Comparison of compression of spring in a moving elevator as it moves with constant velocity in upward and downward. Solution: Compression in spring is same in both cases either elevator is moving upward or downward with constant velocity. Explanation: Given: Case A: When elevator is moving upward with constant velocity. Case B: When elevator is moving downward with constant velocity. Formula used: ∑ F e x t e r n a l = m a a n d F s p r i n g = − k x Where, ∑ F e x t e r n a l : N e t e x t e r n a l f o r c e m = Mass a = Acceleration k = Spring constant x = Compression or elongation in spring Calculation: Case A: Here a diagram has been shown which depicts a man on weighing machine placed in an elevator which is moving with constant velocity in upward direction. Now, free body diagram of man has been shown; As velocity is constant, acceleration is zero. Write the equation from free body diagram of man; ∑ F = m a N − m g = m a N : Normal reaction force Add m g in both side; N − m g = m * 0 N − m g = 0 N = m g (1) Case B: Here a diagram has been shown which depicts a man on weighing machine placed in an elevator which is accelerating with acceleration a in upward direction. Now, free body diagram of man has been shown Write the equation from free body diagram of Man; ∑ F = m a m g − N = m a N = m g − m a N = m g − m * 0 N = m g (2) Compression in spring is directly proportional to normal reaction force ( N ) . Comparing equation 1 a n d 2 , Normal reaction force in both Case A and Case B is same. Therefore, Compression in both case A and B will be same. Conclusion: Normal reaction gives the weight. If elevator moves upward and downward with constant velocity, then normal reaction force is same and equal to weight of man when it is at rest. Compression of spring in both case will be same.

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