Don't feed the animals
Out camping, you decide to hang your food off the ground to keep it away from raccoons and other small scavengers. There are two very tall trees on your campsite apart and you need to hang of food exactly between them so the food remains at least off the ground. You head out to the local camping store where they sell long cords that have different maximum tensions they can provide without breaking. The higher the maximum tension, the more expensive the cord. So you can buy the cheapest appropriate cord, what is the minimum tension in Newtons necessary to support the food?
Details and assumptions
- The acceleration of gravity is .
- The cords are effectively massless.
The answer is 148.12.
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1 solution
Each cord is 2 0 meters long and the distance between the trees is 1 5 meters . Therefore the angle the cords will make with the horizontal when food is hung from the middle is arccos ( 7 . 5 / 1 0 ) = 0 . 7 2 3 rad . The tension in the rope is a constant, so the net vertical force on the hanging food is F N e t = − m g + 2 T sin ( 0 . 7 2 3 ) . The net force must be zero since the package is not moving. Solving for T yields T = 1 4 8 . 1 2 N .