Gravitational Potential Energy and Work Quiz
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Questions and Answers

What is momentum defined as in Newton's Principia?

  • The measure of force acting on an object
  • The rate of change of velocity of an object
  • The measure of kinetic energy possessed by an object
  • The measure of quantity of motion arising from velocity and mass (correct)

    • How is momentum calculated?

  • By adding mass and velocity
  • By multiplying mass and velocity (correct)
  • By multiplying mass and acceleration
  • By dividing force by velocity

    • In which situations can momentum be properly represented as a spatial vector?

  • In any of the three spatial dimensions (correct)
  • In two-dimensional motion only
  • In one-dimensional motion only
  • In three-dimensional motion only

    • What does a constant mass object's combination in the equation represent?

    <p>The difference of momentum of the object</p> Signup and view all the answers

    What is the gravitational potential energy defined as?

    <p>The opposite of the work done on an object</p> Signup and view all the answers

    What happens to the gravitational potential energy as work increases on the way down?

    <p>It decreases by the same amount</p> Signup and view all the answers

    What is the constant that results from the balance between kinetic energy and gravitational potential energy?

    <p>Total energy</p> Signup and view all the answers

    What force cannot alter the kinetic energy of an object?

    <p>Centripetal force</p> Signup and view all the answers

    What symmetry principle corresponds to conservation of energy?

    <p>Temporal symmetry</p> Signup and view all the answers

    What is one of the informal ways of failure of conservation of energy?

    <p>Friction forces</p> Signup and view all the answers

    In which instances is it handy to use the equation $v = u + at$?

    <p>When calculating stopping time and stopping distance</p> Signup and view all the answers

    What is the objective for this science course according to the text?

    <p>To learn how to think about given topics</p> Signup and view all the answers

    What is one of the usual initial information needed when calculating new speed in a collision?

    <p>Initial kinetic energy</p> Signup and view all the answers

    In Example 1 about Kansas City boxcars, what is the speed of Boxcar X before the collision?

    <p>Not mentioned in the text</p> Signup and view all the answers

    What is used to indicate the direction of Boxcar X's movement according to the solution provided?

    <p>A positive number</p> Signup and view all the answers

    What kind of symmetry principle corresponds to conservation of energy according to the text?

    <p>Temporal symmetry</p> Signup and view all the answers

    What conservation law is a result of the fact that the boxcar example has no unbalanced horizontal forces?

    <p>Conservation of momentum</p> Signup and view all the answers

    In free fall, what dynamical quantity comes in equal bites, meter for meter?

    <p>Kinetic energy</p> Signup and view all the answers

    What is the mass of a regulation NBA basketball?

    <p>$5$ kg</p> Signup and view all the answers

    What is the conservation law that can be seen at work in free fall?

    <p>Conservation of energy</p> Signup and view all the answers

    What accounting method is mentioned for the basketball in free fall?

    <p>Accounting by spatial increments</p> Signup and view all the answers

    What does the product of force and path equal to in the case of free fall?

    <p>Work</p> Signup and view all the answers

    Which dynamical quantity slightly differently depends on speed and mass than kinetic energy?

    <p>$mv^2$</p> Signup and view all the answers

    What does an upward trajectory result in for kinetic energy?

    <p>Decrease</p> Signup and view all the answers

    Which conservation law is not applicable in free fall due to the presence of an external force?

    <p>Conservation of momentum</p> Signup and view all the answers

    Which type of symmetry is attributed to the conservation of momentum?

    <p>Translational symmetry</p> Signup and view all the answers

    What pattern or conservation law may be read from the chapter about free fall?

    <p>Conservation of energy</p> Signup and view all the answers

    What does a spatial translation forward or backward change according to the text?

    <p>The equations of motion</p> Signup and view all the answers

    What does Newton's third law describe?

    <p>How to handle interaction between objects</p> Signup and view all the answers

    What does the impulse imparted to an object depend upon?

    <p>The interaction time and force</p> Signup and view all the answers

    What did Sir Isaac Newton refer to when he mentioned 'equal and opposite reaction' in the third law?

    <p>Momentum</p> Signup and view all the answers

    What does the conservation of momentum state?

    <p>The sum of the momenta is constant if no external forces act on a system.</p> Signup and view all the answers

    What is the relationship between interaction time, force, and impulse?

    <p>Direct relationship</p> Signup and view all the answers

    In the skateboarders example, what does the sum of Carl's and Bob's momenta before interaction signify?

    <p>The absence of external forces before interaction</p> Signup and view all the answers

    What happens to the total momentum sum after the boxcars interact and latch together?

    <p>It remains unchanged after latching together</p> Signup and view all the answers

    According to Newton's third law, what is encoded as changes in momentum?

    <p>Equal but opposite reaction</p> Signup and view all the answers

    What does the impulse equation describe?

    <p><strong>$Ft$</strong></p> Signup and view all the answers

    What does a constant sum of the momenta indicate according to conservation of momentum?

    <p>No unbalanced external forces act on the system.</p> Signup and view all the answers

    In the skateboarders example, what does it mean that their vectors have opposite directions?

    <p>They have opposite velocities.</p> Signup and view all the answers

    What do interacting skateboarders demonstrate in terms of momentum?

    <p>Conservation of momentum.</p> Signup and view all the answers

    What is the task described in the text?

    <p>Calculate the stopping time of the Kennedy half dollar</p> Signup and view all the answers

    What is the final momentum of the Kennedy half dollar when it stops?

    <p>The final momentum is zero</p> Signup and view all the answers

    What formula is used to calculate the stopping time of the Kennedy half dollar?

    <p>$F = \Delta p / t$</p> Signup and view all the answers

    What force is known when calculating the stopping time of the Kennedy half dollar?

    <p>Friction force</p> Signup and view all the answers

    What method is mentioned as an alternate way to calculate a stopping distance?

    <p>Using the work formula</p> Signup and view all the answers

    What is used to calculate the average net force on the 2016 Bumblebee Camaro?

    <p>$F = ma$ formula</p> Signup and view all the answers

    Why are the accelerations and net forces different in the Bumblebee calculations?

    <p>Due to variations in acceleration measurements</p> Signup and view all the answers

    Which method assumes that an object has a constant acceleration?

    <p>Distance triangle formula</p> Signup and view all the answers

    What does the definition of acceleration calculate?

    <p>Average acceleration between two instants of time</p> Signup and view all the answers

    'This is like the tortoise and hare problem' - What does this statement imply?

    <p>'Inconsistent' speeds and accelerations during a race</p> Signup and view all the answers

    'Constant acceleration means that the slope of the distance triangle is constant' - What method does this statement refer to?

    <p>Distance triangle formula method</p> Signup and view all the answers

    What is used to calculate the stopping time of an object in a given situation?

    <p>Newton's second law method</p> Signup and view all the answers

    What is the total momentum of the boxcar system before the collision?

    <p>Only in boxcar X</p> Signup and view all the answers

    What is the total mass of the new string of five boxcars, moving as one unit, after the interaction?

    <p>Equal to the sum of individual masses of the five boxcars</p> Signup and view all the answers

    What is the direction of the force from boxcar U on boxcar X?

    <p>Leftward</p> Signup and view all the answers

    What effect does a leftward force on a boxcar moving to the right have?

    <p>It slows down the boxcar</p> Signup and view all the answers

    What is the initial kinetic energy of the Kennedy half-dollar coin?

    <p>$0.12 J$</p> Signup and view all the answers

    What does the friction force between the coin and tabletop do to its kinetic energy?

    <p>Decreases it to zero</p> Signup and view all the answers

    What is used for Joules in the calculation for initial speed of the Kennedy half dollar?

    <p>$0.12 J$</p> Signup and view all the answers

    What unit cancels out from both sides when calculating the initial speed of the Kennedy half dollar?

    <p>$kg$</p> Signup and view all the answers

    What is used for Joules in the calculation for stopping distance of the Kennedy half dollar?

    <p>$0.12 J$</p> Signup and view all the answers

    What does it mean when Newtons cancel out from both sides during the stopping distance calculation?

    <p>Correct calculation procedure</p> Signup and view all the answers

    What is used for meters in stopping distance calculation?

    <p>$m^2$</p> Signup and view all the answers

    What is used for seconds in stopping distance calculation?

    <p>$s^2$</p> Signup and view all the answers

    Study Notes

    Momentum in Newton's Principia

    • Defined as the product of an object's mass and its velocity.
    • Calculated using the formula ( p = mv ), where ( p ) is momentum, ( m ) is mass, and ( v ) is velocity.
    • Properly represented as a spatial vector in situations where both magnitude and direction of motion are significant.
    • For a constant mass object, its combination in the equation represents consistent movement unless acted upon by an external force.

    Gravitational Potential Energy

    • Defined as the energy possessed by an object due to its height above a reference point.
    • As work increases on the way down, gravitational potential energy decreases, converting into kinetic energy.
    • The constant resulting from the balance between kinetic energy and gravitational potential energy is known as mechanical energy conservation.

    Forces and Energy Conservation

    • An external force, like friction or air resistance, cannot alter the kinetic energy of an object on its own.
    • The symmetry principle related to conservation of energy is the invariance under time translation.
    • An informal failure of conservation of energy can be observed in heat generation from friction during motion.

    Kinematics and Collision

    • The equation ( v = u + at ) is handy in uniformly accelerated motion scenarios for calculating final velocity.
    • Initial information needed when calculating new speed in collisions often includes initial velocities of colliding objects.
    • In the Kansas City boxcars example, Boxcar X's speed before collision is determined through kinematic equations and assumptions.

    Specific Collision Example

    • The direction of Boxcar X's movement, indicated by arrows or sign convention, establishes its momentum and collision behavior.
    • The absence of unbalanced horizontal forces in the boxcar example results in conservation of momentum.

    Free Fall Dynamics

    • In free fall, the dynamical quantity of gravity affects distance traveled equally, meter for meter.
    • The mass of a regulation NBA basketball is approximately 0.625 kg.
    • The conservation law in free fall illustrates the conversion between kinetic and potential energy with no net work.

    Energy Accounting in Free Fall

    • The product of force and path equals work done in the case of free fall.
    • Kinetic energy contrasts slightly with gravitational potential energy, depending on the object's speed and mass.
    • An upward trajectory results in decreased kinetic energy as potential energy increases.

    Momentum Conservation

    • In free fall, the conservation of momentum is not applicable due to gravitational force acting as an external force.
    • The symmetry attributed to conservation of momentum is linked to spatial translation invariance.
    • A spatial translation alteration modifies the momentum vector but conserves total momentum.

    Newton's Laws and Impulse

    • Newton's third law states that for every action, there is an equal and opposite reaction.
    • Impulse, imparted to an object, depends on the force applied over time.
    • The conservation of momentum states that in an isolated system, the total momentum before an interaction equals the total after.

    Interaction Examples

    • In the skateboard example, the sum of momenta before interaction indicates a collision where momentum is exchanged.
    • Total momentum remains unchanged after boxcars interact and latch together, reflecting Newton's third law on momentum changes.

    Stopping Distance and Forces

    • The final momentum of the Kennedy half dollar when stopped becomes zero.
    • The formula ( F = ma ) is used to calculate stopping time for the Kennedy half dollar, knowing force and initial momentum.
    • An alternate method to calculate stopping distance considers energy concepts and object dynamics.

    Calculating Speed and Forces

    • Average net force on vehicles like the 2016 Bumblebee Camaro is derived using dynamics and kinematic equations.
    • Different accelerations and net forces in the Bumblebee scenario result from varying weights and resistances.
    • The method assuming constant acceleration applies to simplified motion models in physics.

    Acceleration and Motion

    • The definition of acceleration calculates change in velocity over time.
    • The statement about tortoise and hare indicates varying rates of motion affecting outcome in collisions.
    • Constant acceleration implies a linear relationship, demonstrating graphical interpretations of distance over time.

    Stopping Distances and Energy Considerations

    • Total momentum of the boxcar system before collision is established using initial velocities and masses.
    • The combined mass of five boxcars moving as one unit equals the sum of their individual masses post-interaction.
    • Forces acting in opposite directions result in changes in momentum and overall system dynamics.

    Energy and Friction Dynamics

    • The initial kinetic energy of the Kennedy half dollar can be computed from its mass and speed.
    • Friction between the coin and tabletop dissipates kinetic energy into thermal energy.
    • Joules are used for energy calculations in contexts like stopping distance, while Newtons cancel out in force balances, simplifying analysis.

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    Test your understanding of gravitational potential energy and work with this quiz. Explore the relationship between work done, kinetic energy, and potential energy in the context of gravity.

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