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

ID: 2270009 • Letter: 1

Question

1. 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 27.64 N, student B pulls with a force of 11.21 N, and student C pulls with a force of 38.06 N at an angle ?(theta)=78.5 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.)


2. 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.

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 27.64 N, student B pulls with a force of 11.21 N, and student C pulls with a force of 38.06 N at an angle ?(theta)=78.5 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

F1 = 27.64i

F2 = -11.21j

F3 = -38.06cos(78.5)i + 38.06sin(78.5)j

= -7.576i+ 37.296j


Fnet = F1+F2+F3

= 27.64i -11.21j - 7.576i + 37.296j

= 20.064i + 26.086j


(a)

Magnitude of net force = sqrt( 20.064^2 + 26.086^2)

= sqrt( 402.564 + 680.479)

= 32.91 N


(b)

tan8 = (26.086 / 20.064)

8 = 52.434 degrees with respect to x-axis