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16.6: Appendix 1 Homework Problems

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    Exercise \(\PageIndex{1}\)

    Determine the \(x\) and \(y\) components of the force vector shown below.

    The first quadrant of a standard-orientation Cartesian coordinate plane. A vector of magnitude 800 N extends from the origin, at an angle of 60° from the positive y-axis.
    Figure \(\PageIndex{1}\): problem diagram for Exercise \(\PageIndex{1}\). A vector in the first quadrant of a Cartesian coordinate plane, with its tail at the origin.
    Solution:

    \(F_x = 692.8 \ N\)

    \(F_y = 400 N\)

    Exercise \(\PageIndex{2}\)

    Determine the \(x\), \(y\), and \(z\) components of the vector shown below.

    A three-dimensional Cartesian coordinate system with the x- and y-axes lying in the plane of the screen and the z-axis pointing out of the screen. A force vector with magnitude 6 kN extends to the right, upwards and into the plane of the screen, making a 130° angle with the positive z-axis and a 25° angle with the xz-plane.
    Figure \(\PageIndex{2}\): problem diagram for Exercise \(\PageIndex{2}\). A vector originates from the origin of a Cartesian coordinate system, pointing into the plane of the screen.
    Solution:

    \(F_x = 4.17 \ kN\)

    \(F_y = 2.54 \ kN\)

    \(F_z = -3.50 \ kN\)

    Exercise \(\PageIndex{3}\)

    An 80-lb tension acts along a cable stretching from point O to point A. Based on the dimensions given, break the tension force shown into \(x\), \(y\), and \(z\) components.

    A three-dimensional Cartesian coordinate system with the x- and y-axes lying in the plane of the screen and the z-axis pointing out of the screen. A cable stretches from point O at the origin to point A, which has the coordinates x = 8 inches, y = -12 in., and z = 9 in. A tension force T of magnitude 80 lbs acts along the wire, pointing from O to A.
    Figure \(\PageIndex{3}\): problem diagram for Exercise \(\PageIndex{3}\). A cable with a force acting along it connects the origin of a Cartesian coordinate system to a given point A.
    Solution:

    \(F_x = 56.47 \ lbs\)

    \(F_y = -37.64 \ lbs\)

    \(F_z = 42.35 \ lbs\)

    Exercise \(\PageIndex{4}\)

    Determine the \(x\) and \(y\) components of the sum of the two vectors shown below.

    A standard-orientation Cartesian coordinate plane, where two force vectors radiate out from the origin. One vector has a magnitude of 60 lbs and is directed 60° above the positive x-axis. The other has a magnitude of 30 lbs and is directed 20° below the positive x-axis.
    Figure \(\PageIndex{4}\): problem diagram for Exercise \(\PageIndex{4}\). Two force vectors radiate out from the origin of a Cartesian coordinate plane.
    Solution:

    \(F_{total} = [58.2, 41.7] \ lbs\)

    Exercise \(\PageIndex{5}\)

    There are two forces acting on a barge as shown below (\(\vec{F}_1\) and \(\vec{F}_2\)). The magnitude and direction of \(\vec{F}_1\) is known, but the magnitude and direction of \(\vec{F}_2\) is not. If the sum of the two forces is 600 N along the \(x\)-axis, what must the magnitude and direction of \(\vec{F}_2\) be?

    A standard-orientation Cartesian coordinate plane. The head of a barge is facing the positive x-direction, and located with the midpoint of that head at the origin. Two forces are applied to the barge at the origin: F_1 has a magnitude of 400 N and points 40° above the positive x-axis. F_2 has an unknown magnitude and points at some unknown angle below the x-axis. The sum of the two forces has magnitude 600 N, pointing in the positive x-direction.
    Figure \(\PageIndex{5}\): problem diagram for Exercise \(\PageIndex{5}\). Two forces are applied to the same point on a barge, with the magnitude and direction of one of the force vectors as well as the vector sum being known.
    Solution:

    \(\vec{F}_2 = 390.3 \ N\), at 41.2° below the x-axis

    This page titled 16.6: Appendix 1 Homework Problems is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Jacob Moore & Contributors (Mechanics Map) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.