Question

A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 1.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, it experiences a maximum acceleration of 16 m/s2

find the value of spring constant

find value of the mass

Answer 1

force=ma=kx

k= m*a/x

but work= 1/2 kx^2
k=2*work/x^2

Use the second first to get k, then

a=kx/m

Answer 2

2(1)/.12^2=138.88888888889=138.9N/m
F=kx = mg=kx => ma=kx => m=kx/a
(138.9(.12))/16 = 1.04kg