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

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SUMMARY

The discussion centers on a physics problem involving a 4kg bundle sliding up a 30-degree incline with an initial kinetic energy of 128J and a coefficient of kinetic friction of 0.3. The user initially calculated the distance the bundle would slide as 12.6m using the equation d = 128 / (μmg cos θ). However, the correct distance is 4.3m, indicating a miscalculation in accounting for gravitational potential energy in the energy conservation equation. The user overlooked the work done by gravity, which must be included in the energy balance.

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  • Understanding of Newton's laws of motion
  • Familiarity with the concepts of kinetic energy and gravitational potential energy
  • Knowledge of friction and its coefficient
  • Basic algebra for rearranging equations
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  • Study the effects of friction on motion along inclined planes
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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 + [tex]\mu[/tex]F_f = 0
128 - [tex]\mu[/tex]mg cos [tex]\theta[/tex] d = 0

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

and d = 12.6m

however, the answer is 4.3m, did I mess up any steps above?
 
Last edited:
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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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