Kinetic energy efficiency question

AI Thread Summary
A roller coaster descends 55 meters, converting gravitational potential energy to kinetic energy with an efficiency of 50%. To find the velocity at the bottom, the potential energy lost must equal half of the initial potential energy due to the efficiency loss. The kinetic energy formula, mv²/2, is used to relate the energies, leading to the equation v = (gh)^(1/2). By applying conservation of energy principles, the effective kinetic energy is calculated as half of the potential energy change. This method provides a clear path to determine the roller coaster's velocity at the low point.
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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