13.62A bumper made of a hard spring is to stop a 30ton gondala car which is traveling at 4ft/s as shown. Such a spring developes a restoring force F=100x+12x^3 kips when it si compressed by an amount of x ft. Determine the maximum deflection of the bumper. A spring of free length 12 m and modulus 1 kN/m is attached to a colteinclinedThe vertical spring at13.57of mass 20 kg. The collar is released from rest in the position A, to slide dsmooth vertical rod as shown. If the lowest position reached by the collerdetermine the distance b. (Hint. It leads to a cubic equation in b.)*1.5 m40 N13 66* A 10-kg plunger is released from60°13.58 Refer to Prob. 13.57. If the collar attains a maximum spced tpasses the position A, determine (a) the distance A A, (b) Umax- (Hint. It leadequartic equation in sin 0.)13.59on a smooth rod by a constant force of 40 N as shown. The spring attached to thecollar has a modulus of 50 N/m. and the farthest position reached by the collar is 4.where b - 2 m. Determine the free length L of the spring.5 kghe impact, determine the maximum defle13.67 The 40-lb sphere as shown is rethe spring has a free length of 30 in, andof the sphere when 6 = 90°.Fig. P13.59 and P13.60A 5-kg collar is relcased from rest in the position A, and is slid to the rishe80 mm1.2 m/s13.60 A 5-kg collar is released from rest in the position A, and is slid to the righton a smooth rod by a constant force of 40 N as shown. The spring attached to thecollar has a free length of 1.3 m and a modulus of 50 N/m. Determine the speed oithe collar as it passes through the position A, where b 2 m.13.61* A bumper composed of three springs is to stop a 40-Mg box car which istraveling at a speed of 1.2 m/s as shown. One of the springs is 80 mm shorter tharthe other two. The modulus of the shorter spring is 1.5 MN/m, while the modulusof cach of the two longer springs is 1 MN/m. Determine the maximum deflection oithe bumper.24 in.Fig. P13.61*Nonlinear spring9 in.4 ft/s13.62 A bumper made of a hard spring is to stop a 30-ton gondola car which istraveling at a speed of 4 ft/s as shown. Such a spring develops a restoring forceF = 100x + 12x kips when it is compressed by an amount of x ft. Determine themaximum deflection of the bumper.Fig. P13.6713.68* through 13.77* Usingfollowing problems:Fig. P13.6213.63 Solve Prob. 13.62 if the spring is a soft spring which develops a restoringforce F = 100x 12x kips when it is compressed by an amount of x ft.13.68* Prob. 1213.70* Prob. 1213.72* Prob.1213.74* Prob. 1solution of resulting nonlinear equation.13.76* Prob. 1wwww

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Accepted Answer

Mass of car, m = 30 ton = 27215.5 kg   (If it is metric-ton, 30 metric ton = 30000 kg, in that case…