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A bumper composed of three springs is to stop a 40Mg boxcar which is traveling at 1.2m/s as shown. One of the springs is 88mm shorter than the other two. The modulus of the shorter spring is 1.5MN/m while the modulus of the longer two springs is 1MN/m. Determine the maximum deflection of the bumper

A bumper composed of three springs is to stop a 40Mg boxcar which is traveling at 1.2m/s as shown. One of the springs is 88mm shorter than the other two. The modulus of the shorter spring is 1.5MN/m while the modulus of the longer two springs is 1MN/m. Determine the maximum deflection of the bumper

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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13.61

A bumper composed of three springs is to stop a 40Mg boxcar which is traveling at 1.2m/s as shown. One of the springs is 88mm shorter than the other two. The modulus of the shorter spring is 1.5MN/m while the modulus of the longer two springs is 1MN/m. Determine the maximum deflection of the bumper.

A spring of free length 12 m and modulus 1 kN/m is attached to a colte inclined The vertical spring at 13.57 of mass 20 kg. The collar is released from rest in the position A, to slide d smooth vertical rod as shown. If the lowest position reached by the coller determine the distance b. (Hint. It leads to a cubic equation in b.)* 1.5 m 40 N 13 66* A 10-kg plunger is released from 60° 13.58 Refer to Prob. 13.57. If the collar attains a maximum spced t passes the position A, determine (a) the distance A A, (b) Umax- (Hint. It leade quartic equation in sin 0.) 13.59 on a smooth rod by a constant force of 40 N as shown. The spring attached to the collar 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 kg he impact, determine the maximum defle 13.67 The 40-lb sphere as shown is re the spring has a free length of 30 in, and of the sphere when 6 = 90°. Fig. P13.59 and P13.60 A 5-kg collar is relcased from rest in the position A, and is slid to the rishe 80 mm 1.2 m/s 13.60 A 5-kg collar is released from rest in the position A, and is slid to the right on a smooth rod by a constant force of 40 N as shown. The spring attached to the collar has a free length of 1.3 m and a modulus of 50 N/m. Determine the speed oi the 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 is traveling at a speed of 1.2 m/s as shown. One of the springs is 80 mm shorter thar the other two. The modulus of the shorter spring is 1.5 MN/m, while the modulus of cach of the two longer springs is 1 MN/m. Determine the maximum deflection oi the bumper. 24 in. Fig. P13.61* Nonlinear spring 9 in. 4 ft/s 13.62 A bumper made of a hard spring is to stop a 30-ton gondola car which is traveling at a speed of 4 ft/s as shown. Such a spring develops a restoring force F = 100x + 12x kips when it is compressed by an amount of x ft. Determine the maximum deflection of the bumper. Fig. P13.67 13.68* through 13.77* Using following problems: Fig. P13.62 13.63 Solve Prob. 13.62 if the spring is a soft spring which develops a restoring force F = 100x 12x kips when it is compressed by an amount of x ft. 13.68* Prob. 12 13.70* Prob. 12 13.72* Prob.12 13.74* Prob. 1 solution of resulting nonlinear equation. 13.76* Prob. 1 wwww
Transcribed Image Text:A spring of free length 12 m and modulus 1 kN/m is attached to a colte inclined The vertical spring at 13.57 of mass 20 kg. The collar is released from rest in the position A, to slide d smooth vertical rod as shown. If the lowest position reached by the coller determine the distance b. (Hint. It leads to a cubic equation in b.)* 1.5 m 40 N 13 66* A 10-kg plunger is released from 60° 13.58 Refer to Prob. 13.57. If the collar attains a maximum spced t passes the position A, determine (a) the distance A A, (b) Umax- (Hint. It leade quartic equation in sin 0.) 13.59 on a smooth rod by a constant force of 40 N as shown. The spring attached to the collar 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 kg he impact, determine the maximum defle 13.67 The 40-lb sphere as shown is re the spring has a free length of 30 in, and of the sphere when 6 = 90°. Fig. P13.59 and P13.60 A 5-kg collar is relcased from rest in the position A, and is slid to the rishe 80 mm 1.2 m/s 13.60 A 5-kg collar is released from rest in the position A, and is slid to the right on a smooth rod by a constant force of 40 N as shown. The spring attached to the collar has a free length of 1.3 m and a modulus of 50 N/m. Determine the speed oi the 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 is traveling at a speed of 1.2 m/s as shown. One of the springs is 80 mm shorter thar the other two. The modulus of the shorter spring is 1.5 MN/m, while the modulus of cach of the two longer springs is 1 MN/m. Determine the maximum deflection oi the bumper. 24 in. Fig. P13.61* Nonlinear spring 9 in. 4 ft/s 13.62 A bumper made of a hard spring is to stop a 30-ton gondola car which is traveling at a speed of 4 ft/s as shown. Such a spring develops a restoring force F = 100x + 12x kips when it is compressed by an amount of x ft. Determine the maximum deflection of the bumper. Fig. P13.67 13.68* through 13.77* Using following problems: Fig. P13.62 13.63 Solve Prob. 13.62 if the spring is a soft spring which develops a restoring force F = 100x 12x kips when it is compressed by an amount of x ft. 13.68* Prob. 12 13.70* Prob. 12 13.72* Prob.12 13.74* Prob. 1 solution of resulting nonlinear equation. 13.76* Prob. 1 wwww
Expert Solution
Step 1

GIven data 

Mass of box car = 40 Mg = 40*103 Kg

speed of the box car = 1.2 m/s

modulus of the longer springs = 1 MN/m

modulus of shorter spring = 1.5 MN/m 

difference between the length of longer and shorter spring = 80 cm 

 

To deteremine 

The maximum deflection in the springs 

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