A 7.2-kg mass is hanging from the ceiling of an elevator by a spring with spring

Question

A 7.2-kg mass is hanging from the ceiling of an elevator by a spring with spring constant k = 150N/m whose unstretched length is 80 cm. What is the overall length of the spring when elevator:
• (a) starts moving upward with acceleration a = 0.95m/sec2?
• (b) moves upward at a steady velocity v = 14 m/sec?
• (c) comes to a stop while moving upward at v = 14 m/sec, taking 9 sec. to do so?
• (d) if the elevator measures 3.2 m from floor to ceiling, what is the maximum
acceleration it could undergo without 7.2-kg mass hitting the floor?

Explanation / Answer

a) 7.2 * 0.95 = 150*x x = 0.0456m expansion overall length = 80+4.56 = 84.56m b) no extra elongation or compression because their is no acceleration overall length = 80cm c) a = 14/9 = 1.555m/sec^2 in the downward direction 7.2 * 1.555 = 150*x x = 0.07464m compression overall length = 80-7.464 = 72.536cm d) 3.2*150 = 7.2a a = 66.666 m/sec^2

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