# Calculating potential energy

• Tmtamrak
In summary, the roller-coaster car, with a mass of 800 kg, moves from point A to point B which is 135 ft away at a 40.0° angle below the horizontal. The potential energy of the system is calculated using the formula GPE = mgy cos theta, where m is the mass, g is the acceleration due to gravity, y is the height, and theta is the angle below the horizontal. However, when the angle is zero degrees, the height change is 9.6m and the potential energy of the system is 322,616J. This is different from the original calculation and shows the importance of considering the angle in the formula.

#### Tmtamrak

A 800 kg roller-coaster car is initially at the top of a rise, at point A. It then moves 135 ft, at an angle of 40.0° below the horizontal, to a lower point B.
(a) Choose the car at point B to be the zero configuration for gravitational potential energy of the roller coaster-Earth system. Find the potential energy of the system when the car is at points A and B, and the change in potential energy as the coaster moves.

GPE = mgy cos theta

This is my attempt to solve, however I keep getting that my answer is wrong.
(800kg)(9.8)(41.15m)x cos 40 =247,138.19J

Can someone please let me know what is incorrect in my process?

Tmtamrak said:
A 800 kg roller-coaster car is initially at the top of a rise, at point A. It then moves 135 ft, at an angle of 40.0° below the horizontal, to a lower point B.
(a) Choose the car at point B to be the zero configuration for gravitational potential energy of the roller coaster-Earth system. Find the potential energy of the system when the car is at points A and B, and the change in potential energy as the coaster moves.

GPE = mgy cos theta

This is my attempt to solve, however I keep getting that my answer is wrong.
(800kg)(9.8)(41.15m)x cos 40 =247,138.19J

Can someone please let me know what is incorrect in my process?

Suppose that the angle is zero degrees below the horizontal. What would be the height change?

Why is it different? Just becos.

The height changes by 9.6m...

If I do (800kg)(9.8)(41.15m) = 322,616J
.. but that is not the correct answer either.

Tmtamrak said:
The height changes by 9.6m...

If I do (800kg)(9.8)(41.15m) = 322,616J
.. but that is not the correct answer either.

0 degrees from horizontal is horizontal...