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11.1.4.3: Problems

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    Exercise \(\PageIndex{1}\): Which is the correct free-body diagram?

    A red block is pushed and moves as shown in the animation. In addition, a green block sits on the red block and moves as well. Restart.

    1. Which free-body diagram is correct? Give reasons why the other three diagrams are incorrect.
    2. How would your answer to (a) change if the blocks did not move?

    Exercise \(\PageIndex{2}\): Interpret the free-body diagram

    A free-body diagram for a \(20,000\text{-kg}\) airplane at some instant is shown in the animation (grid size is given in \(40,000\) newtons). Generally, all of the external forces on an airplane can be resolved into four components called weight, lift, thrust, and drag. Restart. You can move a vector around by click-dragging at its tail.

    1. What is the net force on the airplane at this instant?
    2. What is the acceleration of the airplane at this instant?
    3. What can you definitely say about the velocity of the airplane at this instant?
    4. Suppose a classmate in your study group proclaims that "the net force on the airplane is zero and therefore the airplane must be on the ground and at rest." What is the error in your classmate's statement?

    Problem authored by Aaron Titus.

    Exercise \(\PageIndex{3}\): Pull your little red wagon

    A \(100\text{-kg}\) wagon with a \(20\text{-kg}\) block on its frictionless bed is pulled to the right with a constant force (position is given in meters and time is given in seconds). Does the animation obey Newton's laws? Support your answer. Restart.

    Exercise \(\PageIndex{4}\): Pull your little red wagon

    A \(100\text{-kg}\) wagon with a \(20\text{-kg}\) block on its frictionless bed is pulled to the right with an unknown force (position is given in meters and time is given in seconds). Sketch a plot of the force exerted by the hand on the cart as a function of time. Restart.

    Exercise \(\PageIndex{5}\): A buoy is dropped into a lake

    A \(0.010\text{-kg}\) buoy is dropped into a lake as shown in the animation. Before it hits the water, it is in free fall. Restart.

    1. Before the buoy hits the water, what is the net force on the buoy?
    2. At \(t = 1.2\text{ s}\), what is the net force on the buoy?
    3. At \(t = 1.2\text{ s}\), what is the force of the water on the buoy?
    4. At \(t = 4.5\text{ s}\), what is the net force on the buoy? Approximately, what is the velocity of the buoy at this instant? Can the velocity of an object be zero even though the net force on the object is not zero?
    5. At \(t = 4.5\text{ s}\), what is the force of the water on the buoy?
    6. At \(t = 11.0\text{ s}\), what is the net force on the buoy?
    7. At \(t = 11.0\text{ s}\), what is the force of the water on the buoy?
    8. Describe the velocity of the buoy at this instant (\(t = 11.0\text{ s}\)); is it increasing, decreasing, or constant?

    Problem authored by Aaron Titus.

    Exercise \(\PageIndex{6}\): Putted golf ball

    The animation shows a putted golf ball of mass \(0.050\text{ kg}\) as it rolls toward the hole. The putter hit the ball before \(t = 0\text{ s}\) and is no longer in contact with the ball (position is given in meters and time is given in seconds). Restart.

    1. What is the net force on the golf ball during the interval from \(t = 0\) to \(t = 4.2\text{ s}\)?
    2. What is the force of the putter on the golf ball during this interval?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{7}\): A ball constrained to move on a rod

    A \(20\text{-kg}\) ball has a hole with a rod passing through. The rod exerts a force as needed that constrains the ball to move along the rod. An applied force is now added (the "pulling" force) so the ball is pulled as shown (position is given in meters and time is given in seconds). The force vector is shown as a red arrow, and the force makes an angle \(\theta\) with the horizontal. The velocity is given in meters/second. You may adjust the angle and/or the magnitude of the pulling force \((F < 7\text{ N})\). Restart.

    1. How does the acceleration change as you vary the pulling force for a constant angle?
    2. How does the acceleration change as you vary the angle for a constant pulling force?
    3. Combine your answers above to obtain a general mathematical formula for the acceleration of the ball due to an arbitrary applied force.
    4. Determine the general mathematical formula for the normal force the rod exerts on the ball when an arbitrary force is applied to the ball.

    Script authored by Steve Mellema, Chuck Niederriter and modified by Mario Belloni.
    Problem authored by Mario Belloni.

    Exercise \(\PageIndex{8}\): Take a ride in an elevator

    A \(50\text{-kg}\) box is riding in an elevator that accelerates upward or downward at a constant rate (position is given in meters and time is given in seconds). The box rests on a digital scale that records its apparent weight in newtons. The green arrow represents the instantaneous velocity of the elevator and its contents. Adjust the value of the acceleration \((-9.8\text{ m/s}^{2}\leq a\leq 9.8\text{ m/s}^{2})\) and see how it affects the apparent weight. Restart.

    1. What type of force is recorded on the scale?
    2. Draw a free-body diagram for the box when its acceleration is \(4.9\text{ m/s}^{2},\: 0\text{ m/s}^{2}\), and \(-4.9\text{ m/s}^{2}\).
    3. Write a formula for the scale reading as a function of the acceleration of the elevator, the mass of the box, and g.
    4. Determine the value of the elevator's acceleration that would make the force that the scale exerts on the box vanish In other words, how can the box become apparently "weightless?"

    Script authored by Steve Mellema, Chuck Niederriter, and modified by Mario Belloni.
    Problem authored by Mario Belloni.

    Exercise \(\PageIndex{9}\): Rank the accelerations and tensions

    A \(10\text{-kg}\) mass is attached via a massless string over a massless pulley to a hand (position is given in meters and time is given in seconds). The masses in each animation are identical. Restart.

    1. Rank the animations according to the acceleration of the mass, from greatest to least (positive is up).
    2. Rank the animations according to the tension in the string, from greatest to least (positive is up).

    Indicate ties by placing the animation numbers in () please. For example, a suitable response could be: \(1,\:2,\:(3,\:4),\:5,\:6\).

    1. Calculate the acceleration of the mass in each animation.
    2. Calculate the tension of the string in each animation.

    Problem authored by Mario Belloni*.

    *This exercise was adapted from an original Ranking Task Exercise which appears in the book Ranking Task Exercises in Physics, T. O' Kuma, D. Maloney, and C. Hieggelke.

    Exercise \(\PageIndex{10}\): Hoisted boxes

    Two boxes, each of mass \(2.0\text{ kg}\), are connected by a lightweight rope. The boxes are hoisted upward with a constant acceleration as shown in the animation (position is given in meters and time is given in seconds). Restart.

    1. Draw a free-body diagram for each box.
    2. What is the tension in the top rope?
    3. What is the tension in the rope connecting the two boxes?

    Consider an alternative situation in which the system has the same acceleration but the rope between the boxes is not lightweight. It is a steel cable with a total mass of \(1.0\text{ kg}\).

    1. What would be the force of the steel cable on the top box?
    2. What would be the force of the steel cable on the bottom box?

    Problem authored by Aaron Titus.

    Exercise \(\PageIndex{11}\): Modified Atwood's machine

    A \(1.0\text{-kg}\) cart (not shown to scale) on a low-friction track is connected to a string and a hanging object as shown in the animation. Neglect any effects of the pulley on the motion of the system (position is given in meters and time is given in seconds). Restart.

    1. What is the tension in the string?
    2. What is the mass of the hanging object?

    Note that the coordinates for each object (the positive \(x\) direction) are already chosen for you.

    Problem authored by Aaron Titus.

    Exercise \(\PageIndex{12}\): A truck and car collision

    A large \(2000\text{-kg}\) truck and a small compact car collide head-on as shown in the animation (position is given in meters and time is given in seconds). Assume the collision takes place in \(0.05\) seconds. Restart.

    1. Describe the force on each vehicle before, during, and after the collision. Be sure to estimate the magnitudes of these forces and give their directions.
    2. Which vehicle, the car or the truck, experiences the greater force during the collision?

    Exercise \(\PageIndex{13}\): Does the force obey Newton's third law?

    Newton's third law states that whenever two objects interact, they exert equal and opposite forces on each other (position is given in meters and time is given in seconds). The balls in the animations can be dragged around. As you do so, notice how the sizes of the arrows change. Each arrow represents the force on an object (the length of the arrow indicates the magnitude of the force). Which animation, if any, obeys Newton's third law? Restart.

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

    This page titled 11.1.4.3: 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.