Calculating Potential Energy Changes in a Roller Coaster System

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SUMMARY

The discussion focuses on calculating gravitational potential energy (GPE) changes in a roller coaster system, specifically for an 800 kg roller-coaster car moving from point A to point B. The formula used is GPE = mgy cos(theta), where m is mass, g is gravitational acceleration (9.8 m/s²), and y is the vertical height. The user attempts to calculate GPE at both points but encounters errors in their calculations, particularly in determining the height change, which is confirmed to be 9.6 m. The correct GPE at point A is 322,616 J, while the change in potential energy needs to be accurately derived from the correct height difference.

PREREQUISITES
  • Understanding of gravitational potential energy concepts
  • Familiarity with trigonometric functions, particularly cosine
  • Knowledge of unit conversions, specifically feet to meters
  • Basic physics principles related to energy conservation
NEXT STEPS
  • Review the calculation of gravitational potential energy using GPE = mgh
  • Learn about unit conversion techniques between imperial and metric systems
  • Study the application of trigonometric functions in physics problems
  • Explore energy conservation principles in mechanical systems
USEFUL FOR

Physics students, educators, and anyone interested in understanding energy calculations in mechanical systems, particularly in the context of roller coasters and similar applications.

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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