81
Reaction score
0

Homework Statement



I have a hill with a roller coaster cart on it and it goes down and around a loop-the-loop

the radius of the loop is 10m

Diameter=20m

What is the minimum speed the cart needs to go to keep it on the track?

There is no friction, what is the height of the hill?

Homework Equations



Vtop=sqrt rg



The Attempt at a Solution


to get the minimum speed the cart needs to go to keep it on the track is
Vtop= sqrt rg
=sqrt 10m(9.8 m/s^2)
Vtop=9.89 m/s ---------is this correct?

There is no friction, what is the height of the hill?

I don't know what to do for this problem
 
Physics news on Phys.org
I forgot to add the third part, there is a rider on the bottom of the loop in a cart, what is N?

I have Ar=v^2 / r

9.89^2 m/s / 10m = 9.78 m/s

Then F=N-mg=ma

N=mg+ma

N= m (g+a)

N= 60 kg (9.8 m/s^2 + 9.78 m/s) =

N= 1,174.8 is that m/s or N as in Newtons?---------is this correct?
 
The velocity you calculated gives it enough energy to reach the height of the top of the loop, but that doesn't necessarily mean it stays on the track. If that were the speed at the bottom of the loop, how much KE would it have left at the top? What speed do you think it needs to have at the top to stay on the track?
 
No idea Haruspex?
 
If the cart has speed u at the bottom of the loop, how much KE does it have?
How much PE does it gain in reaching the top of the loop?
How much KE then does it have left (as a function of m, r, g and u)?
What forces act on it when it is at the top of the loop?
What is its acceleration if it is still staying on the track at speed v?
What net force is required to achieve that acceleration?
These are the steps you need to go through.
 
Ok, thank you. Any idea about the height of the hill ?
 
SherBear said:
Any idea about the height of the hill ?
Once you know the KE it needs at the bottom of the loop, it's easy to work out the PE it needs at the top of the hill.
 
How can I go through those steps if it only gives me the diameter?
 
Is it 2R - 1/2 R ?

20-5 = 15m ?
 
  • #10
Do you have any answers for the steps I listed? Answer what you can and we can take it from there.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
Replies
7
Views
3K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 12 ·
Replies
12
Views
13K
  • · Replies 10 ·
Replies
10
Views
6K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 16 ·
Replies
16
Views
3K
Replies
5
Views
2K
Replies
12
Views
3K