A tank car coasting freely and horizontally at 4 ft/s is stopped by two spring b

Question

A tank car coasting freely and horizontally at 4 ft/s is stopped by two spring bumpers A and B having constants Ka=28000 lb/ft and Kb=32000 lb/ft. the total compression of the spring assembly at the instant the car stops is 27.580 inches. determine the weight of the tank car.

wt.______________________

A tank car coasting freely and horizontally at 4 ft/s is stopped by two spring bumpers A and B having constants Ka=28000 lb/ft and Kb=32000 lb/ft. the total compression of the spring assembly at the instant the car stops is 27.580 inches. determine the weight of the tank car.

Explanation / Answer

Effective spring effectiveness k_eff for springs in series = 1/ (1/k1 + 1/k2)

k_eff = 1 / (1/28000 + 1/32000)

k_eff = 14933.33 lb/ft

Energy conservation:

KE = Energy stored in spring

1/2*mv^2 = 1/2*k_eff*x^2

m*4^2 = 14933.33*(27.58/12)^2 *32.2

m = 158751.8 lb

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