A 5,000-kg freight car rolls along rails with negligible friction. The car is br

Question

A 5,000-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 = 3,100 N/m. After the first spring compresses a distance of x1 = 27.3 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 = 50.5 cm after first contacting the two-spring system. Find the car's initial speed.

Explanation / Answer

.5*k1*(x1+x2)^2+.5*k2*x2^2=.5*m*v^2 so v=.6 m/s

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