A 1.5-kg box that is sliding on a frictionless surface with a speed of 12 m/s approaches a horizontal spring. (See Figure 5.21.) The spring has a spring constant of 2000 N/m. If one end of the spring is fixed and the other end changes its position,

(a) how far will the spring be compressed in stopping the box?

(b) How far will the spring be compressed when the box’s speed is reduced to half of its initial speed?

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m 1-0000000 FIGURE 5.21 Conservative force and the mechanical energy of a spring See Example 5.13 for description.