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Math Help - work done by lifting block attached to spring

  1. #1
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    work done by lifting block attached to spring

    this problem is in my calc book.

    If one hangs a spring (of constant 10lbs/ft) vertically and attaches a 10lb. weight to the spring, how much work is done in raising the weight 6 inches from where it hangs naturally?

    i drew a free body diagram and deduced that when you are lifting the weight up, the forces of gravity and spring force act downward (since spring force always acts opposite to displacement). so my equation for force is F = mg + kx = 10 + 10x. so i took the integral of that from 0 to 1/2 and i got 6.25 ft lbs or 75 in lbs. but my book's answer is 240 in lbs. how did they get that?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    I see what the book did but I would agree with your answer.

    If you integrate from 0 to 6 you get the 240.

    However the units would not be consistent as the spring constant is expressed in lbs/ft. Therefore if you integrated from 0 to 6 the contribution from the spring would be 180 (in^2)lb/foot as opposed to simply ft lbs if you integrate from 0 to 1/2

    My only other concern is the weight of the spring. Are you to ignore the weight of the spring or is there additional data you haven't provided?
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