a 15g bullet is fired at 840 m/s into a penullum consisting of a 24kg bag of sand. If the bag rises to a height of 80cm, how much energy is converted into thermal energy in the bag?

Emechanical=Ek + Eg
=1/2mv^2 +mgh
=1/5(0.015)(840) + 0
=5292J

Emechanical =Ek + Eg
=1/2mv^2 + mgh
=0 +(24.015)(9.8)(0.8)
=188.28

Total Emechanical = 188.28-5292
=-5103.72, which is the amount of energy convered into thermal energy.

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1. Eheat = Ek - Eg
is the formula you should have used.
Eheat is the portion of the original KE that was converted to heat

I do not understand what your "Emechanical" is, and how it could be negative.

What you call "Total Emechanical" may be the energy converted to heat, except for the minus sign.

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