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 17.26 N, student B pulls with a force of 12.55 N, and student C pulls with a force of 39.52 N at an angle theta (theta) = 83.22 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? 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

Fa=17.26N

Fb=12.55N

Fc=39.52N at angle83.22

Fccos 83.22=39.52cos83.22=4.6656N along negative xaxis

Fcsin 83.22=39.52sin83.22=39.24366N along positive y axis

Fa is along positive xaxis so net force due to Fa and Fccos83.22 wil be17.26-4.6656=12.5944N along positive x axis

Net force due to Fb anb Fcsin 83.22=39.24366-12.55=26.69N along positive y axis

Now net force due to 26.69along positive y axis and 12.5994 along positive xaxis wil be (26.69^2+12.5994^2)^1/2

(Acc to parallelogram law of vectors )=871.21N

And direction with xaxis will be angle beta value of which can be calculated by

tan beta=26.69sin90/12.599+26.69cos90=26.69/12.59=2.12

So angle beta wil be=tan inverse of 2.12=64.75 with positive xaxis

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