Question

Three Black Friday shoppers are all desperately tugging on the same WOW-Zo Toy in such a way that the toy is held motionless off of the store floor. One is pulling with a force of 450 Newtons to the front of the store. A second is pulling with a force of 280 Newtons at an angle of 140 degrees relative to the first. How strong and in what direction is the third person pulling. Please show your work.

Answer 1

Given that Net force on the toy is zero

Fnet = F1 + F2 + F3 = 0

F3 = -(F1 + F2)

Now Using given information:

Suppose direction of F1 is in x-axis

F1 = 450 N in x-axis

F1 = (450 N) i

F2 = 280 N relative to 140 deg from x-axis

F2 = F2x i + F2y j

F2 = 280*cos 140 deg i + 280*sin 140 deg j

F2 = -214.5 i + 180.0 j

So third force will be

F3 = -(F1 + F2)

F3 = -(450 i + (-214.5 i + 180.0 j))

F3 = (214.5 - 450) i - 180 j

F3 = -235.5 i - 180 j

from above we can see that F3 is in 3rd quadrant

Magnitude of third force will be

|F3| = sqrt ((-235.5)^2 + (-180)^2)

|F3| = 296.4 N

Direction of F3 = arctan (F3y/F3x)

Direction = arctan (180/235.5) = 37.4 deg below -ve x-axis

Now since we need direction w.r.t to F1 OR +ve x-axis and F3 is in 3rd quadrant, So

Direction = 180 + 37.4 = 217.4 deg relative to the first shopper

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