10 pts A 6 000-kg freight car rolls along rails with negligible friction. The ca

Question

10 pts A 6 000-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 Figure P7.59. Both springs are described by Hooke's law and have spring constants kl = 1 600 N/m and k2-3 400 N/m. After the first spring compresses a distance of 30.0 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 50.0 cm after first contacting the two-spring system. Find the car's initial speed. 2 000 1 500 E 1000 10 20 30 40 50 60 2 8 2 4

Explanation / Answer

Ws = work done by the spring = A = area under the graph = (0.5) (0.30) (500) + (0.5) (0.60 - 0.30) (2000 - 500) + (0.60 - 0.30) (500) = 450 J

M = mass of car = 6000 kg

v = initial speed of car

Using conservation of energy

kinetic energy of car = spring potential energy of the spring or work done by spring

(0.5) M v2 = Ws

(0.5) (6000) v2 = 450

v = 0.38 m/s

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