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: Conservation of momentum & energy

  1. Dec 18, 2009 #1
    1. The problem statement, all variables and given/known data
    A block of mass m1 = 2 kg slides along a frictionless table with speed 10 m/s. Directly in front of it, and moving in the same direction with a speed of 3 m/s is a block of mass m2 = 5kg. A massless spring with spring constant k = 1120 N/m is attached to the second block. The spring is compressed a maximum amount x. What is the value of x?

    2. Relevant equations
    m1v1 + m2v2 = m1vf1 + m2vf2
    KEi = KEf + 1/2kx^2

    3. The attempt at a solution
    I knew that there would be a maximum compression of the spring when the first block has velocity = 0 m/s. I used cons. of momentum :
    (2 kg)(10 m/s) + (5 kg)(3 m/s) = (5 kg)(Vf) to find Vf = 7 m/s
    then used cons. of energy:
    (0.5)(5 kg)(7 m/s)^2 = 1/2(1120)x^2
    and got x = 0.4677 m

    but the correct answer is 0.250 m
    can anyone help me find the correct answer
  2. jcsd
  3. Dec 18, 2009 #2


    User Avatar
    Homework Helper

    After collision both the masses move together until the compression is maximum. At that instant the common velocity is given by
    m1v1 + m2v2 = (m1+m2)vf.
    Applying the conservation of energy, you can write
    m1v1^2 + m2v2^2 = (m1+m2)vf^2 +1/2*k*x^2.
    Now proceed to find x.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook