a spring of negligible mass has Ks=1600N/m. it is placed vertically with one end

Question

a spring of negligible mass has Ks=1600N/m. it is placed vertically with one end on the floor.
A, how far must the spring be compressed for 3.50j of potential energy to be stored in it?
B,a 1.20kg book is dropped from 0.80m above the top of the spring. what is its kinetic energy just before it contacts the spring?
C. what is its velocity at that point?
D. what distance will the spring be compressed from its equilibrium point? hint don't just set K=Us: there is a Ug term here also. you will have to solve a quadratic equation

Explanation / Answer

Given that the spring constant is k = 1600 N/m
The energy stored in spring is U = 3.50 J
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(a) The potential energy stored in spring is U =(1/2)kx2
                                                                 x = ( 2U / k )1/2
                                                                                           = ------- m
(b) Apply conservation of energy at maximum height at thecompression
                       mgh = (1/2)kd2 - mgd
                        kd2 - 2mgd - 2mgh = 0
                        (1600N/m)d2 - (39.2)d -35.28 = 0
           thenwe get d = 0.16 m

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