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Why does the ball in Galileo's double inclined plane experiment reach the same height? I know how to show it by energy conservation law but am unable to prove it by the equations of motion. Can anyone please help me to prove it.

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    $\begingroup$ Use $\mathbf F = m\mathbf a$, and make the dot product both sides with the allowed elementary displacement in the direction of the incline:$\mathbf F\cdot \mathbf {dr} = m\mathbf a \cdot \mathbf {dr}$. You will get the constancy of the sum of what are called kinetic and potential energy. $\endgroup$ Commented Sep 18, 2023 at 23:08

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