# Roller coaster

1. Nov 4, 2015

### astrololo

1. The problem statement, all variables and given/known data
When the train has passed at the point C, the radii of curvature is 20 m and the apparent weight is 2 2 times bigger than the real weight. At the moment when the picture was taken, the train was at the point s, located 8 m higher than the hollow C. At s, the radii of curvature est 16m. Calculate the quotient between the apparent weight at the point S and the real weight. There is no friction and no air resistance.

http://imgur.com/R2A4pya
2. Relevant equations

Sum of force in y = (mv^2)/radii

Energy at s = energy s

k=mv^2/2

U=m*g*y

3. The attempt at a solution
I know what to do :

I calculate the speed at the point C. I get 62,6 m/s

I put up equations which respect that Es=Ec to find my speed at S

I do the sum of forces at S and find n and divide it by mg.

Now, the only point which Im not sure is what is the height the point S ? I is 48 m ?

2. Nov 4, 2015

### Nathanael

How do you get that?
"The height of the point S" is an incomplete (meaningless) statement. When you measure the height of something, you must measure the height with respect to some reference point. So, from where do you want to measure the height of S?

3. Nov 4, 2015

### astrololo

From 0 at the point C I guess

4. Nov 4, 2015

### Nathanael

Ok, is there anything in the problem statement about that?

Also, double check how you found the speed, because I do not get 62 m/s.

5. Nov 4, 2015

### astrololo

Well, I set up n=2mg

Sum of forces y = mv^2/r

2mg-mg=mv^2/r

2g-g=v^2/20

which gives v = 14 m/s right ? I guess I did an error

6. Nov 4, 2015

### haruspex

Yes.
The problem statement does not say that the train merely coasts up the hill, but presumably that is the intent.

7. Nov 4, 2015

### astrololo

Ok, but what is the height at the point s ? Im not sure, is it 48 m ? 2 times the radii + 8 m.

8. Nov 4, 2015

### haruspex

A clue is that it does not have enough KE to rise much more than 8m.

9. Nov 4, 2015

### astrololo

So it's 8 ???

10. Nov 4, 2015

### Nathanael

Yes, that is most likely what they meant.
(I'm not sure why they said "8 m higher than the hollow C" though... I don't know what the word hollow was supposed to mean here.)

11. Nov 4, 2015

### astrololo

It's a translation from another language lol But the final answer is supposed to be 3/4. Does it give this ?

12. Nov 4, 2015

### haruspex

Yes.
A tip: avoid using inexact numerical values calculated at intermediate steps. Ideally, keep everything in algebraic symbols until the final steps. This prevents the accumulation of rounding errors. In the present case e.g., you can avoid taking a square root to find the velocity, only to find that it's the square of the velocity that's needed.

13. Nov 4, 2015

### astrololo

I obtained the following : quotient= (9,8m+(39,2m)/16)/9,8m=1.25

I feel like there is a minus missing

Last edited: Nov 4, 2015
14. Nov 5, 2015