Answer:
a. Fx = -8.089 N b. Fy = 3.525 N c. 8.824 N d. 336.45°
Explanation:
Since F₁ = 9.2 N and acts at 57° above the negative axis in the second quadrant, its x-component is -F₁cos57° and its y- component is F₁sin57°
Since F₁ = 5.2 N and acts at 53.7° below the negative axis in the third quadrant, its x-component is -F₂cos53.7° and its y- component is -F₂sin53.7°
Part A
What is the x component Fx of the resultant force?
The x component of the resultant force Fx = -F₁cos57° + -F₂cos53.7° = -9.2cos57° + (-5.2cos53.7°) = (-5.011 - 3.078) N = -8.089 N
Part B
What is the y component Fy of the resultant force?
The y component Fy of the resultant force = F₁sin57° + -(F₂sin53.7°) = 9.2sin57° - 5.2sin53.7° = (7.716 - 4.191) N = 3.525 N
Part C
What is the magnitude F of the resultant force?
The magnitude F of the resultant force = √(Fx² + Fy²)
F = √(-8.089² N + 3.525² N) = √65.432 + 12.426 = √77.858 = 8.824 N
Part D
What is the angle ? that the resultant force forms with the negative x axis?
The angle the resultant force makes with the negative x axis is given by
θ = tan⁻¹(Fy/Fx) = tan⁻¹(3.525/-8.089) = tan⁻¹-0.4358 = -23.55°.
To measure it from the negative x axis, we add 360. So, our angle = 360 -23.55 = 336.45°
