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Finding Force and Velocity of Block Mass

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A mass M= 2.5 kg is initially distance H= 1.8 m above a relaxed spring whose force constant k is unknown. The length of the spring is A= .84 m. The mass, released at rest, falls on and compresses the spring to final length B= .25 m in stopping. See attachment for diagram.

a. By applying conservation of energy, find the force constant of the spring.
b. Find the velocity of the mass as it first contacts the spring.
c. Find the velocity, v, of the still moving mass when the spring has been compressed to half of its final compression.

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Provides steps necessary to determine force and velocity.

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a. Between initial position at rest and final position at rest, the block loses potential energy by descending distance (H + A - B). The spring gains potential energy by compressing a distance (A - B). Although the block initially gains speed (and kinetic energy) it loses it again in stopping. Equating energy loss to energy gain, in terms of parameters gives:
(1) M g (H + ...

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