Backpack on a line

  1. 1. The problem statement, all variables and given/known data

    The two trees in the figure are 6.9m apart. A back-packer is trying to lift his pack out of the reach of bears. (a)Calculate the magnitude of the force F that he must exert downward to hold a 15 kg- backpack so that the rope sags at its midpoint by 1.5m . (b)Calculate the magnitude of the force that he must exert downward to hold a 15 kg- backpack so that the rope sags at its midpoint by 0.16m .




    2. Relevant equations



    3. The attempt at a solution
    Distance between the trees =6.6 m

    Half of distance between the trees = b =6.9/2= 3.45 m

    sag at mid point = a = 1.5 m

    Consider the vertical right anglled triangle with ' b ' as base, ' a ' as height and the half portion of rope as hypotenues ' h '

    The hypotenues = h = sq rt [ b^2 + a^2 ] ,

    h = sq rt [ 3.45^2 +1.5^2 ]

    h =3.762 m

    Now the hypotenues ( h = 3.762 m ) represents force Fand side 'a' represents weight 98 N

    F/h =(15kg*9.8)/a

    F /3.762 =147 /1.5 m

    F =368.7 N

    This is answer is not right. I dont know what im doing wrong :S Please guide me
     
  2. jcsd
  3. Mark44

    Staff: Mentor

    So far, so good.
     
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