Two workers are trying to move a heavy crate. One pushes on the crate with a for

Question

Two workers are trying to move a heavy crate. One pushes on the crate with a force , which has a magnitude of 214 newtons (N) and is directed due west. The other pushes with a force , which has a magnitude of 156 N and is directed due north. What are (a) the magnitude and (b) direction of the resultant force + applied to the crate? Suppose that the second worker applies a force - instead of . What then are (c) the magnitude and (d) direction of the resultant force - applied to the crate? In both cases express the direction as a positive angle relative to due west.

Explanation / Answer

F1 = 214(-i) N

F2 = 156(j) N

resultant, F = F1 + F2 = -214i + 156j N

(A) magnitude = sqrt((-214)^2 + 156^2) = 265 N  

(B) direction = tan^-1 ( 156 / 214) = 36 deg to the north

F1 = - 214i

F2 = - 156j

F = F1 + F2 = - 214i - 156j

(C) magnitude = sqrt((-214)^2 + (-156)^2) = 265 N  

(D) theta = 36 deg to the south  

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