A mass resting on a horizontal, frictionless surface is attached to one end of a

Question

A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.4 J of work to compress the spring by 0.14 m. If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 12 m/s^2. Find the value of the spring constant. Express your answer to two significant figures and include the appropriate units. Find the value of the mass. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

a)

workdone = energy =1/2*K*x_max^2

3.4=1/2*k*0.14^2

==>

K=346.94 N/m

b)

a_max=w^2*x_max

12=w^2*0.14

==> w=9.26 rad/sec

now,

1/2*k*x_max^2=1/2*m*v_max^2

3.4=1/2*m*(w*x_max)

3.4=1/2*m*(9.26*0.14)

===> mass, m=5.24 kg

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