The drawing shows three situations in which a block is attached to a spring. The

Question

The drawing shows three situations in which a block is attached to a spring. The position labeled "0 m" represents the unstrained position of the spring. The block is moved from an initial position x0 to a final position xf, the magnitude of the displacement being denoted by the symbol s. Suppose the spring has a spring constant of k = 46.0 N/m.Using the data provided in the drawing, determine the total work done by the restoring force of the spring for each situation.

(a) W=

(b) W=

(c) W=

Explanation / Answer

Upon examination of the diagrams, it is apparent that the work done by the spring's restoring force can be either 1) Positive or 2) Negative.
1) Work is Positive when spring force is the SAME direction
as the block's DISPLACEMENT (s).
and
2) Work is Negative when spring force in OPPOSITE the block's DISPLACEMENT(s)

also
the Work done is based on the differences in spring potential energy = SPE

For Diagram (a):
SPE at 1 m = 1/2kx² = (0.5)(46)(1)² = 23 J
SPE at 3 m = 1/2kx² = (0.5)(46)(3)² = 207 J
SPE = 207 - 23 = 184 J
apply logic: block displacement is to the RIGHT but spring force is to the LEFT.
therefore NET work done by spring force is Negative = -184 J ANS (a)

For Diagram (b):
SPE at 3 m = 207 J {from part a}
SPE at 1 m = 23 J {from part a}
SPE = 207 - 23 = 184 J
apply logic: block displacement is to the RIGHT, spring force is to the RIGHT up to 0,
thereafter, it is to the LEFT. So 184J is Positive Work and 38 J is Negative work.
NET work done by spring force = 207- 23 = +184 J ANS (b)

For Diagram (C):
SPE at 3 m = 1/2kx² = (0.5)(46)(3)² = 207 J
SPE at 3 m = 1/2kx² = (0.5)(46)(3)² = 207 J
SPE = 207 - 207 = 0 J

NET work done by spring force = 0

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