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Simple particles and motion

  1. Jul 20, 2005 #1
    Two particles, A (mass 0.2 kg) and B (mass 0.3 kg), are attached to an inexstensible string which passes over a smooth pulley. A initially rests on a sloping roof that makes a 30 degree angle with the horizontal and B hangs freely below the roof. Find the acceleration, a, of the particles when released from rest.
    (I tried to draw a diagram but it came out looking a mess).
    My workings (T is the tension in the string):
    (1) 0.3g - T = 0.3a
    (2) T - 0.2g sin 30 deg = 0.2a

    (1) T = 0.3g - 0.3a
    (2) 0.3g - 0.3a - 0.1g = 0.2a
    (2) 0.5a = 0.2g
    (2) a = 0.4g
    taking g to be 9.8 m/s/s:
    a = 3.92 m/s/s
    My book says 7.84 m/s/s.
    What did I do wrong?

    Thanks for any help.
    Jimi
     
  2. jcsd
  3. Jul 20, 2005 #2

    OlderDan

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    Try sloping your roof in the other direction. Looks like that would just about give the quoted answer, but I did not calculate it
     
  4. Jul 20, 2005 #3
    According to OlderDan's tip you should replace eq [2] by

    [tex]T + 0.2gsin30^{\circ}[/tex],

    which should give you 4/5g.
     
  5. Jul 20, 2005 #4
    Yep, you're both right, I see it. Thanks.
     
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