A single mass (m 1 = 4.3 kg) hangs from a spring in a motionless elevator. The s

Question

A single mass (m1 = 4.3 kg) hangs from a spring in a motionless elevator. The spring constant is k = 259 N/m.

Now, three masses (m1 = 4.3 kg, m2 = 12.9 kg and m3 = 8.6) hang from three identical springs in a motionless elevator. The springs all have the same spring constant given above.

The elevator is moving downward with a velocity of v = -2.5 m/s but accelerating upward at an acceleration of a = 4.5 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)

What is the magnitude of the force the upper spring exerts on the upper mass?

Explanation / Answer

F3 - m3 g = m3 a ==> F3 = m3 (a+g) = 8.6*(4.5+9.81) = 123.066 N

F2 - F3 - m2 g = m2 a ===> F2 = 12.9*(4.5+9.81) + 123.066 = 307.665 N

F1 - F2 - m1 g = m1 a ===> F1 = 4.3*(4.5+9.81) + 307.665 = 369 N

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