Новое решение
en/6.5.24.md
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| + | ### Statement | ||
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| + | $6.5.24.$ [Insert the problem statement] | ||
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| + | ### Solution | ||
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| + | By folding an isosceles right triangle in half, its new linear dimension is $1/\sqrt2$ of its original dimension. If the electrical potential energy of the original charged triangle is $U$, then the potential energy of the new triangle is $\sqrt2U$, because potential energy varies inversely with distance while the total charge remains the same. Thus, the work done in the first folding is $A=\sqrt2U-U$. If the new triangle is folded once more, then the potential energy of the last triangle is $(\sqrt2)^2U$, and the work done in the second folding is $(\sqrt2)^U-\sqrt2U=\sqrt2A$. | ||
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| + | #### Answer | ||
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| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $6.5.24.$ [Insert the problem statement] | |||
| ### Solution | |||
| By folding an isosceles right triangle in half, its new linear dimension is $1/\sqrt2$ of its original dimension. If the electrical potential energy of the original charged triangle is $U$, then the potential energy of the new triangle is $\sqrt2U$, because potential energy varies inversely with distance while the total charge remains the same. Thus, the work done in the first folding is $A=\sqrt2U-U$. If the new triangle is folded once more, then the potential energy of the last triangle is $(\sqrt2)^2U$, and the work done in the second folding is $(\sqrt2)^U-\sqrt2U=\sqrt2A$. | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||