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11.1.5.3: Problems

  • Page ID
    34088
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    Exercise \(\PageIndex{1}\): A \(2-\text{kg}\) Physics textbook pressed against a wall does not move

    Consider a \(2\text{-kg}\) physics textbook (not drawn to scale) pressed against a wall, which has a coefficient of static friction of \(\mu_{s} = 0.3\) and a coefficient of kinetic friction of \(\mu_{k} = 0.2\) as shown in the animation (position is given in meters and time is given in seconds)Restart.

    1. Draw a free-body diagram for the book, showing all the forces that act.
    2. What is the net force on the book? Include both magnitude and direction in your answer.
    3. What is the minimum force of the push represented by the hand?
    4. What happens to the motion of the book and to the forces if the push is greater than your answer to (c)?

    Exercise \(\PageIndex{2}\): A \(2-\text{kg}\) Physics textbook pressed against a wall moves

    Consider a \(2\text{-kg}\) physics textbook (not drawn to scale) pressed against a wall, which has a coefficient of kinetic friction of \(\mu_{k} = 0.4\) as shown in the animation (position is given in meters and time is given in seconds)Restart.

    1. Draw a free-body diagram for the book, showing all the forces that act.
    2. What is the net force on the book? Include both magnitude and direction in your answer.
    3. What is the force of the push represented by the hand?

    Exercise \(\PageIndex{3}\): A \(2-\text{kg}\) Physics textbook pressed against a wall moves

    Consider a \(2\text{-kg}\) physics textbook (not drawn to scale) pressed against a wall, which has a coefficient of kinetic friction of \(\mu_{k} = 0.4\) as shown in the animation (position is given in meters and time is given in seconds)Restart.

    1. Draw a free-body diagram for the book, showing all the forces that act.
    2. What is the net force on the book? Include both magnitude and direction in your answer.
    3. What is the force of the push represented by the hand?

    Exercise \(\PageIndex{4}\): A block is pushed by a varying force

    A woman pushes on a block with an unknown force as shown in the animation (position is given in meters and time is given in seconds). At \(t = 2\) seconds she doubles the force applied to the block. Determine the coefficient of kinetic friction between the block and the table. Restart.

    Exercise \(\PageIndex{5}\): A \(4-\text{kg}\) block sits on an \(8-\text{kg}\) block pushed across the floor

    A \(4\text{-kg}\) block sits on an \(8\text{-kg}\) block that is pushed across the floor as shown (position is given in meters and time is given in seconds)Restart.

    1. Which free-body diagram is correct? Give reasons why the other three diagrams are incorrect.
    2. Draw the correct free-body diagram and label the force that causes each interaction.

    Be sure to include the force of friction if two surfaces are rubbing against each other. Remember that the length of an arrow is proportional to the value of the quantity being represented, and its length does not represent the actual size of the quantity.

    Exercise \(\PageIndex{6}\): A \(10.0-\text{kg}\) block sits on a \(20-\text{kg}\) block

    A \(10.0\text{-kg}\) block sits on a \(20\text{-kg}\) block as shown (position is given in meters and time is given in seconds). There is friction between the top and the bottom block, but the surface between the bottom block and the table is frictionless. Restart.

    1. Draw free-body diagrams for both blocks.
    2. Find the net force on each block.
    3. Find the force of the push.

    Exercise \(\PageIndex{7}\): A \(12-\text{kg}\) box slides on a rough \(26.56^{\circ}\) ramp

    A \(12-\text{kg}\) box slides on a rough (meaning that there is friction) \(26.56^{\circ}\) ramp as shown in the animation (position is given in meters and time is given in seconds)Restart.

    1. Draw a free-body diagram for the box, showing all the forces that act.
    2. What is the net force on the box? Include both magnitude and direction in your answer.
    3. What is the value for the coefficient of kinetic friction?

    Exercise \(\PageIndex{8}\): Take a ride on a Ferris wheel

    In the animation, a Ferris wheel rotates at constant speed as shown (position is given in meters and time is given in minutes). Each square represents a chair on the Ferris wheel. Restart.

    1. Draw the free-body diagram for a chair on the Ferris wheel when it is at the points (a), (b), (c), and (d).
    2. What forces act on a rider when the rider is at points (a), (b), (c), and (d)?
    3. What is the acceleration of the rider when the rider is at points (a), (b), (c), and (d)?
    4. If the rider has a mass of 100 kg, what is the size and direction of the net force on the rider at points (a), (b), (c), and (d)?

    Script authored by Aaron Titus.
    Problem authored by Wolfgang Christian and Mario Belloni.

    Exercise \(\PageIndex{9}\): A mass sits on a turntable

    A mass sits on a turntable as shown (position is given in meters and time is given in seconds)Restart.

    1. What force provides the centripetal acceleration?
    2. Which vector represents the net force on the object?

    Exercise \(\PageIndex{10}\): A puck resting on an air hocket table is attached to a string

    A puck resting on an air hockey table is attached to a string and given an initial tangential push such that it travels in a circle at constant speed (position is given in meters and time is given in seconds)Restart.

    1. What is the magnitude of the acceleration of the puck?
    2. Draw the free-body diagram for the puck.
    3. What is the tension in the string if the puck has a mass of \(0.1\text{ kg}\)?

    Exercise \(\PageIndex{11}\): A \(5\)-gram coin is on a rotating turntable

    A \(5\)-gram coin is on a rotating turntable as shown (position is given in meters and time is given in seconds)Restart.

    1. What is the coin's acceleration during the animation?
    2. Draw a free-body diagram for the coin.
    3. Determine the minimum value of \(\mu_{s}\) for this motion to occur.

    Exercise \(\PageIndex{12}\): The spring can be stretched by click-dragging the blue ball

    The spring can be stretched by click-dragging the blue ball as shown in the animation (position is given in centimeters and time is given in seconds). Slowly drag the spring back and forth out of the equilibrium position and answer the following questions. Restart.

    1. Over what range of compression and stretching is Hooke's law valid?
    2. Find the elastic limit of the spring.
    3. Determine the spring constant of the spring.

    Exercise \(\PageIndex{13}\): A \(200\)-gram brick falls onto a platform

    A \(200\)-gram brick falls onto a platform as shown in the animation (position is given in meters and time is given in seconds). The animation stops when the brick is in equilibrium. Determine the spring constant of the spring. Restart.

    Exercise \(\PageIndex{14}\): A ball is fired at a block connected to a spring

    A ball on a frictionless table is fired at a block that is connected to a very light spring as shown (position is given in meters and time is given in seconds)Restart.

    1. For each animation, draw the force vs. time graph for the orange ball.
    2. Suppose you wanted to determine \(x(t)\) for the orange ball. Are Newton's laws an effective way to determine \(x(t)\) for the orange ball? Why or why not?

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


    This page titled 11.1.5.3: 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.