Question

A pen contains a spring with a spring constant of 216 N/m. When the tip of the pen is in its retracted position, the spring is compressed 4.60 mm from its unstrained length. In order to push the tip out and lock it into its writing position, the spring must be compressed an additional 6.90 mm. How much work is done by the spring force to ready the pen for writing? Be sure to include the proper algebraic sign with your answer.

Answer 1

k = 216 N/m

spring compression Xi = 4.6 mm = 4.6*10^-3 m

additional  compression Xf = 6.9 + 4.6 mm = 11.5*10^-3 m

Work done = change in spring potential energy

= 1/2*k*Xf ^2 - 1/2*k*Xi^2 = 1/2*k* ( Xf ^2 -Xi ^2 )

= 1/2*216*0.0115^2 - 0.0046^2 )

=0.01199772 J = 11.9977*10^-3 J

work done by spring force = - 11.9977*10^-3 J answer

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