Physics Practice Problems Springs & Elastic Potential Energy Practice Problems Solution: An experimental apparatus with mass m is placed on...

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Solution: An experimental apparatus with mass m is placed on a vertical spring of negligible mass and pushed down until the spring is compressed a distance exttip{x}{x}. The apparatus is then released and reaches its maximum height at a distance h above the point where it is released. The apparatus is not attached to the spring, and at its maximum height it is no longer in contact with the spring. The maximum magnitude of acceleration the apparatus can have without being damaged is exttip{a}{a}, where a > g.What should the force constant of the spring be?What distance exttip{x}{x} must the spring be compressed initially?

Problem

An experimental apparatus with mass m is placed on a vertical spring of negligible mass and pushed down until the spring is compressed a distance . The apparatus is then released and reaches its maximum height at a distance h above the point where it is released. The apparatus is not attached to the spring, and at its maximum height it is no longer in contact with the spring. The maximum magnitude of acceleration the apparatus can have without being damaged is , where a > g.

What should the force constant of the spring be?

What distance must the spring be compressed initially?