Don't feed the animals

Classical Mechanics Level 2

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 \(15~\mbox{meters}\) apart and you need to hang \(20~\mbox{kg}\) of food exactly between them so the food remains at least \(1~\mbox{m}\) off the ground. You head out to the local camping store where they sell \(20~\mbox{m}\) 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 \(-9.8~\mbox{m/s}^2\).
  • The cords are effectively massless.

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