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

[SherBear]

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

 

[SherBear]

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?

 

[haruspex]

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?

 

[SherBear]

No idea Haruspex?

 

[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.

 

[SherBear]

Ok, thank you. Any idea about the height of the hill ?

 

[haruspex]

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.

 

[SherBear]

How can I go through those steps if it only gives me the diameter?

 

[SherBear]

Is it 2R - 1/2 R ?

20-5 = 15m ?

 

[haruspex]

Do you have any answers for the steps I listed? Answer what you can and we can take it from there.