A 19 kg box slides 4.0 m down the frictionless ramp shownin the figure , then co

Question

A 19 kg box slides 4.0 m down the frictionless ramp shownin the figure , then collides with a spring whose spring constantis 220N/m What is the maximum compression of thespring? At what compression of the spring does thebox have its maximum speed? A 19 kg box slides 4.0 m down the frictionless ramp shownin the figure , then collides with a spring whose spring constantis 220N/m What is the maximum compression of thespring? What is the maximum compression of thespring? At what compression of the spring does thebox have its maximum speed? At what compression of the spring does thebox have its maximum speed?

Explanation / Answer

The gravitational potential energy is converted completely toelastic potential energy of the spring. mgh = 1/2kx2 19kg * 9.8m/s2 * 4m (assuming 4m is the actualheight and not the length of the ramp) = 1/2 * 220N/m*x2 (744.8N/110N/m) = 2.602m At the moment the spring starts to compress, the block beginsto slow down, so the block would have its maximum speed when thecompression is 0m. (744.8N/110N/m) = 2.602m At the moment the spring starts to compress, the block beginsto slow down, so the block would have its maximum speed when thecompression is 0m.

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