Any Stratagies??

Question

Two trees are 7.6m apart. Calculate the mafnitude of the force F a backpacker must exert to hold a 16kg backpack so that the rope sags at its midpoint by:

A. 1.5m

B. 0.15m

Answer 1

I am assuming that the rope is suspended from each tree at exactly the same height, secureed to one tree, and the hiker is applying tension downward to the rope over a frictionless branch. Also, we will assume the rope weight is negligible.


Evaluate the forces acting on the backpack

Gravity:
16*9.81

The two ropes pulling the backpack upward. Note the rope has tension,T, equal to the force the hiker is pulling the rope.

Call the angle a.
Tan(a)=sag/3.8

for A =1.5/3.8
for B =0.15/3.8

The vertical forces are
2*Sin(a)*T=16*9.81

The factor of 2 is because there are two rope segments pulling upward on the backpack

T=8*9.81/Sin(a)
wher a=ATan(sag/3.8)

A. T= 94 N
B. T=529 N

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