A spring of negligible mass has force constant = 1500 N/m. You place the spring

Question

A spring of negligible mass has force constant = 1500 N/m.

You place the spring vertically with one end on the floor. You then drop a book of mass 1.50 onto it from a height of 0.900 above the top of the spring. Find the maximum distance the spring will be compressed.
Take the free fall acceleration to be 9.80 . Express your answer using two significant figures.

Explanation / Answer

The kinetic energy KE of the book, at impact, is converted to PE of the compressed spring. -->s = 0.5at^2 = 0.6 = 4.9t^2 --->t^2 = 0.122 --->t = 0.349 second --->Velocity = at = (9.8)(0.349) = 3.420 m/s --->KE = 0.5mv^2 = 0.75(11.70) = 8.775 J ----->Spring PE = 0.5kx^2 = 8.775 = 900x^2 --->x^2 = 0.00975 ---_>x = 0.099 meter

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