University Physics with Modern Physics with Mastering Physics (11th Edition)

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7.76: The kinetic energy K after moving up the ramp the distance s will be the energy initially stored in the spring, plus the (negative) work done by gravity and friction, or . ) cos (sin 2 1 k 2 s mg kx K α μ + - = Minimizing the speed is equivalent to minimizing K , and differentiating the above expression with respect to
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Unformatted text preview: and setting = ′ d K d gives ), sin (cos k--= mgs or k 1 tan = , = k 1 arctan . Pushing the box straight up ) 90 ( ° = maximizes the vertical displacement h , but not sin h s = ....
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