Gravitational Potential Energy and Work Quiz

Podcast Beta

Play an AI-generated podcast conversation about this lesson

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?

The difference of momentum of the object Signup and view all the answers

What is the gravitational potential energy defined as?

The opposite of the work done on an object Signup and view all the answers

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

It decreases by the same amount Signup and view all the answers

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

Total energy Signup and view all the answers

What force cannot alter the kinetic energy of an object?

Centripetal force Signup and view all the answers

What symmetry principle corresponds to conservation of energy?

Temporal symmetry Signup and view all the answers

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

Friction forces Signup and view all the answers

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

When calculating stopping time and stopping distance Signup and view all the answers

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

To learn how to think about given topics Signup and view all the answers

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

Initial kinetic energy Signup and view all the answers

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

Not mentioned in the text Signup and view all the answers

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

A positive number Signup and view all the answers

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

Temporal symmetry Signup and view all the answers

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

Conservation of momentum Signup and view all the answers

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

Kinetic energy Signup and view all the answers

What is the mass of a regulation NBA basketball?

$5$ kg Signup and view all the answers

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

Conservation of energy Signup and view all the answers

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

Accounting by spatial increments Signup and view all the answers

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

Work Signup and view all the answers

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

$mv^2$ Signup and view all the answers

What does an upward trajectory result in for kinetic energy?

Decrease Signup and view all the answers

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

Conservation of momentum Signup and view all the answers

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

Translational symmetry Signup and view all the answers

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

Conservation of energy Signup and view all the answers

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

The equations of motion Signup and view all the answers

What does Newton's third law describe?

How to handle interaction between objects Signup and view all the answers

What does the impulse imparted to an object depend upon?

The interaction time and force Signup and view all the answers

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

Momentum Signup and view all the answers

What does the conservation of momentum state?

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

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

Direct relationship Signup and view all the answers

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

The absence of external forces before interaction Signup and view all the answers

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

It remains unchanged after latching together Signup and view all the answers

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

Equal but opposite reaction Signup and view all the answers

What does the impulse equation describe?

$Ft$ Signup and view all the answers

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

No unbalanced external forces act on the system. Signup and view all the answers

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

They have opposite velocities. Signup and view all the answers

What do interacting skateboarders demonstrate in terms of momentum?

Conservation of momentum. Signup and view all the answers

What is the task described in the text?

Calculate the stopping time of the Kennedy half dollar Signup and view all the answers

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

The final momentum is zero Signup and view all the answers

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

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

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

Friction force Signup and view all the answers

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

Using the work formula Signup and view all the answers

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

$F = ma$ formula Signup and view all the answers

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

Due to variations in acceleration measurements Signup and view all the answers

Which method assumes that an object has a constant acceleration?

Distance triangle formula Signup and view all the answers

What does the definition of acceleration calculate?

Average acceleration between two instants of time Signup and view all the answers

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

'Inconsistent' speeds and accelerations during a race 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?

Distance triangle formula method Signup and view all the answers

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

Newton's second law method Signup and view all the answers

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

Only in boxcar X 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?

Equal to the sum of individual masses of the five boxcars Signup and view all the answers

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

Leftward Signup and view all the answers

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

It slows down the boxcar Signup and view all the answers

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

$0.12 J$ Signup and view all the answers

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

Decreases it to zero Signup and view all the answers

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

$0.12 J$ Signup and view all the answers

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

$kg$ Signup and view all the answers

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

$0.12 J$ Signup and view all the answers

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

Correct calculation procedure Signup and view all the answers

What is used for meters in stopping distance calculation?

$m^2$ Signup and view all the answers

What is used for seconds in stopping distance calculation?

$s^2$ 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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

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.