Did I Make an Error in My Conservation of Energy Calculation?

AI Thread Summary
The discussion revolves around a calculation of how far a 4kg bundle will slide up a 30-degree incline with an initial kinetic energy of 128J and a coefficient of kinetic friction of 0.3. The user initially applies the conservation of energy principle but overlooks the gravitational potential energy change as the bundle ascends the incline. The correct approach requires accounting for both the work done against friction and the increase in gravitational potential energy. After correcting for these factors, the calculated distance should be 4.3m instead of the initially computed 12.6m. The error highlights the importance of including all forms of energy in conservation calculations.
leolaw
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So this is the quaiton that i have problem w/:
A 4kg bundle starts up a 30 degree incline with 128J of kinetic energy. How far willl it slide up the incline if the coefficient of kinetic friction between bundle and incline is 0.3?

Because E_initial + Work = E_final and the Work done in the system in this problem is just the fricition force, so I have
128 + \muF_f = 0
128 - \mumg cos \theta d = 0

since that d is what we are looking for, rearranging this equation gives me:
128 / (\mumg cos \theta) = d

and d = 12.6m

however, the answer is 4.3m, did I mess up any steps above?
 
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Don't forget that gravity also does work on the object. (Or, alternatively, make sure that energy includes both kinetic and gravitational PE.)
 
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