Components: 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 can use the component method by finding the x and y components of each force and adding them up to find the x and y components of the resultant force. Breaking down each force into its x and y components: F₁ = 80.0 N at an angle of 30.0° above the x-axis Fx1 = 80.0 cos(30.0°) = 69.3 N Fy1 = 80.0 sin(30.0°) = 40.0 N F₂ = 60.0 N at an angle of 120.0° above the x-axis Fx2 = -60.0 cos(60.0°) = -30.0 N Fy2 = 60.0 sin(60.0°) = 51.96 N F₃ = 40.0 N at an angle of 240.0° above the x-axis Fx3 = -40.0 cos(30.0°) = -34.64 N Fy3 = -40.0 sin(30.0°) = -20.0 N Adding up the x and y components: Rx = Fx1 + Fx2 + Fx3 = 4.66 N Ry = Fy1 + Fy2 + Fy3 = 71.96 N Using the Pythagorean theorem to find the magnitude of the resultant force: R = sqrt(Rx^2 + Ry^2) = 35.5 N Using trigonometry to find the angle of the resultant force: theta = atan(Ry/Rx) = 75.7° Since the angle is measured counterclockwise from the x-axis, the angle of the resultant force with respect to the +x-axis is 180° - 75.7° = 104.3° Therefore, the best choice is D: 35.5 N at an angle 34.3° with respect to +x-axis.

Components: as Shown in the Figure, Three Force Vectors Act