58. Your boss hands you a bag containing four springs, A, B, C, and D, and tells

Question

58. Your boss hands you a bag containing four springs, A, B, C, and D, and tells you that they all have the same relaxed length. He wants you to rank them by the values of their spring Figure P8.57 constants. He locks you in a room with only the springs, a ruler, and a pad and pencil, and tells you to knock when youre done. Each spring has a hook on one end and a handgrip on the other. There is nothing in the room you can use to measure inertia. After thinking for a few minutes, you hook springs A and B together, stand on one handgrip with your foot, and pull on the other handgrip with your hand until the combina tion spring has been stretched to double its original length (Figure P8.58). You notice that spring, a makes up 65% of the stretched length and spring B makes up the other 35%. You work your way through the rest of the springs and tabu late the results: Figure P8.58 65% 3A 35% Based on these results, what are the numerical values in the ratio kn: kg: he : kp one Combination Percent of stretched length A/B A 65, B 35 A/C A 70, C 30 A/D A 67, D 33 answers are A:B:C:D= 1-4:9:5.25

Explanation / Answer

Using , F= k*x

Let free length be l.

As same force is applied at each end of combinations, the we have,

ka*0.65=kb*0.35

ka*0.7=kc*0.3

ka*0.67=kd*0.37

So, the ratio is,

0.35:0.65:0.82:0.64

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