Energy Equation for a Roller Coaster on a Full Circular Loop

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SUMMARY

The energy equation for a roller coaster moving through a full circular loop involves the conservation of mechanical energy, expressed as KA + UA = KB + UB. At the top of the loop (point B), the roller coaster retains kinetic energy if it has sufficient speed from point A. The correct gravitational potential energy equation is Ug = mgh, not Ug = 1/2(mgh) as initially stated. Understanding these principles is crucial for accurately determining the kinetic energy at various points along the roller coaster's path.

PREREQUISITES
  • Understanding of kinetic energy (KE) and gravitational potential energy (PE) equations.
  • Familiarity with the concept of mechanical energy conservation.
  • Basic knowledge of physics principles related to motion and forces.
  • Ability to perform calculations involving mass, height, and velocity.
NEXT STEPS
  • Study the principles of mechanical energy conservation in physics.
  • Learn how to calculate kinetic energy using the equation KE = 1/2m(v^2).
  • Explore gravitational potential energy calculations with Ug = mgh.
  • Investigate the effects of speed and height on roller coaster dynamics.
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in the dynamics of roller coasters and energy conservation principles.

Np14
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Homework Statement


What is the energy equation for a roller coaster already in motion from the ground with to the top of a full circular loop = point B in the image. My question is would the car still have kinetic energy at the top of the loop?

Homework Equations


Kinetic Energy Equation 1/2m(v^2), Gravitational Potential Energy Equation Ug = 1/2(mgh)

The Attempt at a Solution


This is a yes or no question, I don't know what work I can really show.

The equation I figured out: K = Ug + K
Not sure if it is correct please help.
 

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To answer "yes" or "no" you need to show some work, namely a calculation of the kinetic energy at point B. For that you will need the kinetic energy at point A. Do you know (or have information) what it is? Also, the equation you figured is incorrect. Mechanical energy conservation means that the kinetic + potential at point A is the same aas kinetic + potential at point B.
KA + UA = KB + UB.
 
Last edited:
Np14 said:

Homework Statement


What is the energy equation for a roller coaster already in motion from the ground with to the top of a full circular loop = point B in the image. My question is would the car still have kinetic energy at the top of the loop?

Homework Equations


Kinetic Energy Equation 1/2m(v^2), Gravitational Potential Energy Equation Ug = 1/2(mgh)

The Attempt at a Solution


This is a yes or no question, I don't know what work I can really show.

The equation I figured out: K = Ug + K
Not sure if it is correct please help.
First of all: The opening sentence of the problem statement is garbled as if you left out some words in one or more places.

What is the energy equation for a roller coaster already in motion ?⋅?⋅?⋅?⋅? from the ground with ?⋅?⋅?⋅?⋅? to the top of a full circular loop = point B in the image.​

upload_2019-2-8_7-17-38.png


Above is the screen shot of a 2× enlargement of the image you uploaded . (The combination of enlargement and of using a screen shot makes it a little fuzzy.)

In addition to that, you have have an incorrect expression for Gravitational Potential Energy. The correct expression is: Ug = mgh .

Beyond that:
I entirely agree with (Dr.) @kuruman's comments.

.
 

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