[20 pts] A 2.00 kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, horizontal surface and then up a frictionless incline with slope 37 degrees. (a) What is the speed of the block as it slides along the horizontal surface after having left the spring? (b) How far does the block travel up the incline before starting to slide back down?

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  1. For (a), assume all of the stored sproing potential energy is coinverted to kinetic energy.

    (1/2)kX^2 = (1/2)mV^2
    V = sqrt(k/m)* X
    where X (=0.22 m) is the amount of spring compression and k is the spring constant, 400 N/m.

    For (b), assume all of the initial stored potential energy is converted to gravitational potential energy.

    (1/2)kX^2 = m g x' sin 37.

    Solve for the distance x' that it slides.

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