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Backpack on a line 
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#1
Oct2508, 07:45 PM

P: 114

1. The problem statement, all variables and given/known data
The two trees in the figure are 6.9m apart. A backpacker 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
Oct2508, 08:40 PM

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P: 21,402

[QUOTE=itryphysics;1929899] Now the hypotenues ( h = 3.762 m ) represents force Fand side 'a' represents weight 98 N [quote] The weight is wrong. The mass of the pack is 15 kg, so its weight is 15 * 9.8 = 147 N. Your later work seems to use the right value. You said you didn't think this was correct. What's the answer you believe is correct? 


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