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4.9: Chapter 4 Homework Problems

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    Exercise \(\PageIndex{1}\)

    Determine if the two systems below are statically equivalent.

    A horizontal rod held off the ground by two supports: one at the right end, and the other 10 feet to the left of the first. A downwards point force of 60 lbs is applied at the midpoint between these supports, and another downwards point force of 40 lbs is applied 3 feet to the left of the support on the left.
    Figure \(\PageIndex{1}\): part 1 of the problem diagram for Exercise \(\PageIndex{1}\). A horizontal bar held off the ground by two supports experiences two point forces at different points along its length.
    A horizontal rod held off the ground by two supports: one at the right end, and the other 10 feet to the left of the first. A downwards point force of 100 lbs is applied to the rod, 2 feet to the right of the support on the left.
    Figure \(\PageIndex{2}\): part 2 of the problem diagram for Exercise \(\PageIndex{1}\). A horizontal bar held off the ground by two supports experiences a single point force partway along its length.
    Solution

    No, they are not equivalent.

    Exercise \(\PageIndex{2}\)

    Determine if the set of forces in A is statically equivalent to the set of forces and moments in B.

    System A (on the left) consists of a uniform cross composed of two 60-cm rods joined at their midpoints, with an upwards force of 200 N applied to the end of the cross's left arm, a leftwards force of 200 N applied to the end of the upper arm, an upwards force of 200 N applied to the midpoint of the right arm, and a rightwards force of 100 N applied to the end of the lower arm. System B (on the right) consists of an identical cross with an upwards force of 200 N applied to the end of the left arm, a leftwards force of 100 N applied to the end of the upper arm, an upwards force of 200 N applied to the end of the right arm, a rightwards force of 200 N applied to the lower arm, and a clockwise moment of 30 N-m about the cross center.
    Figure \(\PageIndex{3}\): problem diagram for Exercise \(\PageIndex{2}\). Two uniform crosses of equal dimensions experience a set of forces (system A, left) and a set of forces and moments (system B, right).
    Solution

    No, they are not equivalent.

    Exercise \(\PageIndex{3}\)

    Determine the equivalent point load (magnitude and location) for the distributed force shown below.

    A horizontal bar 5 meters long is attached to a wall at its left end. Starting at the point 2 meters to the right of the wall, it experiences a downwards distributed force over the rest of its length that varies linearly in magnitude: starting at 50 N/m and decreasing to 20 N/m at the right end.
    Figure \(\PageIndex{3}\): problem diagram for Exercise \(\PageIndex{3}\). A horizontal bar attached to a wall at one end experiences a distributed force, which varies linearly, over part of its length.
    Solution

    \(F_{eq} = 105 \, N\)

    \(x_{eq} = 3.29 \, m\) (measured from wall)

    Exercise \(\PageIndex{4}\)

    Determine the equivalent point load (magnitude and location) for the distributed force shown below.

    A horizontal bar 18 feet long is attached to a wall at its left end. It experiences a distributed force whose magnitude starts at 0 lb/ft at the left end, increases linearly tp 600 lbs/ft at the point 6 feet to the right of the wall, and decreases linearly to 0 lb/ft at the right end of the bar.
    Figure \(\PageIndex{4}\): problem diagram for Exercise \(\PageIndex{4}\). A horizontal bar attached to a wall experiences a distributed force over its length, with magnitude varying linearly according to a piecewise force function.
    Solution

    \(F_{eq} = 5400 \, lbs\)

    \(x_{eq} = 8 \, ft\) (measured from wall)

    This page titled 4.9: Chapter 4 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.