If 6 J of work is needed to stretch a

vegetars8t 2021-12-16 Answered
If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?
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jean2098
Answered 2021-12-17 Author has 38 answers
Let the natural length be l
Then we can write
6=10l12lkxdx
6=[12kx2]10l12l
6=12k[(12l)2(10l)2] Equation 1
And
10=12l14lkxdx
10=[12kx2]12l14l
10=12k[(14l)2(12l)2] Equation 2
Divide Equation 2 by Equation 1
106=(14l)2(12l)2(12l)2(10l)2
Recall that: a2b2=(ab)(a+b)
53=(14l12+l)(14l+12l)(12l10+l)(12l+10l)
53=(2)(262l)(2)(222l)
53=13l11l
Cross Multiply
555l=393l
Add 5l on both sides
55=39+2l
Subtract 39 drom both sides
16=2l
Divide both sides by 2
8=l
Result: Natural length of the spring is 8 cm

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