Question 1032884: 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.
Tractor<-----------Stump
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.
Stump
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Tractor
(The tractor is pulling <--- way)
I know this has to do with algebraic and geometric vectors but i'm not sure what to do to even start.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 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.
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Compare it to a wire strung horizontally supported at each end.
Putting a weight on the wire means the weight is subject to 3 forces:
1) gravity,
2) the tension of the wire to the left, and
3) to the right.
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The vector sum of the 3 forces has to equal zero for equilibrium.
W = weight
T1 is the tension to the left,
T2 tension to the right.
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If the weight bends the wire at the support point so that the angle = eg, 178 degrees, the vertical component of the wire's tension is T1*cos(89)
T1 = T2
W/2 = T1*cos(89)
T1 = W/(2*cos(89))
T1 = T2 =~ 28.65*W
A much greater force.
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