Kinetic energy efficiency question

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Homework Help Overview

The problem involves a roller coaster descending from a height of 55m and converting gravitational potential energy to kinetic energy with an efficiency of 50.0%. The original poster seeks to determine the velocity of the roller coaster at the bottom of the first low point.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between gravitational potential energy and kinetic energy, with some questioning how to apply the efficiency equation to find velocity. Others mention the need to consider the kinetic energy formula and conservation of energy principles.

Discussion Status

The discussion is active, with participants providing insights into the relationships between energy forms and efficiency. Some guidance has been offered regarding the application of energy equations, but no consensus has been reached on a specific method to find the velocity.

Contextual Notes

There is an indication that the original poster may have omitted necessary details in their initial post, which could affect the ability to provide assistance. The discussion also highlights the 50% energy loss due to efficiency, which is a critical aspect of the problem.

13physicsdude
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Homework Statement



A roller coaster descends 55m from the top of the first high point to the first low point in the track. The roller coaster converts gravitational potential energy to kinetic energy with an efficiency of 50.0%. What is the velocity of the roller coaster at the bottom of the first low point?

Homework Equations



Efficiency= (Eout/Ein)100%

The Attempt at a Solution



I have no clue how to do it! I don't understand how to use the efficiency equation to get velocity, please help!
 
Last edited:
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13physicsdude said:

The Attempt at a Solution


You forgot to fill out this part, you'll need to before we can help you :wink:
 
Ein is gravitational potential energy, Eout is kinetic energy. Take into account the formula for kinetic energy, mv^2/2.
 
then .5mgh=.5mv^2 then v=(gh)^(.5) solve to get
 
Using conservation of energy, the energy of roller coaster+earth system is conserved, in an ideal case, i.e. change in potential energy = change in kinetic energy. However, in this case there is 50% loss of energy, i.e. only half of the potential energy change equals the kinetic energy change. I think you have your answer now! :)
 

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