Question on Law conservation of Mechanical Energy

AI Thread Summary
The discussion revolves around calculating the height at point C of a roller coaster using the conservation of mechanical energy principle. The initial height at point A is 0.45 km, with a speed of 20 m/s, and point B is at 0 m height. The calculated speed at point B is 96 m/s, leading to a height at point C of 0.457 km, which raises concerns about its accuracy based on the diagram. Participants clarify that point C should be higher than point A since the velocity at C is less than at A, indicating the coaster has ascended past its initial height. The calculations and reasoning emphasize the importance of understanding energy conservation in determining heights in roller coaster dynamics.
LiveEz
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Homework Statement


Assuming no friction or air resistance, calculate the height at C if at point A, the roller coaster had a speed of 20 m/s, and height of 0.45 km. The height at point B is 0 m. The speed at C is 15.6m/s.

So basically the roller coaster starts from A which is 0.45 Km high and moves forward (down) with a speed of 20m/s and the roller coaster dips down to point B where the height is 0 m. Then the roller coaster goes up to point C.

Homework Equations


Eti = Etf (Initial mechanical energy = final mechanical energy)
Ek = mv^2/2
Eg= mgh
g= 9.80 m/s^2

The Attempt at a Solution



I used the the law of mechanical energy equation and had to find the velocity of point B to move on to find the height of point c.
So using the given information and the equations, I found that the velocity at point B is 96 m/s (rounded to significant digits)and using the velocity of Point B and the other information given I was able to determine that the height is 0.457 km a point C.

But... the height for point c seems wrong according the diagram.
I could be wrong but I think point c should be less than the height of point A, according to the diagram.
 
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LiveEz said:
But... the height for point c seems wrong according the diagram.
I could be wrong but I think point c should be less than the height of point A, according to the diagram.
I haven't checked your calculations, but why would you think that point C should be lower than point A? I assume point C is meant to be the highest point reached by the coaster?
 
Conservation of energy

1/2mv^2 + mgh = 1/2mv^2 + mgh

you can drop the mass out since the mass is constant. thus,

1/2v1^2 + gh1 = 1/2v2^2 +gh2

Use a and b to find the speed at b, and then b and c to find the height at c
 
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