A 7,000 -kg freight car rolls along rails with negligible friction. The car is b

Question

A 7,000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law and have spring constants k1 = 1,700 N/m and k2 = 3,500 N/m.After the first spring compresses a distance of x1 = 31.2 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest x2 = 48.5 cm after first contacting the two-spring system. Find the car's initial speed.

Explanation / Answer

spring energy = 0.5 k x^2

ttal energy = 0.5 * (1700 * 0.485^2 + 3500 * (0.485-0.312)^2) = 252.317 J = 0.5 *m * v^2 = kinetic energy of freight

252.317 = 0.5 * 7000 * v^2

V = 0.268m/s

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