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 60.10 N, student B pulls with a force of 18.63 N, and student C pulls with a force of 59.79 N at an angle (theta)=73.93 degrees above the -x axis. (The drawing is not to scale.)

You want to determine the net force acting on the book. This will involve adding the three vectors: break the vectors into components, combine the components, and then reconstruct the net vector (magnitude and direction).

What are the x and y components of the force due to Student A? (Note that you need to get both of the components right to get the question right.)

x-comp:  
y-comp:  

What are the x and y components of the force due to Student B?

x-comp:  
y-comp:  

What are the x and y components of the force due to Student C?

x-comp:  
y-comp:  

What are the x and y components of the net force on the textbook due to all three students?

x-comp:  
y-comp:  

What is the magnitude of the net force on the textbook due to the forces from all three students?

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. (Remember the units for an angle in degrees is deg)

Explanation / Answer

break into vector x, y components
A = 60.10 i
B = -18.63 j
C = -59.79cos73.93 i + 59.79sin73.93 j
C = -23.80 i + 54.84 j

R = A + B + C
R = (60.10 - 23.80) i + (-18.63 + 54.84) j
R = 36.3 i + 36.21 j

|R| = (36.32 + 36.212)
|R| = 2628.85
|R| = 51.27 N

tan = 36.21 / 36.3
= 49.68o above the positive x axis

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