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For part (a), ${x}_{A}=0$ and ${x}_{B}=6\text{cm}$ ; for part (b), ${x}_{B}=6\text{cm}$ and ${x}_{B}=12\text{cm}$ . In part (a), the work is given and you can solve for the spring constant; in part (b), you can use the value of k , from part (a), to solve for the work.
Check Your Understanding The spring in [link] is compressed 6 cm from its equilibrium length. (a) Does the spring force do positive or negative work and (b) what is the magnitude?
a. The spring force is the opposite direction to a compression (as it is for an extension), so the work it does is negative. b. The work done depends on the square of the displacement, which is the same for $x=\pm 6\phantom{\rule{0.2em}{0ex}}\text{cm}$ , so the magnitude is 0.54 J.
Give an example of something we think of as work in everyday circumstances that is not work in the scientific sense. Is energy transferred or changed in form in your example? If so, explain how this is accomplished without doing work.
When you push on the wall, this “feels” like work; however, there is no displacement so there is no physical work. Energy is consumed, but no energy is transferred.
Give an example of a situation in which there is a force and a displacement, but the force does no work. Explain why it does no work.
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