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11.2.1.3: Problems

  • Page ID
    34134
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    Exercise \(\PageIndex{1}\): Hydraulic lift

    The animation shows a model of a hydraulic lift. The gray areas are circular lids on top of the yellow fluid inside the lift (position is given in centimeters)Restart

    1. What force is required on the left side to support the \(40\text{-kg}\) mass?
    2. If the mass is lifted up \(1\text{ cm}\), how far down does the fluid on the left need to be pushed?

    Problem authored by Anne J. Cox.

    Exercise \(\PageIndex{2}\): Mercury barometer

    A tube contains a column of mercury while the bottom container of mercury is open to the atmosphere to form a mercury barometer (position is given in tenths of meters and pressure given in pascals). What is the atmospheric pressure? Restart.

    Problem authored by Anne J. Cox.

    Exercise \(\PageIndex{3}\): Find the density of object in water

    Find the density of the object being immersed in the water bucket. The initial reading on the spring scale is \(19\text{ N}\). One full revolution of the spring scale represents a change of \(10\text{ N}\). Restart.

    Problem authored by Peter Sheldon and Mario Belloni.

    Exercise \(\PageIndex{4}\): Pressure and buoyant force of block suspended in water

    The blue liquid is an oil with \(\rho = 850\text{ kg/m}^{3}\) (position is given in centimeters and the dimension of the oil containers into the screen is \(20\text{ cm}\))Restart.

    1. If the mass is 150 g, what is the tension on the wire at the following times: \(0.4\text{ s},\: 1.5\text{ s}\) and \(4\text{ s}\)?
    2. What is the gauge pressure at the top of the mass at \(t = 1.5\text{ s}\) and \(t = 4\text{ s}\)?
    3. Some students find the answers to questions (a) and (b) (the tension in the wire and the gauge pressure) inconsistent. Explain why they are consistent with each other.

    Note that gauge pressure is the difference in pressure due to the surface of the water (the absolute pressure would be the pressure due to the atmosphere at the surface plus the pressure due to the water).

    Problem authored by Anne J. Cox.

    Exercise \(\PageIndex{5}\): How much weight will a boat hold?

    How much more mass can this "boat" sitting in water hold and still float? The dimension of the "boat" into the screen is \(8\text{ cm}\) (position is given in centimeters and time is given in seconds)Restart.

    Problem authored by Anne J. Cox

    Exercise \(\PageIndex{6}\): Find the density of a fluid

    A block is lowered into a liquid as shown (position is given in centimeters, time is given in seconds, and force is given in newtons). The dimension of both containers into the screen is \(20\text{ cm}\). The dimension of the block into the screen is \(10\text{ cm}\). What is the density of the liquid? Restart.

    Problem authored by Anne J. Cox.

    Exercise \(\PageIndex{7}\): Wood floating in water on an elevator

    Shown is a block of wood floating in a bucket of water. The bucket is placed in an elevator as shown in the animation (position is in meters and time is in seconds)Restart.

    1. Elevator in free fall: If the picture on the left represents the orientation of the wood when the elevator is stationary, which animation correctly depicts the new orientation of the wood while the elevator is in free fall as shown (assume a broken cable)?

    Animation 1a | Animation 2a | Animation 3a

    1. Elevator rising: If the picture on the left represents the orientation of the wood when the elevator is stationary, which animation correctly depicts the new orientation of the wood while the elevator is moving as shown?

    Animation 1b | Animation 2b | Animation 3b

    Problem authored by Mario Belloni and Anne J. Cox.

    Exercise \(\PageIndex{8}\): Hot-air balloon fight

    As the air inside a hot-air balloon is heated, the density of the air inside the balloon decreases and the balloon expands (see Chapter 20 and the Kinetic Theory and Ideal Gas Law Illustrations for a detailed explanation). The animation shows a hot-air balloon ascending with constant acceleration (position is given in meters and time is given in seconds). If the balloon fabric and basket have a combined mass of \(300\text{ kg}\), what is the density of the air inside the balloon? (Neglect the volume of the basket). The density of the air outside the balloon is \(1.3\text{ kg/m}^{3}\). Restart.

    Problem authored by Anne J. Cox.

    Exercise \(\PageIndex{9}\): Ice melting

    An ice cube melts in a glass of water as shown in the animation (position is given in centimeters and time is given in minutes). Which animation correctly shows what the final water level will be? Explain. Restart.

    Exercise \(\PageIndex{10}\): Water-oil mixture

    The animation is color coded as follows: Blue is water, red is oil, and brown is a wood block initially floating at the interface. A pump, which starts at \(t = 1\text{ s}\), removes the oil. Which animation is physical? (In other words, which animation obeys the laws of physics?) Explain. Restart.

    Problem authored by Peter Sheldon and Mario Belloni.

    Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.


    This page titled 11.2.1.3: Problems is shared under a CC BY-NC-ND license and was authored, remixed, and/or curated by Wolfgang Christian, Mario Belloni, Anne Cox, Melissa H. Dancy, and Aaron Titus, & Thomas M. Colbert.