One end of an unstretched spring of stiffness constant k 1 is attached to the ce

Question

One end of an unstretched spring of stiffness constant k1 is attached to the ceiling of an elevator, and a 1.50 kg mass is connected to the other end. The ends of another unstretched spring of stiffness constant k2 are attached to the bottom of the mass and to the floor of the elevator as shown below. When the mass is released, the top spring stretches 40.0 cm and bottom spring is compressed by this same amount. When the elevator accelerates upward, the top spring stretches an additional 8.00 cm.

(a) What is the elevator's acceleration?

Explanation / Answer

Mass = 1.5kg Since the spring K1 stretches 40cm when the mass is released. We know F = 1/2kx = mg = 14.7N To produce 8cm of stretch, the force must be 40cm/8 = 5 1/5 of the original force = 2.94N F=ma 2.94 = ma 1)a = 1.96m/s 2)To stretch 52cm, the force must be 19.11N F = ma 19.11 = ma a = 12.74m/s

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