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: Collisions- Simple Algebra Problem

  1. May 31, 2005 #1
    Collisions-- Simple Algebra Problem...


    So... I think I'm having a simple algebra problem-- I was just wondering if someone could point out my error. This is the problem:

    Block 1, of mass [tex]m_{1}[/tex], moves across a frictionless surface with speed [tex]u_{i}[/tex]. It collides elastically with block 2, of mass [tex]m_{2}[/tex], which is at rest ([tex]v_{i}=0[/tex]). After the collision, block 1 moves with speed [tex]u_{f}[/tex], while block 2 moves with speed [tex]v_{f}[/tex]. Assume that [tex]m_{1} > m_{2}[/tex], so that after the collision, the two objects move off in the direction of the first object before the collision.


    What is the final speed [tex]u_{f}[/tex] of block 1?

    So-- I find [tex]m_{2}v_{f}[/tex] using the law of conservation of momentum:
    [tex]m_{2}v_{f} =m_{1}u_{i}-m_{1}u_{f}[/tex]

    And I find [tex]m_{2}v_{f}^2[/tex] using the law of conservation of kinetic energy:
    [tex]m_{2}v_{f}^2 = m_{1}(u_{i} - u_{f})(u_{i} + u_{f}).[/tex]

    Then I find [tex]v_{f}[/tex] using only [tex]u_{i}[/tex], and [tex]u_{f}[/tex]:
    [tex]v_{f} =\displaystyle{\frac{-(u_{i}+u_{f})-(u_{i}+u_{f})}{-2}}[/tex]

    Now, I have to substitute what I just found for [tex]v_{f}[/tex] into the conservation of momentum formula, and solve for [tex]u_{f}[/tex]. ...But I guess I'm having difficulty singling out the [tex]u_{f}[/tex].

    This is what I've got:

    [tex]m_{1}u_{1} = m_{1}u_{f} + m_{2}(\displaystyle{\frac{-(u_{i}+u_{f})-(u_{i}+u_{f})}{-2}})[/tex]
    ...And here, I think I messed my algebra up, but when I simplify that, I get:
    [tex]m_{1}u_{1} = m_{2}(u_{f} + u_{i}) + m_{1}u_{f}[/tex]

    Is that right? ...If not/if so, how do I get the [tex]u_{f}[/tex] on just one side?
  2. jcsd
  3. May 31, 2005 #2

    Doc Al

    User Avatar

    Staff: Mentor



    I have no idea what you are doing here. This expression simplifies to: [itex]v_{f} = u_{i}+u_{f}[/itex], which is incorrect.

    You can rewrite the momentum equation to get
    [tex]v_{f} = \frac{m_1}{m_2} (u_{i} - u_{f})[/tex]
    Perhaps this is what you meant? Now just plug that into the KE equation to eliminate [itex]v_f[/itex] and simplify.

    Amazingly, it is right. (It's equivalent to what you get when you do the "plugging in" that I suggest above.) So I suspect you made a typo earlier on. To simplify this expression, just multiply it out and move all terms containing [itex]u_f[/itex] to one side and all other terms to the other side.
  4. May 31, 2005 #3
    woo, okay. thanks. I got it. ...Really, much appreciated.

    Thanks again... (Eh, I'm having a really hard time in this class- if you couldn't tell. AND I made the mistake of taking it as a 7-week course. ...I obviously didn't know what I was in for. Really, thanks again.)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook