As shown in the figure,three force vectors act on an object.The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N,and = 40.0 N,where N is the standard SI unit of force.The resultant force acting on the object is given by
A)180 N at an angle 60.0° with respect to +x-axis.
B)60.0 N at an angle 90.0° with respect to +x-axis.
C)20.0 N at an angle 34.3° with respect to +x-axis.
D)35.5 N at an angle 34.3° with respect to +x-axis.
E)40.0 N at an angle 60.0° with respect to +x-axis.

Question

As shown in the figure,three force vectors act on an object.The magnitudes of the forces as shown in the figure are  = 80.0 N,  = 60.0 N,and  = 40.0 N,where N is the standard SI unit of force.The resultant force acting on the object is given by 
A)180 N at an angle 60.0° with respect to +x-axis. 
B)60.0 N at an angle 90.0° with respect to +x-axis. 
C)20.0 N at an angle 34.3° with respect to +x-axis. 
D)35.5 N at an angle 34.3° with respect to +x-axis. 
E)40.0 N at an angle 60.0° with respect to +x-axis.

Quizplus · Accepted Answer

To find the resultant force, we can use the vector addition method.

First, let's resolve each force vector into its x and y components:

F1 = 80.0 N at 0° = (80.0 cos 0°)i + (80.0 sin 0°)j
     = 80.0i

F2 = 60.0 N at 120° = (60.0 cos 120°)i + (60.0 sin 120°)j
     = -30.0i + 51.96j

F3 = 40.0 N at 240° = (40.0 cos 240°)i + (40.0 sin 240°)j
     = -20.0i - 34.64j

Note: We use j direction for y-component here.

The negative sign in F2 and F3's i component is because they act in the negative x direction.

Now, we can add these components together to get the resultant force:

Fres = F1 + F2 + F3
        = (80.0 - 30.0 - 20.0)i + (51.96 - 34.64)j
        = 30.0i + 17.32j

To find the magnitude and direction of this vector, we can use trigonometry:

|Fres| = sqrt((30.0)^2 + (17.32)^2) = 35.5 N

θ = arctan(17.32/30.0) = 34.3°

Therefore, the answer is D) 35.5 N at an angle 34.3° with respect to +x-axis.

As Shown in the Figure,three Force Vectors Act on an Object.The