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Questions and Answers
What is momentum defined as in Newton's Principia?
What is momentum defined as in Newton's Principia?
How is momentum calculated?
How is momentum calculated?
In which situations can momentum be properly represented as a spatial vector?
In which situations can momentum be properly represented as a spatial vector?
What does a constant mass object's combination in the equation represent?
What does a constant mass object's combination in the equation represent?
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What is the gravitational potential energy defined as?
What is the gravitational potential energy defined as?
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What happens to the gravitational potential energy as work increases on the way down?
What happens to the gravitational potential energy as work increases on the way down?
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What is the constant that results from the balance between kinetic energy and gravitational potential energy?
What is the constant that results from the balance between kinetic energy and gravitational potential energy?
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What force cannot alter the kinetic energy of an object?
What force cannot alter the kinetic energy of an object?
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What symmetry principle corresponds to conservation of energy?
What symmetry principle corresponds to conservation of energy?
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What is one of the informal ways of failure of conservation of energy?
What is one of the informal ways of failure of conservation of energy?
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In which instances is it handy to use the equation $v = u + at$?
In which instances is it handy to use the equation $v = u + at$?
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What is the objective for this science course according to the text?
What is the objective for this science course according to the text?
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What is one of the usual initial information needed when calculating new speed in a collision?
What is one of the usual initial information needed when calculating new speed in a collision?
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In Example 1 about Kansas City boxcars, what is the speed of Boxcar X before the collision?
In Example 1 about Kansas City boxcars, what is the speed of Boxcar X before the collision?
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What is used to indicate the direction of Boxcar X's movement according to the solution provided?
What is used to indicate the direction of Boxcar X's movement according to the solution provided?
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What kind of symmetry principle corresponds to conservation of energy according to the text?
What kind of symmetry principle corresponds to conservation of energy according to the text?
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What conservation law is a result of the fact that the boxcar example has no unbalanced horizontal forces?
What conservation law is a result of the fact that the boxcar example has no unbalanced horizontal forces?
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In free fall, what dynamical quantity comes in equal bites, meter for meter?
In free fall, what dynamical quantity comes in equal bites, meter for meter?
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What is the mass of a regulation NBA basketball?
What is the mass of a regulation NBA basketball?
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What is the conservation law that can be seen at work in free fall?
What is the conservation law that can be seen at work in free fall?
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What accounting method is mentioned for the basketball in free fall?
What accounting method is mentioned for the basketball in free fall?
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What does the product of force and path equal to in the case of free fall?
What does the product of force and path equal to in the case of free fall?
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Which dynamical quantity slightly differently depends on speed and mass than kinetic energy?
Which dynamical quantity slightly differently depends on speed and mass than kinetic energy?
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What does an upward trajectory result in for kinetic energy?
What does an upward trajectory result in for kinetic energy?
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Which conservation law is not applicable in free fall due to the presence of an external force?
Which conservation law is not applicable in free fall due to the presence of an external force?
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Which type of symmetry is attributed to the conservation of momentum?
Which type of symmetry is attributed to the conservation of momentum?
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What pattern or conservation law may be read from the chapter about free fall?
What pattern or conservation law may be read from the chapter about free fall?
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What does a spatial translation forward or backward change according to the text?
What does a spatial translation forward or backward change according to the text?
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What does Newton's third law describe?
What does Newton's third law describe?
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What does the impulse imparted to an object depend upon?
What does the impulse imparted to an object depend upon?
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What did Sir Isaac Newton refer to when he mentioned 'equal and opposite reaction' in the third law?
What did Sir Isaac Newton refer to when he mentioned 'equal and opposite reaction' in the third law?
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What does the conservation of momentum state?
What does the conservation of momentum state?
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What is the relationship between interaction time, force, and impulse?
What is the relationship between interaction time, force, and impulse?
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In the skateboarders example, what does the sum of Carl's and Bob's momenta before interaction signify?
In the skateboarders example, what does the sum of Carl's and Bob's momenta before interaction signify?
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What happens to the total momentum sum after the boxcars interact and latch together?
What happens to the total momentum sum after the boxcars interact and latch together?
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According to Newton's third law, what is encoded as changes in momentum?
According to Newton's third law, what is encoded as changes in momentum?
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What does the impulse equation describe?
What does the impulse equation describe?
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What does a constant sum of the momenta indicate according to conservation of momentum?
What does a constant sum of the momenta indicate according to conservation of momentum?
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In the skateboarders example, what does it mean that their vectors have opposite directions?
In the skateboarders example, what does it mean that their vectors have opposite directions?
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What do interacting skateboarders demonstrate in terms of momentum?
What do interacting skateboarders demonstrate in terms of momentum?
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What is the task described in the text?
What is the task described in the text?
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What is the final momentum of the Kennedy half dollar when it stops?
What is the final momentum of the Kennedy half dollar when it stops?
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What formula is used to calculate the stopping time of the Kennedy half dollar?
What formula is used to calculate the stopping time of the Kennedy half dollar?
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What force is known when calculating the stopping time of the Kennedy half dollar?
What force is known when calculating the stopping time of the Kennedy half dollar?
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What method is mentioned as an alternate way to calculate a stopping distance?
What method is mentioned as an alternate way to calculate a stopping distance?
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What is used to calculate the average net force on the 2016 Bumblebee Camaro?
What is used to calculate the average net force on the 2016 Bumblebee Camaro?
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Why are the accelerations and net forces different in the Bumblebee calculations?
Why are the accelerations and net forces different in the Bumblebee calculations?
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Which method assumes that an object has a constant acceleration?
Which method assumes that an object has a constant acceleration?
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What does the definition of acceleration calculate?
What does the definition of acceleration calculate?
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'This is like the tortoise and hare problem' - What does this statement imply?
'This is like the tortoise and hare problem' - What does this statement imply?
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'Constant acceleration means that the slope of the distance triangle is constant' - What method does this statement refer to?
'Constant acceleration means that the slope of the distance triangle is constant' - What method does this statement refer to?
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What is used to calculate the stopping time of an object in a given situation?
What is used to calculate the stopping time of an object in a given situation?
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What is the total momentum of the boxcar system before the collision?
What is the total momentum of the boxcar system before the collision?
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What is the total mass of the new string of five boxcars, moving as one unit, after the interaction?
What is the total mass of the new string of five boxcars, moving as one unit, after the interaction?
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What is the direction of the force from boxcar U on boxcar X?
What is the direction of the force from boxcar U on boxcar X?
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What effect does a leftward force on a boxcar moving to the right have?
What effect does a leftward force on a boxcar moving to the right have?
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What is the initial kinetic energy of the Kennedy half-dollar coin?
What is the initial kinetic energy of the Kennedy half-dollar coin?
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What does the friction force between the coin and tabletop do to its kinetic energy?
What does the friction force between the coin and tabletop do to its kinetic energy?
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What is used for Joules in the calculation for initial speed of the Kennedy half dollar?
What is used for Joules in the calculation for initial speed of the Kennedy half dollar?
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What unit cancels out from both sides when calculating the initial speed of the Kennedy half dollar?
What unit cancels out from both sides when calculating the initial speed of the Kennedy half dollar?
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What is used for Joules in the calculation for stopping distance of the Kennedy half dollar?
What is used for Joules in the calculation for stopping distance of the Kennedy half dollar?
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What does it mean when Newtons cancel out from both sides during the stopping distance calculation?
What does it mean when Newtons cancel out from both sides during the stopping distance calculation?
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What is used for meters in stopping distance calculation?
What is used for meters in stopping distance calculation?
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What is used for seconds in stopping distance calculation?
What is used for seconds in stopping distance calculation?
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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.
Studying That Suits You
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Description
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.
