Mechanical energy into thermal energy

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SUMMARY

The discussion centers on calculating the maximum speed of a roller coaster with a height of 94.5 meters and determining the percentage of mechanical energy lost to thermal energy due to friction. The theoretical maximum speed is calculated to be 43.1 m/s, while the actual maximum speed observed is 4.1 m/s, resulting in an energy loss of 8.9%. The key formula used is Wnc = Efinal - Einitial, where Efinal is kinetic energy (Ek) and Einitial is gravitational potential energy (Eg).

PREREQUISITES
  • Understanding of gravitational potential energy (Eg) and kinetic energy (Ek)
  • Familiarity with the work-energy principle
  • Basic algebra for percentage calculations
  • Knowledge of friction's impact on mechanical systems
NEXT STEPS
  • Study the work-energy theorem in detail
  • Learn how to calculate energy losses in mechanical systems
  • Explore the effects of friction on roller coaster dynamics
  • Investigate the principles of energy conservation in physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy transformations, as well as educators seeking to explain concepts related to energy loss in mechanical systems.

anna sung
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Homework Statement


the roller coaster is 94.5m high at its highest point. what is the maximum possible speed of the roller coaster? the roller coaster's actual maximum speed is 4.1m/s.what percentage is lost to thermal energy due to friction?

Homework Equations


Wnc= Efinal-Eintial
the part i didnt get is highlighted in red.
please help me


The Attempt at a Solution


Wnc= Efinal- Eintial
Efinal= Ek
Einitial=Eg
after i got the numbers i said (Wnc/Einitial)*100 to get the percentage. but it did not get me to the answer.
the answer on the book is = 8.9%
and its maximum speed is = 43.1 m/s
 
Physics news on Phys.org
divide Wnc by the energy that it should've had (with the 43.1 m/s velocity, .5m(43.1)^2)
and then multiply by 100
 

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