Two forces, F? 1 and F? 2, act at a point, as shown in the picture. (Figure 1) F? 1 has a magnitude of 9.20 N and is directed at an angle of

Question

Two forces, F? 1 and F? 2, act at a point, as shown in the picture. (Figure 1) F? 1 has a magnitude of 9.20 N and is directed at an angle of ? = 57.0 ? above the negative xaxis in the second quadrant. F? 2 has a magnitudeof 5.20 N and is directed at an angle of ? = 53.7 ? below the negative x axis in the third quadrant.

Part A

What is the x component Fx of the resultant force?

Express your answer in newtons.

Part B

What is the y component Fy of the resultant force?

Express your answer in newtons.

Part C

What is the magnitude F of the resultant force?

Express your answer in newtons.

Part D

What is the angle ? that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

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Ngọc Hoa 4 years 2021-09-01T09:17:48+00:00 1 Answers 3 views 0

Answers ( )

  1. trungdung22
    0
    2021-09-01T09:19:36+00:00
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    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°

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )