Energy conservation of a child on a swing

AI Thread Summary
The maximum speed of a child on a swing is 4.9 m/s, with a height of 0.7 m at the lowest point. The discussion focuses on calculating the height at the highest point of the swing using energy conservation principles. There is confusion regarding the cancellation of terms in the equations used, specifically whether gravitational acceleration (g) cancels out. It is clarified that while mass (m) cancels across all terms, g only cancels in terms where it appears. The resolution emphasizes the importance of correctly applying energy conservation in the context of the swing's motion.
mikefitz
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The maximum speed of a child on a swing is 4.9 m/s. The child’s height above the ground at the lowest point is 0.7 m. How high above the ground is he at his highest point?
http://img208.imageshack.us/img208/9949/untitledyx0.png

Above is the work done to solve the problem. I don't understand how they went from the blue to the red equation. Wouldn't the two g's cancel out since you would need to divide the left side by mg?
 
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mikefitz said:
Wouldn't the two g's cancel out since you would need to divide the left side by mg?
You divide all terms by mg. The m's all cancel, since an m appears in all three terms. But g's only cancel in the two terms that had g's--the KE term does not have a g to cancel.
 

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