A 4000-kg freight car rolls along rails with negligible friction. The car is bro

Question

A 4000-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 with k1 = 1700 N/m and k2 = 3300 N/m. After the first spring compresses a distance of 27.9 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 49.5 cm after first contacting the two-spring system. Find the car's initial speed. m/s

Explanation / Answer

Let the initial speed of car is v m/s

Now, using conservation of energy

0.5 * m * V^2 = 0.5 * k1 * 0.495^2 + 0.5 * k2*(0.495 - 0.279)^2

0.5 * 4000 * v^2 = 0.5 * 1700 * 0.495^2 + 0.5 * 3300 *0.216^2

solving for v

v = 0.38 m/s

the speed of cars is 0.38 m/s

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