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lk_10_10 · Jun 7, 2010, 05:20 PM

Two workers are trying to move a heavy crate. One pushes on the crate with a force , which has a magnitude of 455 newtons and is directed due west. The other pushes with a force , which has a magnitude of 335 newtons and is directed due north.
What are the magnitude and direction of the resultant force + applied to the crate? (Express the direction relative to due west.)??

ebaines · Jun 8, 2010, 06:03 AM

First the magnitude of the resultant: because these two forces are perpendicular to each other, you can use the Pythagorean Theorem to calculate the resultant's magnitude. If $F_w$ is the force operating toward the west, and $F_n$ is the force in the north direction, then:

$<br /> F_{Total} = \sqrt { F_w^2 + F_n^2} = \sqrt {455N^2 + 335N^2}<br />$

Now the directon: you can express this by calculating the arc tangent between the two force vectors. They want you to determine the angle of the resultant as measured from the western force, so that would be
$<br /> \theta = \arctan \left( \frac {F_n} {F_w} \right)= \arctan \left( \frac {335 N} {455 N} \right)<br />$

Post back with your final answers and we'll check it for you.

cmorton · Jun 7, 2011, 05:20 PM

Magnitude is 570.92
Direction is 36 degrees
North of west

ebaines · Jun 8, 2011, 05:36 AM

Originally Posted by cmorton

magnitude is 570.92
direction is 36 degrees
north of west

Why are you posting an answer to a question that is a year old? And your answer is not quite right - the direction is correct, but check the magnitude.