1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: A mass hung from two attached springs

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    A light spring with constant k1 is hung from an elevated support. From its lower end a second light spring is hung, which has spring constant k2. An object of mass m is hung at rest from the lower end of the second spring.

    a) Find the total extension distance of the pair of the springs.

    2. Relevant equations

    F= ma
    Fs = kx

    3. The attempt at a solution

    I treated the two springs as a single device and made the following equation for the forces acting on the mass:

    Fnet = 0
    Fs1 + Fs2 - mg = 0
    k1x + k2x = mg
    (k1 + k2)x = mg
    x = mg/(k1 + k2)

    But this answer is incorrect. (Correct answer: x = mg(1/k1 + 1/k2).

    Would someone be able to clarify what is happening in this system? I seem to be missing something...
  2. jcsd
  3. Oct 27, 2011 #2
    Seems like you need to treat each spring as a separate system. They have different spring constants so will put out different forces.

    k1x = mg gives x1=mg/k1 similarly x2 = mg/k2
    add x1 and x2 gives you total distance the spring is stretched.

    Just my $0.02, this is my first year taking calculus based physics as well.
  4. Oct 27, 2011 #3
    Hm I see. I was wrong to assume the forces on each spring would be the same...

    Thank you! And I hope your physics course(s) are going well :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook