Question 1032664: Chaz is using a rope tied to his tractor to remove an old tree stump from a field. Which method given below, a or b, will result in the greatest force applied to the stump? Assume that the tractor will exert the same amount of force using either method.
Explain your answer by showing an example using real numbers. Note that the length of the rope does not change between each scenario.
a. Tie the rope to the stump and pull.
b. Tie one end to the stump and the other end to a nearby pole. Then, pull on the rope perpendicular to it at a point about halfway between the two.
(p.s.)I do school online and its hard to get help from anyone. I know that i have to do something with the geometric/algebraic Vectors but im not sure what to do from there. Anything would helpful :)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! a. The amount of force  that the tractor can exert is applied to the stump.
b. How close is that nearby pole, how tight is the rope, and how is it tied?
I envision something like this:
 The forces shown are the forward pull of the tractor (F), and the reaction forces of the stump and the pole, jointly pulling the tractor backwards.
The rope is a physics-problem rope that has no mass, and transmits 100% of the force applied, without stretching.
As neither one (tractor, pole or stump) is moving, the net force on the middle of the rope is zero.
The forward component of each force is
F for the tractor pull,
-0.5F for the reaction of the stump,
-0.5F for the reaction of the pole,
0.5F for the forwards pulling action on the stump, and
0.5F for the forwards pulling action on the pole.
The rightwards components of the forces are
0 for the pull of the tractor because it is pulling straight ahead,
-2.5F for the reaction of the stump pulling the tractor to the left,
2.5F for the reaction of the pole pulling the tractor to the right (cancelling the leftwards pull from the stump),
2.5F for the rightwards action pull on the stump, and
-2.5 for the leftwards action pull on the pole.
The 2.5F to 0.5F ratio of sideways to backwards R force component magnitudes is the same as the ratio of the 5ft and 1ft corresponding sides of the similar green triangle.
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