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 component method. We can break up each force vector into its x and y components, and add up all the x components to get the x component of the resultant force, and add up all the y components to get the y component of the resultant force.

Using trigonometry, we can find the x and y components of each force vector:

F1x = 80 cos(30°) = 69.3 N
F1y = 80 sin(30°) = 40 N

F2x = 60 cos(150°) = -30 N
F2y = 60 sin(150°) = 45 N

F3x = 40 cos(45°) = 28.3 N
F3y = 40 sin(45°) = 28.3 N

Now we can add up the x and y components:

Rx = 69.3 N - 30 N + 28.3 N = 67.6 N
Ry = 40 N + 45 N + 28.3 N = 113.3 N

The magnitude of the resultant force is:

R = sqrt(Rx^2 + Ry^2) = sqrt((67.6 N)^2 + (113.3 N)^2) = 130.5 N

The direction of the resultant force is:

theta = atan(Ry/Rx) = atan((113.3 N)/(67.6 N)) = 59.7°

So 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