0 As000-kg freight car rolls along ralis with negligible friction. The car is br

Question

0 As000-kg freight car rolls along ralis with negligible friction. The car is brought to rest by a combination of two colled springs as lilustrated in the figure below. Both springs are described by Hooke's law and have spring constants with 1-1700 N/m and k-3000 N/m. After the first spring compresses a distance of 31.8 cm, the second spring acts with the first to increase the force as aditional compression occurs as shown in the graph. The car comes to rest 53.s em after first contacting the two-spring system. Find the car's initial speed. × m/s Total force Distance (cm)

Explanation / Answer

First spring is compressed by 53.5 cm

k1 = 1700 N/m

PE of the spring = 0.5 k1x2 = 0.5*1700*0.5352 = 243.29J

second spring compressed by 53.5 - 31.8 = 21.7 cm

k2 = 3000 N/m

PE of the spring = 0.5*3000*0.2172 = 66.15

conserving the energy

KE of the car = Total PE stored in the springs

0.5 mv2 = 243.29 + 66.15 = 309.44 J

speed of the car = sqrt(2*309.44/1000) = 0.79 m/s

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