5. On a separate sheet of paper (preferably, lincar graph paper), find the resul

Question

5. On a separate sheet of paper (preferably, lincar graph paper), find the resultant of the following two vectors using the parallelogram method. FA is a force vector with magnitude of 10.0 N and makes an angle of 25.0° with thex-axis. FB is a force vector with a magnitude of 5.00 N and makes an angle of 45.0o with the x-axis. Specify both the magnitude of the resultant and its direction with respect to the x-axis. 6. Use the mathematical method to find the resultant of FA and FB given in problem 5. 7. The force vector Fc acts on a body, along with the forces FA and FB given in problem 5. Fchas amagnitude of 15.0 N and acts in the first quadrant at an angle of 10.0° to the y-axis. Use the polygon method to solve for the resultant of these three forces. An object with a mass of 80.0 kg sits on a ramp with a 30.0° slope with respect to the ground. hat is the magnitude of the component of the object's weight parallel to the ramp? Assume this uation occurs on the surface of the Earth. f the resultant of forces acting on a body has a magnitude of 100.0 N and makes an angle of 30 h the x-axis, what are the magnitude and direction (with respect to the x-axis) of the equilibrant

Explanation / Answer

5-6: FA = 10 (cos25i + sin25j )

FA = 9.06i + 4.23 j

FB = 5 ( cos45i + sin45j) = 3.54i + 3.54j

R = FA + FB = 12.6i + 7.77 j

magnitude = sqrt(12.6^2 + 7.77^2) = 14.8 N

direction = tan^-1(7.77/12.6) = 31.7 deg

7. FC = 15 ( sin10i + cos10j)

FC = 2.60 i + 14.77 j

R = FA + FB + FC = 15.2 i + 22.54 j

magnitude = sqrt(15.2^2 + 22.54^2) = 27.2

direction = tan^-1(22.54/15.2) = 56 deg

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