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3-Energy

Slideshow: Work Energy & Power Notes (under construction) or Work and Energy Notes (previous version)

Textbook: Chapter 6 in Mastering Physics (get online code for registration on about page of google classroom)

What is in this unit?

We study primarily mechanical energy, which includes kinetic, potential (gravitational and elastic), and microscopic internal energy (including thermal energy).

We will learn about how laws of conservation work with energy. The total energy within a system remains constant unless there is a transfer of energy in or out of the system and work done by external forces is the agent of change for energy. Energy conservation is an alternate analysis we can use for situations we are already familiar with, like objects traveling down inclined planes and around vertical loops, but offers the advantage that it can be used even when the forces (and therefore acceleration) are not constant.

A major component of our study is understanding that the same scenario can be analyzed differently depending on how the system being analyzed is described. Knowing how to select a system definition that will allow the total energy of the system to be constant can simplify problems immensely.

Equations on the chart vs derived equations

All standard equations are represented on the formula chart as shown with each topic below.

The only derivations you will be expected to do is create applications of the conservation of energy, ΣEinitial + ΔE = ΣEfinal. Creating a system of bar charts tracking the energy in the system will be our graphical tool to help students set up the application of the this law.

Topic Explanations and Facts

3.1 Translational Kinetic Energy

Students describe the translational kinetic energy of an object in terms of the object’s mass and velocity.

Translational Kinetic Energy is

calculated by K=1/2 mv^2
a scalar quantity that is always positive
measured in Joules
the energy that an object has based on the translation (or linear change in position of its center of mass). This contrasts with rotational kinetic energy, which describes the energy an object has due to its rotation.

3.2 Work

Students describe the work done on an object or system by a given force or collection of forces.

Work

is the amount of energy transferred into or out of a system by an external force exerted on that system over a distance.
- Work-Energy Theorem states "the change in an object's kinetic energy is equal to the net work by all forces on the object"

- - ΔK=ΣW=ΣF//d

is a scalar quantity that is positive if the force transfers into the system and negative if the force transfers energy out of the system.
For a constant force work is determined by only the component of force that is parallel to the displacement of the point of application.
- W = F//d = Fdcosθ (for constant forces only)

Conservative Forces

are path independent
- meaning the energy transfer/transformation only depends on the starting and ending positions.
- returning to the same position results in zero work from that force
examples: spring forces (for ideal springs) and gravitational force
when conservative forces are internal to the system (not external) no work is done, instead they are associated with transformation to/from potential energies.

Nonconservative Forces

are path dependent.
- Longer paths to get to the same location tend to exchange more energy than shorter paths.
examples: friction and air resistance
- Energy dissipated by friction is typically equated to frictional force time the length of the path over which the force is exerted
  - ΔEmech = Ff d cosθ

Area under a F// (d) graph

Work is equal to the area under a graph of a force as a function of displacement.

3.3 Potential Energy

Potential Energy, U

is a scalar quantity, measured in joules
potential energy is part of a system where objects WITHIN the system interact through conservative forces
- a system of just a single object cannot have mechanical potential energy
the amount of potential energy is indicated by the position of objects within a system
- a position of zero potential energy can be assigned in order to simplify analysis

Elastic Potential Energy

When an ideal spring within a system is stretched or compressed, the amount of elastic potential energy is based on the spring constant of the spring, k, and varies with the distance the spring is stretched or compressed from its equilibrium length Δx
- Us = ½ k (Δx)2
- Pro tip: be prepared to find the spring constant from the slope of a graph of U as a function of Δx.

Gravitational Potential Energy

Any 2 objects, but especially moons, planets, and stars, have gravitational potential energy based on their masses and distance between center
- Ug = -G(Mm/r)
near the surface of a planet where g is approximately constant it is easier to approximate changes in gravitational potential energy based on the change in height above a reference point.
- ΔUg=mgΔy

Total Potential Energy

When a system has both gravitational and elastic potential energy the total energy is the sum of the potential energies
- Vertical mass oscillators can be simplified immensely by setting the total potential energy (U=1/2 k Δx^2) to be zero at the equilibrium position and measuring Δx from equilibrium instead of from the spring's natural length.

3.4 Conservation of Mechanical Energy

Energy a system can have:

single objects can only have kinetic energy
For elastic energy to be present, an elastic object, like a spring, must interact with another object within the system
For gravitational potential energy to be present, both objects involved in the gravitational force must be part of the system (for example, the earth must be part of the system for interactions in our classroom)

Conservation of Energy

Energy is conserved in all interactions.
A system can be selected so that the total energy of the system is constant
If the system selected does change in total energy, that change in energy is equal to the energy transferred into or out of the system.

Mechanical Energy

ME is the sum of a system's kinetic and potential energies
If the work done on a system is zero and there are no nonconservative forces within the system, then the total mechanical energy of the system is constant

Energy Bar Charts

- Bar charts can be used to track energy exchanges within a system with constant energy or to track transfers into or out of the system when work is present.
- Use this awesome practice at UniverseAndMore to understand how different system definitions affect how the energy of s system is represented.

3.5 Power

Power

is the rate at which energy changes with respect to time due to energy conversion or transfer in or out of the system
P is measure in Watts (W) which are the equivalent of 1 Joule per second
average power is defined by Pavg = ΔE/Δt & since W = ΔE, Pavg = W/Δt
instantaneous power delivered by a constant force parallel to the object's velocity can be described by Pinst = F//v=Fv cosθ
- This is particularly useful for finding the force needed to maintain a constant velocity in the face of drag or friction

Instructional Videos

Viral Videos

Runaway truck needs to get rid of energy

This truck's brakes failed while on a steep mountain and needed to slow down without wrecking. Luckily, some road engineers have thought of this and have a place for them to dissipate that energy.

Trampoline Trick gets insane!!

Define a system and explain the energy transformations/work being done to the person jumping.

Common Misconceptions:

Misconception: Energy gets used up or runs out.

Correct principle: Energy is a conserved quantity that cannot be created or destroyed. It can be transformed from one form to another (like converting into potential energy or thermal energy), or it can be transferred to another objects (work done).

Misconception: Something not moving can't have any energy.

An object that is not moving will not have any kinetic energy, but it can have internal energy (thermal, chemical and nuclear potential energies) and depending upon how you define your system, it may have potential energy due to its position relative to another object.

Misconception: A force acting on an object does work even if the objects does not move.

Correct principle:

Misconception: Energy is destroyed in transformations from one type to another.

Misconception: Energy can be recycled.

Misconception: Gravitational potential energy is the only type of potential energy.

Misconception: When an object is released to fall, the gravitational potential energy immediately becomes all kinetic energy.

Misconception: Energy is not related to Newton's laws.

Misconception: Energy is a force.

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