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 Hight 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.

 

[nlightner]

Your approach to solving this problem is correct, but you may have made a calculation error when finding the kinetic energy at point C. Double check your calculations to make sure you are using the correct values for mass and velocity. Also, make sure you are using the correct units for energy (Joules) in all of your calculations. If you are still having trouble, try plugging in the given answer for kinetic energy at point C (2.4x106 J) into the equation Ek = 0.5 x M x V2 and solve for the velocity. This should give you the correct answer for the speed at point C.