Study Notes on Work, Energy, and Power

Problem Solving Steps

  • The general steps for problem-solving are:
    1. Diagram
    2. Givens
    3. Equation
    4. Solution

Unit 8 - Big Ideas

  • The main topics covered are:
    • Work, Energy & Power
    • Kinetic Energy (KE) and Potential Energy (PE)
    • Conservation of Energy

Importance of Energy

  • Energy is a basic concept in science.
  • Energy serves as a model for understanding various phenomena.

Learning Strategies

  • Effective learning strategies include:
    • Understanding key terms & vocabulary
    • Reading relevant material
    • Taking and discussing notes
    • Conducting Labs and reviewing examples
    • Solving problems & asking questions

Unit Goals

  • The goals for this unit are to understand:
    • Work, Energy & Power
    • Kinetic Energy (KE) and Potential Energy (PE)
    • Conservation of Energy

Learning Objectives

  • Understand the basic definition of work through notes, discussion, and questions.

Today's Learning Objectives

  • Identify when a force performs work.
  • Calculate work performed.
  • Calculate power.

Part 01 - Work

  • Work is the product of a force and a distance, measured in Newton-meters (N·m).

The Joule (J)

  • Work and Energy are measured in Joules (J).
  • J=N<br/>eqmJ = N <br /> eq m

Work (W)

  • Work is a quantity.
  • Work is performed by forces.

Conditions for Work

  • Work is only performed when an object is moving.
  • Work is done when a force acts on an object and the direction of the force is parallel to the direction the object is moving.

Zero Work Conditions

  • A force performs no work on an object when the object is not moving.
  • A force performs no work on an object when the direction of the force is perpendicular to the direction the object is moving.

Calculating Work

  • Work is a scalar quantity.
  • When the direction of the force is parallel to the direction the object is moving: W=F∣dW = F_{|}d

Quantities, Units & Symbols

  • Work (W) is measured in Joules (J).
  • Force (F) is measured in Newtons (N).
  • Distance (d) is measured in Meters (m).

Negative Work

  • When the direction of the force and the direction of the motion are opposite, work is negative.

Question

  • Fred slides a 1.0kg book across a 1.0m table with a force of 5N at constant velocity.
  • Task: Draw a free-body diagram and calculate the work done by each of the forces.

Calculating Work Example

  • Given: d= 1.0m, f=5N
  • W=FdW = Fd where F=5NF = 5N and d=1.0md = 1.0m

Power (P)

  • Power is the rate at which work is performed.
  • P=W/ΔtP = W/\Delta t

Watt (W)

  • Power is measured in Watts.
  • A Watt (W) is a joule per second.
  • W=J/sW = J/s

Calculating Work (Revisited)

  • When the direction of the force is parallel to the direction the object is moving, the work done by the force is calculated by: W=F∣dW = F_{|}d

When a Force Does No Work

  1. When a force acts on an object and the direction of the force is perpendicular to the direction the object is moving.
  2. When the object is not moving.

About Energy

  • An Introduction to the Nature of Energy

Objective

  • Students will understand examples of energy by participating in a lesson including, notes, pair share, questions and activity.

Big Ideas

  • Work, Energy & Power
  • KE and PE
  • Conservation of Energy

Units

  • The Joule (J) is the unit used for measuring work and energy.

An Introduction to the Types of Energy

  • Energy is a property of matter; it's a property of systems.

Definitions of Energy and Work

  • Energy is the capacity to perform work.
  • Work is the transformation (or transfer) of energy.

Chemical Potential Energy

  • Chemical Potential Energy is the energy stored in chemical bonds.

Heat Energy

  • Heat Energy is the energy that transfers between objects because they have different temperatures.

Kinetic Energy

  • Kinetic Energy is the energy of motion.

Elastic Potential Energy

  • Elastic Potential Energy is the energy stored in elastic objects like springs or rubber bands.

Electric Potential Energy

  • Electric Potential Energy is the energy that charged objects have due to their position in an electric field (i.e., because of a voltage source).

Gravitational Potential Energy

  • Gravitational Potential Energy is the energy objects have due to their position in a gravitational field (i.e., because they can fall).

Note on Potential Energy

  • It is common to refer to Gravitational Potential Energy as simply Potential Energy (PE).

Recap: Energy and Work

  • Energy is the capacity to perform work. Work is the transformation of Energy.
  • Work and Energy can be thought of as a single concept.

Types of Energy (Summary)

  • Heat
  • Kinetic Energy
  • Chemical Potential Energy
  • Elastic Potential Energy
  • Electric Potential Energy
  • Gravitational Potential Energy

Different Types of Energy

  • There are many different types of energy. Some examples are:
    • Chemical Potential Energy
    • Heat Energy
    • Gravitational Potential Energy
    • Elastic Potential Energy
    • Kinetic Energy
    • Electrical Potential Energy

Other Forms of Energy

  • Sound Waves are a transfer of energy
  • Light is a transfer of energy
  • Nuclear Power plants transform the energy of atoms into electric energy

Mechanical Energy

  • Kinetic energy (KE) and potential energy (PE<em>gPE<em>g and PE</em>ePE</em>e) are types of mechanical energy (ME).
  • KEKE, PE<em>gPE<em>g and PE</em>ePE</em>e are the only types of ME we will calculate in this class.

Energy Transformations

  • Energy is being transformed from one form to another such as potential to kinetic.

Big Ideas

  • Work, Energy & Power
  • KE and PE
  • Conservation of Energy

Kinetic energy is the energy of Motion

Gravitational potential energy is the energy of Position

Understanding PE and KE

Kinetic Energy

  • Objects in motion have Kinetic Energy (KE).
  • If an object increases speed, it gains KE.
  • If two objects have the same speed, the one with the most mass has the most KE.

Kinetic Energy Defined

  • Kinetic Energy (KE) depends on:
    • Mass (m)
    • Speed (v)
  • KE=(1/2)mv2KE = (1/2)mv^2

Gravitational Potential Energy

  • Objects gain Gravitational Potential Energy (PE) as they gain height.
  • If two objects have the same mass, the higher object has more PE.
  • If two objects have the same location, the object with more mass has more PE.

Gravitational Potential Energy Defined

  • Gravitational Potential Energy (PE) depends on:
    • Mass (m)
    • Height (h)
    • Acceleration of gravity (g)
  • PE=mghPE = mgh

Height

  • Height is measured from a specified location.

Sample Problem: Gravitational Potential Energy

  • How much PE does a 2kg rock lose when it falls 5m?
    • m=2kg
    • h=5m
    • g=9.8m/s\textasciicircum{2}
    • PE =?
  • PE=mgh=(2kg)(9.8m/s2)(5m)=98JPE = mgh = (2kg)(9.8m/s^2)(5m) = 98J

Sample Problem: Kinetic Energy

  • What is the KE of a 6kg fox running at a speed of 3m/s?
    • m=6kg
    • v=3m/s
    • KE=?J
  • KE=(1/2)mv2=(1/2)(6kg)(3m/s)2=27JKE = (1/2)mv^2 = (1/2)(6kg)(3m/s)^2 = 27J

Hooke's Law

Restoring Force

  • A force that restores a system to an equilibrium position is called a restoring force.
  • Systems that exhibit restoring forces are called elastic.

Hooke's Law

  • Fspring=−kxF_{spring} = -kx
    • FspringF_{spring} = Restoring force (N)
    • k = Spring Constant (N/m)
    • x = Displacement (m)

Elastic Potential Energy

  • A stiffer or stronger spring (one with a large k) can usually store more energy than a smaller spring.
  • If two springs have the same spring constant, the spring with the greatest displacement has more PEePE_e.

Elastic Potential Energy

  • Elastic Potential Energy (PE) depends on:
    • Spring Constant (k)
    • Displacement (x)
  • PE=(1/2)kx2PE = (1/2)kx^2

Recap Equations

  • Potential Energy: PE=mghPE = mgh
  • Kinetic Energy: KE=(1/2)mv2KE = (1/2)mv^2

The two types of mechanical energy which we will calculate are PE and KE.

Mechanical Energy

  • Kinetic energy (KE) and gravitational potential energy (PE) are types of mechanical energy (ME).
  • KE and PE are the only types of ME we will calculate in this class.

Part 4 - Conservation of Energy (PE and KE)

Conservation of Mechanical Energy

  • When a quantity (such as ME) remains constant, we say it is conserved.
  • Conservation of ME is when the total ME of a system remains constant.
  • ME<em>total=KE+PE</em>e+PEgME<em>{total} = KE + PE</em>e + PE_g

Conservation of Mechanical Energy (Typical Condition)

  • Typically, the total KE+PE of a system is conserved when no work is done on the system by forces other than gravity.

ME equation

  • ME<em>total=KE+PE</em>g+PEeME<em>{total} = KE + PE</em>g + PE_e

Conservation of ME

  • Conservation of ME is when the total ME of an object remains constant

Which should be modeled as freefall?

Part 5 - Conservation of Energy PE and KE

Frictionless Model

  • Typically, the total KE+PE of a system is conserved when no work is done on the system by forces other than gravity.
  • Total KE+PE is not conserved when forces like friction or applied forces perform work on the system.
  • The Zero Friction Model means we will consider friction to be zero for objects with low friction wheels or sliding with low friction.

Freefall Model

  • The Freefall Model means we will consider drag to be zero for objects considered to be in freefall.

Energy is Not Always Conserved

  • Total KE + PE is not conserved when forces like friction or applied forces perform work on the system.

Renewable Energy

  • Our society uses energy to function.
  • The energy we use can be classified into two types: renewable and non-renewable.

Fossil Fuels

  • Oil, coal, and natural gas are fossil fuels.
  • The US relies on these fuels as a main source of energy.
  • Fossil fuels are a non-renewable source of energy.

Renewable Energy

  • Wind power
  • Solar power
  • Hydroelectric
  • Geothermal energy
  • Biomass energy

A Question

  • What types of ME will we calculate in this class?
  • KE and PE

Three Types of ME

1.    KE=12m(v2)=\frac{1}{2}m(v^2)
2.    PEg=mghPE_g = mgh
3.    PEe=12k(x2)PE_e = \frac{1}{2}k(x^2)

Is ME Conserved?

Three Types of ME

  • Three types of Mechanical Energy (ME):
    KE = ½m(v2)
    PE g =mgh
    PE e = ½k(x2)

The Conservation of PE+KE

  • Solving Problems Involving the Conservation of Mechanical Energy

Conservation of ME

  • ME<em>total=KE+PE</em>g+PEeME<em>{total} = KE + PE</em>g + PE_e
  • Typically, MEtotalME_{total} is conserved when:
    • No work is done by forces other than gravity
    • No heat is produced by kinetic friction

The Idea

  • {ME<em>totalME<em>{total}}initial = {ME</em>totalME</em>{total}}final
  • {KE + PE<em>gPE<em>g + PE</em>ePE</em>e}initial = {KE + PE<em>gPE<em>g + PE</em>ePE</em>e}final

Problem Solving Steps

  1. Read and identify the problem
  2. List the given quantities
  3. Identify the types of ME<em>initialME<em>{initial} and ME</em>finalME</em>{final}
  4. Solve

A 3.0kg flower pot falls 1.5m from a window ledge to the ground. What is the flower pot’s velocity when it impacts with the ground.

  • Given Information
    m = 3.0kg
    h = 1.5m
    vi = 0
    vf = ?

The Work Kinetic Energy Theorem

Work

  • A force on a moving object does positive work when it acts in the same direction as motion and negative work when it acts in the opposite direction.

Whats happening to the ME of these bicycles?

Work/KE Theorem

  • The Work-Kinetic Energy Theorem states that the change in an object’s KE is equal to the net work done on it.
  • Wnet=ΔKEW_{net} = \Delta KE