9KP You push your hand against a horizontal spring, com- pressing the spring by

Question

9KP You push your hand against a horizontal spring, com- pressing the spring by 25 cm. The spring constant is 340 N/m. a) What is the elastic potential energy of the spring? You then reduce your push on the spring until it is compressed by only 18 cm. (b) What is the elastic potential energy now? (c) What was the change in elastic potential energy going from the first situation to the second situation? (d) How much work did the spring do on your hand going from the first situation to the second situation?

Explanation / Answer

(a) k = 340 N/m

x1 = 25 cm = 0.25 m

Elastic potential energy, Pi = (1/2)*k*x1^2 = 0.5*340*0.25^2 = 10.625 J

(b) x2 = 18 cm = 0.18 m

Pf = (1/2)*k*x2^2 = 0.5*340*0.18^2 = 5.508 J

(c) Change in elastic potential energy = Pi - Pf = 10.625 - 5.508 = 5.117 J

(d) Work done by the spring = Change in the potential energy = 5.117 J

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