Car moving up Inclined Plane question

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The discussion revolves around calculating the work done by a car moving up an inclined plane, focusing on the relationship between potential energy (PE), kinetic energy (KE), and energy lost to friction. The original poster is uncertain about the correct approach to include friction in their calculations, particularly whether it should be expressed in terms of heat. They emphasize that the work performed by a force is determined by the force's magnitude and the distance moved in its direction. The conversation highlights the complexities of energy transformations in this scenario. Overall, the key concern is accurately accounting for energy losses due to friction in the calculations.
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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