Física 1 - Aula 11 - Energia Potencial | UFPR 2021

Energy Potential: Part 2

Introduction to Energy Potential

• The lecture is part of a series on potential energy, specifically focusing on gravitational and elastic potential energy.

• The session continues from the previous class (Class 10), emphasizing the importance of reviewing prior material for better understanding.

Key Concepts in Energy Potential

• Two main topics are covered: gravitational potential energy and elastic potential energy, along with the principle of conservation of energy.

• Conservation of energy is highlighted as a fundamental concept in physics that everyone should understand.

Calculating Gravitational Potential Energy

• The variation in gravitational potential energy is defined through work done against gravity, expressed as ΔPE = -W.

• Work can be calculated using the integral of force over distance, particularly when dealing with variable forces.

Understanding Work and Energy Relationships

• An example illustrates lifting an object against gravity to gain gravitational potential energy; higher elevation results in greater stored energy.

• The formula for calculating work done while lifting an object involves integrating force over displacement.

Deriving Gravitational Potential Energy Formula

• By applying integration techniques, the relationship between work done and change in height leads to the equation for gravitational potential energy: PE = mgh.

• This formula connects back to basic school-level physics concepts where gravitational potential energy is often introduced as PE = mgh.

Elastic Potential Energy Overview

• Transitioning to elastic potential energy, similar principles apply where work done on a spring or elastic material results in stored energy.

• The calculation involves integrating force applied over displacement, leading to expressions like PE_elastic = (1/2)kx² when starting from rest.

Conservation of Mechanical Energy Principle

• A practical example demonstrates how mechanical energy conservation applies during free fall; initial gravitational potential converts into kinetic as it falls.

• The total mechanical energy remains constant if no external forces (like friction or air resistance) act on the system.

Summary and Application

• Understanding these principles allows for solving various problems involving both types of potential energies and their transformations into kinetic forms.

Understanding Energy Conservation in Physics

Solving a Problem with Energy Conservation

• The speaker begins by explaining a problem involving energy conservation, substituting numbers into an equation to find the solution.

• The result of the calculation is approximately 7.43, indicating that the initial steps were straightforward but emphasizes understanding energy conservation principles.

Kinetic and Potential Energy Variations

• The discussion shifts to the variation of kinetic energy, defined as the difference between final and initial kinetic energies.

• The potential energy variation is also introduced, leading to a combined equation representing both forms of energy.

Isolating Final Velocity

• The speaker isolates terms to derive an expression for final velocity based on initial conditions and gravitational effects.

• A negative sign appears in calculations due to changes in height, which is crucial for determining accurate results.

Work Done by Non-Conservative Forces

• Introduction of non-conservative forces like friction alters mechanical energy; variations are no longer zero when such forces are present.

• An example illustrates how external work affects mechanical energy through frictional forces acting against motion.

Calculating Work Done by Friction

• The concept of work done (W = F·d·cos(θ)) is explained, emphasizing its dependence on force direction relative to displacement.

• A numerical example shows how friction can remove energy from a system, resulting in a net loss reflected in mechanical energy calculations.

Exploring Internal Energy Changes

Impact of Friction on Mechanical Energy

• Further examples illustrate how internal energies change due to external work done against friction during movement.

Analyzing Forces Acting on Objects

• A scenario with two kilograms moving under various forces demonstrates how these interactions affect overall motion and acceleration.

Applying Newton's Laws

• Newton's second law is applied to analyze forces acting on objects while considering both gravitational and normal forces.

Understanding Acceleration and Forces

Equations Relating Force and Motion

• Deriving equations relating kinetic and potential energies helps understand how different factors influence object motion under varying conditions.

Evaluating System Dynamics with External Forces

• Discussion includes evaluating systems where external forces alter expected outcomes based on conservation laws.

Thermal Energy Considerations

Transitioning Between Forms of Energy

• Emphasis on thermal energy increases due to dissipative processes like friction highlights real-world implications of theoretical concepts.

Visualizing Energy Transformations

Graphical Representation of Energy Changes

• Visual aids help illustrate transitions between potential and kinetic energies throughout an object's trajectory.

Practical Applications: Real-Life Examples

Demonstrating Conservation Principles

• Real-life scenarios demonstrate conservation principles effectively through relatable experiments or visualizations.

Understanding Elastic Potential Energy and Gravitational Potential Energy

Calculating Elastic Potential Energy

• The discussion begins with the calculation of elastic potential energy using the formula U = 1/2 k x^2 , where k is the spring constant (184 N/m) and x is the compression distance (0.1 m).

• The speaker emphasizes that if a stone were released from a compressed spring, its elastic potential energy would convert to gravitational potential energy as it rises.

Conservation of Mechanical Energy

• The conservation of mechanical energy principle is introduced, stating that initial mechanical energy equals final mechanical energy in the absence of dissipative forces like friction.

• Initial energies include elastic potential and kinetic energies, while final energies consist of gravitational potential and kinetic energies at maximum height.

Analyzing Energies at Different Points

• At the lowest point, all energy is elastic; at maximum height, all energy becomes gravitational. The transition between these states illustrates conservation principles.

• The speaker notes that both initial and final kinetic energies are zero when starting from rest and reaching maximum height.

Variations in Gravitational Potential Energy

• To find variations in gravitational potential energy during ascent, one can equate initial elastic potential to final gravitational potential.

• This leads to calculating changes in gravitational potential as equal to 62.7 J, indicating how much work was done against gravity.

Maximum Height Calculation

• The maximum height reached by the stone can be derived from rearranging the equation for gravitational potential: h = kx^2/2mg .

Frictional Forces and Thermal Energy

Block on a Surface with Friction

• A block weighing 3.5 kg compresses a spring with a spring constant of 640 N/m before moving across a surface with kinetic friction (coefficient = 0.25).

Work Done Against Friction

• As the block moves 7.8 meters before stopping due to friction, calculations involve determining work done by friction using W = -F_d cdot d .

Force Analysis

• To calculate force of friction ( F_f = mu_k N ), where normal force equals weight since there’s no vertical acceleration.

Total Work Done

• Total work done against friction results in an approximate value of -67 J, representing lost mechanical energy converted into thermal energy.

Kinetic Energy Before Stopping

• Prior to entering the region with friction, the block's maximum kinetic energy was also calculated as approximately 67 J based on lost work due to friction.

This structured summary captures key concepts discussed within each timestamped section while providing clear insights into physics principles related to elasticity and mechanics.