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Valter edited Aug 30, 2026, 7:49 PM

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		+	### Statement
		+
		+	$2.3.15.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	### Statement
		+
		+	$2.3.15.$ What minimum work must be done to raise a long uniform pole of length $l$ and mass $m$ lying on the ground to a vertical position?
		+
		+	### Solution
		+
		+	For a uniform pole, its center of mass is located exactly in the middle. When lying on the ground, the height of its center of mass is $0$. When placed vertically, the center of mass is raised to a height of $h = \frac{l}{2}$.
		+
		+	The minimum work done is equal to the increase in the potential energy of the center of mass:
		+	$$A = mgh = mg\frac{l}{2}$$
		+
		+	#### Answer
		+	$$A = mg\frac{l}{2}$$
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$2.3.15.$ [Insert the problem statement]

			### Solution

			### Statement

			$2.3.15.$ What minimum work must be done to raise a long uniform pole of length $l$ and mass $m$ lying on the ground to a vertical position?

			### Solution

			For a uniform pole, its center of mass is located exactly in the middle. When lying on the ground, the height of its center of mass is $0$. When placed vertically, the center of mass is raised to a height of $h = \frac{l}{2}$.

			The minimum work done is equal to the increase in the potential energy of the center of mass:
			$$A = mgh = mg\frac{l}{2}$$

			#### Answer
			$$A = mg\frac{l}{2}$$

			#### Answer

			[Insert a concise answer or boxed result]