A spring with stiffness constant k has an unknown mass hanging fromits free end.

Question

A spring with stiffness constant k has an unknown mass hanging fromits free end. When a mass m1 = 2kg is added, the springextends by .3 meters. If a mass m2 = 5kg is addedinstead, the spring extends by .85 meters. What are the values of the spring constant and the unknown mass(mu)?

This seems simple enough, setup up the 2 equations with 2unknowns. Fs = -kx -> g(mu+m1)=-kx1 (andm2 is substituted in for m1 for a second equation along withx2).

Set one eq. equal to k: k = -g(mu+m1)/x1

substitute that in for k on the second eq:g(mu+m2)=(g(mu+m1)x2)/x1 (negative signs on k andg cancel)
simplifies into: mu=(m1x2-x1m2)/(x1-x2)
plug in numbers -> 1.7-1.5/-.55 = -.36 kg formu.  

My question is, why are we getting a negative mass?

This is just one way weve been trying this problem, we solved for kfirst other times (turns out to be around 54 or 55) but we stillare getting a negative mass for mu. Played around with downbeing up (positive accel and positive delta x) and viceversa.

Any help is appreciated, this problem is tormenting us.

Explanation / Answer

call the unknown mass M.   The idea seems tobe (although the problem is poorly worded) that: .     M + m1    stretches thespring   30 cm .     M + m2 stretches thespring    85 cm .     But I'm making a big assumption here. Theproblem does not explicity say that the spring stretches 30 cm dueto the unknown mass and the added 2 kg. It seems to imply that the30 cm is only due to the 2 kg. But that is inconsistent with the 85cm and the 5 kg. . Since k is constant, the stretch should be proportionalto the mass hanging. So you can write a simple ratio (which you gotfrom writing your equations and doing some algebra...) .     ( M + m2) / ( M + m1) =   85 / 30 . Now consider this...   let's not do anycalculations. Just consider the possibilities of M: it couldbe anywhere from 0 to infinity. .           noticethe ratio on the right side is    85/30 =     2.83 . On the left, if M = 0   then the ratiois     2.5 . A M goes to infinity,  the ratio on the leftbecomes 1 . So the left side, for all possible values of M, rangesfrom    2.5 to 1.   It will never equalthe ratio on the right side for any positive value of M. . Which means... assuming we are interpreting the problemcorrectly, the numbers are bad. This does happen... even people whowrite textbooks make mistakes. Ultimately you will just have tobring it to the attention of your prof, since he/she is the finalword in your work in this class. . I would just ask your prof if you are interpreting the problemcorrectly... that is, 30 cm stretch is due to m1 plus unknownmass. If your prof can't clarify the problem, then at least youleave it up to him/her to decide what to do next (choose adifferent textbook?) . Good luck.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.