critical thinking vectors
Jeff is trying to use a long piece of rope to remove a car from some deep mud. Which method should he use to exert more force on the car? Assume that Jeff will exert the same amout of force using either method. Explain your answer.
a. Tie one end of the rope to the car and pull.
b. Tie one end of the rope to the car and the other end to a nearby tree. Then push on the rope perpendicular to it at a point about halfway between the car and the tree.
I think it must be "b", but I don't know exactly how to explain why.
Ok, edit. I did some calculations: apply a force of 10N perpendicular to the rope, displacing it 1 degree, and the tension in the rope on either side of the displacement is about 573N. The tension goes down with each degree of displacement. I dont know, however, if I am sort of missing the point. I can prove that it works, but why? This is a math class, not physics -- resolution of vectors. Looking at my drawings, the applied force is the leg of a right triangle, and the tension is the hypotenuse. The other leg does not really seem to enter into it -- dissipated force? Anyway, for the purpose of "Explain your answer" -- the hyp is always longer than a leg, thus the benefit?