Two workers are trying to move a heavy crate. One pushes on the crate with a for
ID: 1509678 • Letter: T
Question
Two workers are trying to move a heavy crate. One pushes on the crate with a force , which has a magnitude of 359 newtons (N) and is directed due west. The other pushes with a force , which has a magnitude of 257 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
Given forces acting on the crate
worker 1 applied push of 359 N , due west, F1
worker 2 applied push of 257 N due north, F2
the resultant force is in Fr = sqrt(F1^2+F2^2+2F1F2 Cos 90)
Fr = sqrt(F1^2 +F2^2)
FR = sqrt(359^2+257^2)
Fr = 441.509 N
the direction is west of north
angle is Tan theta = 257/359
theta = arc tan(257/359)
= 35.59 degrees
B)
if the two workers acts in the opposite direction to the initial condition that is due south and east
magnitude is same as above
the angle is
theta = 360 - 35.59
= 324.41 degrees east of south
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