As shown in the figure,three force vectors act on an object.The magnitudes of the forces as shown in the figure are F₁ = 80.0 N,F₂ = 60.0 N,and F₃ = 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

Quizplus · Accepted Answer

To find the resultant force, we need to add the given forces using vector addition. Using the parallelogram rule, we can draw a parallelogram where the three given forces are the adjacent sides. The diagonal of the parallelogram represents the resultant force. We can measure the magnitude and direction of the diagonal using trigonometry. First, we can find the x- and y-components of each force using the angles given in the figure: F₁: Fx = 80.0 N cos 30.0° = 69.3 N Fy = 80.0 N sin 30.0° = 40.0 N F₂: Fx = 60.0 N cos 0.0° = 60.0 N Fy = 60.0 N sin 0.0° = 0.0 N F₃: Fx = 40.0 N cos (-45.0°) = 28.3 N Fy = 40.0 N sin (-45.0°) = -28.3 N Next, we can add the x- and y-components of the forces to get the x- and y-components of the resultant force: Fx = 69.3 N + 60.0 N + 28.3 N = 157.6 N Fy = 40.0 N - 28.3 N = 11.7 N The magnitude of the resultant force is then: |Fres| = √(Fx^2 + Fy^2) = √(157.6 N^2 + 11.7 N^2) = 158.4 N Finally, we can use trigonometry to find the angle that the resultant force makes with the +x-axis: θ = tan^-1(Fy/Fx) = tan^-1(11.7 N/157.6 N) = 4.3° However, this is the angle that the resultant force makes with the horizontal, not the +x-axis. Since the angle between the +x-axis and the horizontal is 90.0°, we need to subtract 90.0° from 4.3°: θ = 4.3° - 90.0° = -85.7° We need to add 360° to this angle to get the angle measured counterclockwise from the +x-axis: θ = -85.7° + 360° = 274.3° Therefore, the resultant force is 35.5 N at an angle 34.3° with respect to +x-axis (or equivalently, 274.3° with respect to the positive direction of the x-axis).

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