Work and Energy: Concepts and Applications

PSI - Progressive Science Initiative

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Work and Energy (2024-10-27)

• Table of contents available at www.njctl.org for the Work and Energy presentation
• Sections include: System and Environment, Work, Kinetic Energy, Gravitational Potential Energy, Elastic Potential Energy, Conservation of Energy, GPE and Escape Velocity, and Power.

What is Energy?

• Energy is a fundamental concept described by Richard Feynman, a Nobel prize-winning physicist.
• Feynman stated that energy is a quantity that remains constant throughout the natural world's transformation.
• Feynman's work was primarily on mechanics, radiation, and heat, presented in 1963.
• Energy is as fundamental as space and time
• Energy is related to motion and forces.

System and Environment

• A system is a specific portion of the universe
• The environment is everything outside the system boundary.
• The system can be a particle, a group of particles, an object, an area or space.
• Define boundaries to isolate forces and matter in a system, to solve calculations with energy.
• If only internal forces are acting on a closed system, and no mass crosses the boundary, then the systems energy will remain un-changed.
• External forces and matter moving across the boundary changes the energy of the system.
• In solving problems, it is often possible to isolate a single object, or a small number of objects to calculate changes to Energy.

Closed System

• A system unaffected by anything in the environment
• Objects in the system cannot leave, nor can any outside object enter
• No outside forces affect anything inside the system
• Energy is neither transferred in nor out of the system

Open System

• A system that is affected by its environment.
• Objects in the system can leave it, and outside objects can enter it.
• Forces inside the system can affect the environment
• Energy can be transferred into or out from the system.

Work

• Work is the ability to increase or decrease the amount of energy at a given position-time in space.
• Work can change the motion of objects
• Work is measured in joules (J), which is the same unit as energy.

What is Work?

• Physics' work is different than common usage
• Work, by definition is the exertion of a force over a displacement where only the component of force in the direction of movement is taken into account
• If an object is held still, even if there is a force applied to the object, there is no work being done (no displacement).

Work Equation

• Work = Force x displacement cos θ
• θ is the angle between the force and displacement

Positive Work

• Work is positive when force and displacement are in the same direction
• Energy of the system increases

Negative Work

• Work is negative when force and displacement are in opposite directions
• Energy of the system decreases

Zero Work

• When an object moves perpendicularly to the direction of the force, or no movement occurs, the work is zero.
• Energy of the system remains unchanged

Two-Dimensional Forces and Work

• When a force is applied at an angle to the direction of displacement, resolve the force into components that are parallel and perpendicular to the displacement to determine the work done
• Only the parallel component affects work calculation

Vector Multiplication

• Many physics problems involve vectors (magnitude and direction)
• Summation and subtraction of such vectors often use trigonometry
• Multiplying vectors using scalars is also common in many physics problems
• Calculating work involves vector multiplication, frequently using the scalar dot product

Scalar Dot Product

• A scalar dot product of two vectors provides a scalar result
• Multiply the magnitude of the component of one vector that is aligned with the other vector times the magnitude of the second vector
• The maximum positive value for the dot product is when both vectors are aligned in the same direction
• The maximum negative value for the dot product is when both vectors are aligned in opposite directions
• Dot product equals zero when vectors are perpendicular

Kinetic Energy

• Kinetic energy is the energy of motion
• The equation of KE is 1/2 massvelocity squared
• Unit of measure is Joules (J)

Work-Kinetic Energy Equation

• If only constant external forces act in the same direction of the displacement, positive work is done
• The amount of work done results in a change of the energy (Kinetic) of an object

This quiz explores key concepts in work and energy, including kinetic energy, gravitational potential energy, and the conservation of energy. Designed for students, it offers insights into how energy transforms in natural systems. Prepare to test your understanding of fundamental energy principles!