Two individuals are attempting to relocate a sofa by applying forces in the indi

Question

Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If F1 = 300 N and F2 = 390 N, determine the vector expression for the resultant R of the two forces. Then determine the magnitude R of the resultant and the angle which it makes with the positive x-axis (measured counterclockwise from the x-axis).

Chapter 2, Problem 2/007 GO Tutorial Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If F1 300 N and F2-390 N, determine the vector expression for the resultant R of the two forces. Then determine the magnitude R of the resultant and the angle which it makes with the positive x-axis (measured counterclockwise from the x-axis) 65° Answers: i + i) N R= =

Explanation / Answer

Given,

F1 = 300 N ; F2 = 390 N ;

the resultant force in cartesian form will be:

R = (F1 + F2 cos(theta))i + F2 sin(theta)j

R = (300 + 390 x cos65)i + (390 x sin65 )j

R = ( 464.8 i + 353.5 j ) N

magnitude will be:

lRl = sqrt (464.8^2 + 353.5^2) = 583.95 N

direction would be:

phi = tan-1 (353.5/464.8) = 37.25 deg

Hence, lRl = 583.95 N and phi = 37.25 deg

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