# Backpack on a line

1. Oct 25, 2008

### itryphysics

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. Oct 25, 2008

### Staff: Mentor

So far, so good.

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