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Homework Help: Impulsive Tension Question

  1. Jul 18, 2012 #1
    1. The problem statement, all variables and given/known data
    An object of mass 3m is connected by means of a light, inextensible string to a scale pan of mass m. The object rests on the ground. The string passes over a smooth pulley and the scale pan hangs suspended. An object of mass m, falling from rest a distance h above the scale pan, lands on it and does not bounce. Show that the mass of 3m will rise to a height h/5.

    Sorry but there's no diagram given! The answer I got was 4h/5 instead! :(

    2. Relevant equations

    3. The attempt at a solution
    To find the speed of the scale pan before the string becomes taut:

    To find the speed of the scale pan/speed at which the 3m object jerks in motion:
    Take upwards direction as negative:
    -I = 2mv-2m√(2gh) (this is the change in momentum of the scale pan)
    -I = -3mv

    Equate both to get:

    This speed, v is the initial speed of the upward motion of the 3m mass.
    v=0 (mass of 3m rise to a height of h/5 and stop)
    To find acceleration, a:

    For the 3m mass (it's going upwards):
    For the scale pan+object of mass m (going downwards):

    Equate both equations:

    Using an equation of linear motion:
    0=(2√(2gh)/5)^2 + 2(-g/5)s

    Did I do something wrong in the middle? Was I on the right track in the first place? Thanks!! :D :smile:
  2. jcsd
  3. Jul 18, 2012 #2


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    hi jiayingsim123! :smile:

    (try using the X2 button just above the Reply box :wink:)
    no, the 2m√(2gh) is wrong …

    only the mass m was moving, the pan was stationary! :redface:

    (btw, i find this sort of problem easier if i pretend everything is in a straight line …

    in this case, a mass m collides with a stationary mass 4m :wink:)​
  4. Jul 18, 2012 #3
    Hi tiny-tim, thanks for helping out again!
    But I thought the mass m drops onto the scale pan, meaning both of it will move downwards as a single entity and therefore the total mass is 2m? So isn't it a mass of 2m colliding with a stationary mass of 3m?
  5. Jul 18, 2012 #4


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    there's 4m of stationary mass, isn't there?? :smile:

    (you're being confused by the fact that the 4m is in two parts)

    only a mass of m was originally moving, and 4m wasn't :wink:
  6. Jul 19, 2012 #5
    Okay thanks for clearing that up, tiny-tim!! You're really awesome! :)
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