One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance $h$ above the floor. A block of mass $M$ is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance $x$. The block is released and strikes the floor a horizontal distance $D$ from the edge of the table. Air resistance is negligible. Derive expressions for the following quantities only in terms of $M$, $x$, $D$, $h$, and any constants.

Question

One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance $h$ above the floor. A block of mass $M$ is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance $x$. The block is released and strikes the floor a horizontal distance $D$ from the edge of the table. Air resistance is negligible. Derive expressions for the following quantities only in terms of $M$, $x$, $D$, $h$, and any constants.(a) The time elapsed from the instant the block leaves the table to the instant it strikes the floor.
, (b) The horizontal component of the velocity of the block just before it hits the floor.
, (c) The work done on the block by the spring.
, (d) The spring constant.
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Jason · Accepted Answer

$t = \sqrt{\dfrac{2h}{g}}$
$v_x = D \sqrt{\dfrac{g}{2h}}$
$W = \dfrac{M g D^{2}}{4h}$
$k = \dfrac{M g D^{2}}{2h x^{2}}$

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