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 A bar, which has a magnitude of 597 newtons (N) and is directed due west. The other pushes with a force B bar, which hac a magnitude of 194 N and is directed due to north. what are (a) the magnitude and (b) direction of the resultant force A vector + B vector applied to a the crate? Suppose that the second worker applied a force. B vector instead of B vector. what then are (c) the magnitude and (d) direction of the resultant force A vector - B vector applied to the crate? In both cases express tyhe direction as a positive angle relative to due west.

Explanation / Answer

This is a right-triangle problem since both forces are orthogonal. The directions "due west" and "due north" are understood to mean that both forces are attempting to move towards west and north, hence a northwest-ward direction.

Let 'x' represent the magnitude of the force:

x=sqrt(597^2 + 194^2)

x=627.7 N

Let the ratios of west and north represent the tangent:

tan(x)=194/597

in degrees:

x=18 degrees

So the magnitude of approximately 627.7 N would be applied approximately 18-degrees above due west.

c,d)

if the force is applied to the east instead of the west the magnitude stays the same i.e 627.7 N but the resultant force is applied 18 degrees east of due north

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