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 53.97 N, student B pulls with a force of 23.63 N, and student C pulls with a force of 78.96 N at an angle (theta)=78.34 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

Ax = 53.97 N

Ay = 0

Bx = 0

By = -23.63 N

Cx = -78.96*cos78.34 = -15.96 N

Cy = 78.96*sin78.34 = 77.33 N

Fx = Ax + Bx + Cx = 53.97-15.96 = 38.01 N

Fy = Ay + By + Cy = 0-23.63+77.33 = 53.7

Fnet = sqrt(Fx^2+Fy^2) = 65.8 N

direction = tan^-1(Fy/Fx) = +54.71

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