Answered: A 3.00 ✕ 105 kg subway train is brought…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 4OQ

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A 3.00 ✕ 10⁵ kg subway train is brought to a stop from a speed of 0.500 m/s in 0.300 m by a large spring bumper at the end of its track. What is the force constant k of the spring (in N/m)?

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$D a t a' s g i v e n a r e m a s s o f t h e t r a i n; m = 3 \times 10^{5} K g i n i t i a l v e l o c i t y o f t h e t r a i n; U = 0.5 m / s F i n a l v e l o c i t y o f t h e t r a i n; V = 0 m / s d i s \tan c e c o v e r e d b e f o r e s t o p p i n g; S = 0.3 m r e t a r d a t i o n o f t h e t r a i n; a = ? a p p l y N e w t o n' s e q u a t i o n o f m o t i o n V^{2} = U^{2} + 2 a S 0 = {(0.5)}^{2} + 2 \times a \times 0.3 0 = 0.25 + 0.6 a - 0.25 = 0.6 a a = \frac{- 0.25}{0.6} = - 0.42 m / s^{2} a = - 0.42 m / s^{2}$

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