A spring and block are in the arrangement of the figure below. Whenthe block is

Question

A spring and block are in the arrangement of the figure below. Whenthe block is pulled out to x = +4.5 cm, we must apply a force of magnitude360 N to hold it there. We pull the blockto x = +14.0 cm and then release it. (a) A spring in its relaxed state. The originof an x axis has been placed at the end of the spring thatis attached to a block. (b) The block is displaced by Vector d , and the spring isstretched by a positive amount x. Note the restoring force Vector F s exerted bythe spring. (c) The spring is compressed by a negative amount x.Again, note the restoring force. For each of the following, find how much work the spring does onthe block when the block moves from the first point given to thesecond point given (a) xi = 9.0 cm to x = 3.5cm 1 J (b) xi = 9.0 cm tox = -3.5 cm 2 J (c) xi = 9.0 cm tox = -9.0 cm 3 J (d) xi = 9.0 cm tox = -14.0 cm 4 J

Explanation / Answer

Since there is no friction force, the work done by the springequal to the change in potential: W = V = 1/2 k(x22-x12) When we pull to x = 4.5 cm, we need the force 360 N ==> k =360/0.045 = 1333 N/m (a) xi = 9.0 cm to x = 3.5cm
W = 4.58 J

(b) xi = 9.0 cm tox = -3.5 cm
W=4.58 J

(c) xi = 9.0 cm tox = -9.0 cm
W = 0 J

(d) xi = 9.0 cm tox = -14.0 cm
W = -7.67 J (a) xi = 9.0 cm to x = 3.5cm
W = 4.58 J

(b) xi = 9.0 cm tox = -3.5 cm
W=4.58 J

(c) xi = 9.0 cm tox = -9.0 cm
W = 0 J

(d) xi = 9.0 cm tox = -14.0 cm
W = -7.67 J

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