Calculating Potential Energy Changes in a Roller Coaster System

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Homework Help Overview

The discussion centers around calculating gravitational potential energy changes in a roller coaster system, specifically analyzing the energy at two points, A and B, with point B designated as the zero potential energy reference. The problem involves understanding the implications of height changes and angles in the context of gravitational potential energy calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to calculate the gravitational potential energy using the formula GPE = mgy cos theta, but express confusion over the results. Questions arise regarding the correctness of their calculations and the impact of changing angles on height and potential energy.

Discussion Status

Several participants are sharing their calculations and questioning the accuracy of their results. There is an ongoing exploration of how different angles affect the height change and potential energy, with no clear consensus reached on the correct approach or solution.

Contextual Notes

Participants are working under the assumption that point B is the zero potential energy reference and are grappling with the implications of angle adjustments on their calculations. There is mention of a specific height change of 9.6m, but the relevance of this figure to the overall calculations is still being examined.

Tmtamrak
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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?
 
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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?

Now put zero into your formula instead of 40.

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...
 

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