Question

8.) Two forces with magnitudes of 45 pounds and 62 pounds are applied to an object. The magnitude of the resultant is 100 pou
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Answer #1

8) For two vectors A and B inclined at an angle \theta resultant vector R is usually given by the equation

R = VA2+B2+2AB cos 8

Putting the values given,

100 = V452 + 622 + 2 x 45 x 62 cos e

or, 100% = 45% +622 + 2 x 45 x 62 cos 0

100 – 45 – 622 or, cos 6 = = 0.7403 2 x 45 x 62

or, 0 = 42.24

If \phi be the angle between R and A then we must have

tan = B sind A+B cose

or, tan 62 sin 42.24 = 45 +62 cos 42.24° +62 cos 42.240 = 0.4585

or, o = 24.6325

This is the angle between the resultant vector and 45 pound force.

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