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8.5: Chapter 8 Homework Problems

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    Exercise \(\PageIndex{1}\)

    A 50-kg box is being pulled across a surface by a force of 200 N in the direction shown below. If the coefficient of friction is 0.3, what is the rate of acceleration of the box and how far will the box move in a three-second period?

    A 50-kg box sitting on a flat horizontal surface experiences a force of 200 N that pulls up and to the right, at 20° above the horizontal.
    Figure \(\PageIndex{1}\): problem diagram for Exercise \(\PageIndex{1}\). A box is pulled across a horizontal surface by a force directed 20° above the horizontal.
    Solution

    \(a = 1.23 \, m/s^2\)

    \(s = 5.52 \, m\)

    Exercise \(\PageIndex{2}\)

    A 3-kg cannonball is shot out of a cannon with an initial velocity of 300 m/s at a 25-degree angle. A headwind exerts a constant 5 N horizontal force. How far will the cannonball travel horizontally before hitting the ground?

    A stretch of flat ground contains a cannon at the left end, pointing rightwards and upwards at 25° above the horizontal. The parabolic path that its cannonball is expected to take before hitting the ground is indicated with a dashed line. The cannonball is currently in flight, experiencing a force of 5 N that points directly leftwards from the headwind.
    Figure \(\PageIndex{2}\): problem diagram for Exercise \(\PageIndex{2}\). Diagram of the parabolic path the cannonball is expected to travel before hitting the ground to the right of the cannon, with the leftwards headwind force on the ball shown.
    Solution

    \(d = 6470 \, m\)

    Exercise \(\PageIndex{3}\)

    A 1-kg block sits on a rotating table as shown below. If the static coefficient of friction is assumed to be 0.4, what is the maximum angular velocity \((\dot{\theta})\) that can be achieved before the block begins to slip?

    A small, cube-shaped block sits near the outer edge of a level, circular table, 2 meters from the table's center. The table is rotating in the counterclockwise direction as viewed from above.
    Figure \(\PageIndex{3}\): problem diagram for Exercise \(\PageIndex{3}\). A small block sits 2 meters from the center of a level, rotating circular table.
    Solution

    \(\dot{\theta} = 1.4 \, \frac{rad}{s}\)

    Exercise \(\PageIndex{4}\)

    A 5-kg instrument is held via a cable to a space station. The instrument and space station are both rotating at a rate of 0.5 rad/s when the space station begins retracting the cable at a constant rate of 0.25 m/s.

    • What is the tension in the cable at this instant?
    • What will the angular acceleration \((\ddot{\theta})\) of the cable be? Hint: there are no forces in the \(\theta\) direction.
    A small dot (the instrument) is drawn some distance directly above a large circle (the space station). The two bodies are connected by a cable, and the distance between the two is 12 meters. The entire system is rotating counterclockwise at a rate of 0.5 rad/s. The distance between the two bodies is decreasing at a rate of 0.25 m/s.
    Figure \(\PageIndex{4}\): problem diagram for Exercise \(\PageIndex{4}\). A space station and a cable-connected instrument, rotating as a system, draw closer together as the station pulls in the cable at a constant rate.
    Solution

    \(T = 15 \, N\)

    \(\ddot{\theta} = 0.0208 \, \frac{rad}{s^2}\)

    This page titled 8.5: Chapter 8 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.