The helicopter view in the figure below shows two people pulling on a stubborn m
ID: 1658893 • Letter: T
Question
The helicopter view in the figure below shows two people pulling on a stubborn mule. (Take F1 = 115 N and F2 = 66.0 N. ) 75.0 60.0° (a) Find the single force that is equivalent to the two forces shown. magnitude 27.22 Your response differs from the correct answer by more than 10%. Double check your calculations. N counterclockwise from the +x-axis (b) Find the force a third person would have to exert on the mule to make the net force equal to zero. magnitude direction counterclockwise from the +x-axisExplanation / Answer
Given
forces
F1 = 115 N , F2 = 66.0 N
acting in a direction with respect to x axis is F1 is 60 degreees , and F2 is 105 degrees
let the components of the forces are
F1 = F1x i + F1y j = F1 cos theta i + F1 sin theta j
F1 = 115cos60 i + 115 sin60 j
F1 = 57.5 i + 99.6 j
F2 = F2x i + F2y j = F2 cos theta i + F2 sin theta j
F2 = 66cos105 i + 66 sin105 j
F2 = -17.08 i + 63.75 j
the net force is
F = F1+F2
F = (F1x+F2x)i +(F1y+F2y)
F = (57.5-17.08)i + (99.6+63.75) j
F = 40.42 i + 163.35 j
net force is F = sqrt((40.42)^2 + (163.35)^2 )
= 168.277 N
the direction is theta = arc tan(163.35/40.42) = 76.01 degrees
a) the force that is equivalent to the two forces is F = 168.227 N
the direction is 76 degrees counter clockwise direction
b) To make the mule so that the net force acting on it is zero
should apply 168.277 N in 256 degrees from counter clock wise direction ( in the third quadrant)
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