Three students converge on the last textbook in the store. All three grab it and

Question

Three students converge on the last textbook in the store. All three grab it and begin to pull in the directions shown in the above figure. Student A exerts a force of 75.00 N, student B pulls with a force of 31.40 N, and student C pulls with a force of 97.11 N at an angle (theta)=79.47 degrees above the -x axis.
Considering these three forces (ignore the force of gravity on the book), what is the magnitude of the net force on the book? (Note: The figure is not drawn to scale.)

Give the angle of the resultant force with respect to the +x-axis. Assume the counter-clockwise direction to be positive and the clockwise direction to be negative.

Explanation / Answer

Lets write down the components for all the vectors

Vector A, Component along X axis is 75 N

Component along Y-Axis is 0 N

Vector B, Component along X axis is 0 N

Component along Y-Axis is 31.4 N

Vector C, Component along X axis is 97.11 Cos (180-79.47) N = 97.11 Cos (100.53) N

Component along Y-Axis is 97.11 Sin (100.53 ) N

Net Component along X axis is 75 + 97.11 Cos (100.53) N = 57.25 N

Net Component along Y - axis is 31.4 + 97.11 Sin (100.53 ) N = 126.87 N

NET FORCE is root of squares of X and Y components = 139.19 N

Angle made is tan inverse ( 126.87/57.25) = 65.71 degrees with respect to X -axis

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