An object with mass m = 1kg is connected to a horizontal spring with spring cons

Question

An object with mass m = 1kg is connected to a horizontal spring with spring constant k = 500N/m and equilibrium position at x0 = 10cm (for x > x0, the force is directed toward the origin). The object is initially held at rest at position x = 15cm. You grab the object and move it slowly to position x = 30cm. For the questions below, assume the object begins at rest at 15cm, and finishes at rest at 30cm.

(a)]How much work did you do on the object?

(b)How much work does the spring do on the object, if the spring is not in the system?

(c)What is the total work done on the block, if the person and spring are not in the system?

Explanation / Answer

a) change in spring's P.E. = k (xf^2 - xi^2 ) /2

     xf is distance of final position w,r,t x0   = 30 -10 = 20 cm = 0.2 m

   xi is distance of initial position w,r,t x0 = 15 = 10 = 5 cm = 0.05 m

gain in P.E. = 500 x (0.2^2 - 0.05^2 ) /2 = 9.375 J

change in K.E. = 0

so work done by you = 9.375 J

b) work done by spring = - 9.375 J

C)total work done = change in K.E. = 0

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