Car moving up Inclined Plane question

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SUMMARY

The discussion focuses on calculating the work done by a force on a car moving up an inclined plane, specifically addressing the relationship between potential energy (PE), kinetic energy (KE), and energy lost to friction. The user proposes that the total work done equals the sum of PE, the change in KE, and the energy lost to friction. However, they express uncertainty about how to quantify the energy lost to friction, particularly in terms of its conversion to heat. The key takeaway is the need to accurately account for frictional forces when analyzing energy expenditure in inclined plane scenarios.

PREREQUISITES
  • Understanding of potential energy (PE) and kinetic energy (KE) concepts
  • Familiarity with work-energy principles in physics
  • Knowledge of friction and its effects on motion
  • Basic mathematical skills for calculating forces and distances
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  • Research the calculation of energy lost to friction in inclined planes
  • Study the work-energy theorem and its applications
  • Explore methods for measuring heat energy generated by friction
  • Learn about different types of friction (static, kinetic) and their implications in physics problems
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Students studying physics, educators teaching mechanics, and anyone interested in understanding the dynamics of objects on inclined planes.

Ronaldo95163
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My question and attempted solution are in the pics below...not sure if what I did was correct though :/

I was thinking that the work done would have been equal to PE+Change in KE + Energy Lost to friction...but not sure how to calculate the energy lost to friction as I'm not sure if it has to be calculated in a specific form eg heat
 

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Work performed by a force = magnitude of the force x distance moved in the precise direction of that force. The energy expended will probably mostly end up as heat, but that is not important here.
 

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