Explanation As the car is brought to rest by a combination of two coiled spring its final kinetic energy is zero and as both the spring are at rest initially so initial elastic potential energy of both the springs is zero. Write the expression for work done by the first spring on the car. W s 1 = 1 2 k 1 x i 1 2 − 1 2 k 1 x f 1 2 (I) Here, W s 1 is work done by the first spring, k 1 is force constant for first spring, x i 1 is initial stretch of the first spring whose value is zero as spring is at normal state initially and x f 1 is final stretch of the first spring. Substitute 0 for 1 2 k 1 x i 1 2 in equation (I) as x i 1 is zero. W s 1 = 0 − 1 2 k 1 x f 1 2 (II) Write the expression for work done by the second spring on the car. W s 2 = 1 2 k 2 x i 2 2 − 1 2 k 2 x f 2 2 (III) Here, W s 2 is work done by the second spring, k 2 is force constant for second spring, x i 2 is initial stretch of the second spring whose value is zero as spring is at normal state initially and x f 2 is final stretch of the second spring. Substitute 0 for 1 2 k 2 x i 2 2 in equation (II) as x i 2 is zero. W s 2 = 0 − 1 2 k 2 x f 2 2 (IV) Write the expression for change in kinetic energy of the system. Δ K = 1 2 m v f 2 − 1 2 m v i 2 (V) Here, Δ K is change in kinetic energy, m is mass, v i is initial velocity and v f is final velocity. Substitute 0 for 1 2 m v f 2 in equation (V). Δ K = 0 − 1 2 m v i 2 (VI) As energy of the system is conserved, therefore work done by both the spring together is equal to change in kinetic energy. Write the expression for change conservation of energy for the system. Δ K = W s 1 + W s 2 (VII) Substitute 0 − 1 2 m v i 2 for Δ K , 0 − 1 2 k 1 x f 1 2 for W s 1 and 0 − 1 2 k 2 x f 2 2 for W s 2 in equation (VII)

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

9th Edition

ISBN: 9781305932302

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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