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: 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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper


    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! :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook