Two forces, F ? 1 and F ? 2, act at a point, as shown in the picture. (Figure 1)

Question

Two forces, F? 1 and F? 2, act at a point, as shown in the picture. (Figure 1) F? 1 has a magnitude of 9.80N and is directed at an angle of ? = 60.0? above the negative xaxis in the second quadrant. F? 2 has a magnitude of 7.00N and is directed at an angle of ? = 53.9? below the negative x axis in the third quadrant.

Part A

What is the x component Fx of the resultant force?

Express your answer in newtons.

Part B

What is the y component Fy of the resultant force?

Express your answer in newtons.

Part C

What is the magnitude F of the resultant force?

Express your answer in newtons.

Part D

What is the angle ? that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

Express your answer in degrees.

Two forces, F? 1 and F? 2, act at a point, as shown in the picture. (Figure 1) F? 1 has a magnitude of 9.80N and is directed at an angle of ? = 60.0? above the negative xaxis in the second quadrant. F? 2 has a magnitude of 7.00N and is directed at an angle of ? = 53.9? below the negative x axis in the third quadrant. Part A What is the x component Fx of the resultant force? Express your answer in newtons. Part B What is the y component Fy of the resultant force? Express your answer in newtons. Part C What is the magnitude F of the resultant force? Express your answer in newtons. Part D What is the angle ? that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis. Express your answer in degrees.

Explanation / Answer

Note that          
          
F1 =    9.8   N  
t1 = the reference angle of F1 =    120   degrees  
F2 =    7   N  
t2 = the reference angle of F2 =    233.9   degrees  
          
Thus, their x and y components are          
          
F1x =    -4.9   N  
F1y =    8.487048957   N  
F2x =    -4.124374501   N  
F2y =    -5.655929187   N  
          
Thus, the sum of the x components are          
          
Fx =    -9.024374501   N   [ANSWER, PART A]
Fy =    2.83111977   N   [ANSWER, PART B]
          
The magnitude of the resultant force, by Pythagorean theorem is          
          
|F| =    9.458042836   N   [ANSWER, PART C]
          
For the angle, we have          
          
theta (angle of the resltant force) = |Arctan(Fy/Fx)| =    17.417644   degrees   [ANSWER, PART D]
          
DONE!          

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