How Do You Calculate Energy and Speed of a Roller Coaster at Different Points?

[Amjad1112]

Homework Statement

A 4.0X10⁴ (or 40,000) Kg roller coaster starts from rest at point A. Neglecting friction, calculate its potential energy relative to the ground, its kinetic energy and speed at points B, C, and D.

http://img189.imageshack.us/img189/6162/1234q.png
(scanned Image, if you can't see the first number its 54 m)
The answers are given =
Point B:
E_k = 1.5x10⁷ J
E_g = 5.9x10⁶ J
V = 28 m/s
Point C:
E_k = 2.4x10⁶ J
E_g = 1.8x10⁷ J
V = 11 m/s
Point D:
E_k = 7.2x10⁶ J
E_g = 1.4x10⁷ J
V = 19 m/s

Homework Equations

Gravitational Potential Energy = Mass X Gravity X height or E_g= M X g X h
Kinetic Energy = 1/2 MV² or Ek= 0.5 X M X V²
Total Energy = Gravitational Potential Energy + Kinetic Energy Or E_T= E_g + E_k

The Attempt at a Solution

OK so i got Point B right
But the problem is point C

Point A: is the Total energy so to get it
E_g= 40,000 X 9.81 X 54
E_k = 0 Because its at rest
E_t= E_g + E_k
E_t = 21189600

Point B:
E_g= 40,000 X 9.81 X 15
E_g= 5886000 Or 5.9x10⁶ Which is the answer they gave us
E_k= 21189600 - 5886000
E_k= 15303600 or 1.5x10⁷ Which is also the right answer
E_k= 1/2 MV²
15303600=(0.50)(40,000) V₂
765.18 = V²
27.6 = V or 28 Which is the right answer

Point C:
E_g= 40,000 X 9.81 X 47
E_g= 18442800 or 1.8x10⁶ Which is the right answer
E_k= E_T - E_g
E_k= 21189600 - 18442800
E_k= 2746800 or 2.7x10⁶ Which is WRONG because the answer is 2.4x10⁶

What do you think?

 

[Doc Al]

Point C:
E_g= 40,000 X 9.81 X 47
E_g= 18442800 or 1.8x10⁶ Which is the right answer
E_k= E_T - E_g
E_k= 21189600 - 18442800
E_k= 2746800 or 2.7x10⁶ Which is WRONG because the answer is 2.4x10⁶

What do you think?

Your answer looks correct to me.