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!

How to find magnitude of initial displacement?

  1. Mar 7, 2013 #1
    A mass of 130 g is held by a horizontal spring constant 22 N/m. It is displaced from its equilibrium position and released from the rest. As it passes through its equilibrium position, its speed is 4.2 m/s.

    a) find work done on the spring.
    1/2(.13kg)(4.2)^2= 1.14 (correct)

    b) what is the magnitude of the initial displacement?
    I dont know what to do for this , Im guessing were suppose to find distance but I dont know how.
  2. jcsd
  3. Mar 7, 2013 #2
    You have the work correct. Now you have to know how much displacement has been done for that amount of work.

    The equation for the force of a spring is F = -kx, where x is the distance displaced from equilibrium. Thus, the work, which is ∫F dx = -k x^2 / 2. The negative sign signifies that the work is done on the system.

    Thus, your value for work, W = k x^2 / 2, so x = √(2W/k).
  4. Mar 7, 2013 #3
    can I do 0.13kg/22=0.005 m to get displacement?
  5. Mar 7, 2013 #4
    never mind x=sqrt(2*1.14/22)=0.32 m
    Thank you!
  6. Mar 7, 2013 #5
    You are nearly right, but you forgot to include velocity. The displacement would be x = v√(m/k).

    Your units do not make sense in that answer. (displacement ≠ kg / (N / m))

    --- After your second comment, you are correct.
    Last edited: Mar 7, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted