A 8000 kg freight car rolls along rails with negligible friction. The car is bro

Question

A 8000 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 slaw with k_1 = 1500 N/m and k_2 = 3100 N/m. After the first spring compresses a distance of 15.0 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 60.0 cm after first contacting the two-spring system. Find the car's initial speed.

Explanation / Answer

area of the graph give work done

work = area of triangle + area of trapezium

work = (1/2)*k1*x1*x1 + (k1*x1 + k1*x2 + k2*(x2-x1))*(x2-x1)/2

work = ((1/2)*1500*0.15*0.15) + (1500*0.15 + (1500*0.6) + (3100*(0.6-0.15)))*(0.6-0.15)/2

work = 583.8 J

from work energy relation work = change in KE

Work = K2 - K1

K2 = finalKE = 0

K1 = (1/2)*m*v1^2

583.8 = (1/2)*8000*v1^2

v1 = 0.38 m/s

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