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27 March, 19:01

A 57 g ice cube can slide without friction up and down a 33 ∘ slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 12 cm. The spring constant is 20 N/m. When the ice cube is released, what distance will it travel up the slope before reversing direction?

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  1. 27 March, 22:32
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    The springs stored energy is transferred to the cube as kinetic energy and then by the slop the KE is converted to height energy.

    0.5. k. x^2 = 0.5. m. v^2 = m. g. ∆h

    0.5. 50. (0.1^2) = 0.05. 9.8. ∆h

    ∆h = 0.51 m = 51 cm

    This is the height gained

    Distance along the slope = ∆h / sin 60 = 0.589 = 59 cm

    In the second case, the stored spring energy is converted into height energy AND frictional heat energy.

    The height energy is m. g. d sin 60 where d is the distance the cube moves along the slope.

    The Frictional energy converted is F. d

    F (the frictional force) = µ. N

    N (the reaction to the component of the gravity force perpendicular to the surface of the slope) = m. g. cos60

    Total energy converted

    0.5. k. x^2 = (m. g. dsin60) + (µ. m. g. cos60. d)

    Solve for d

    d = 0.528 = 53 cm
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