Mechanical Energy Conservation

Summary

In this video tutorial by The Physics Classroom, the focus is on understanding the conservation of mechanical energy. It explains the concept by examining situations where only conservative forces, like gravity, act on a system, resulting in a constant total mechanical energy. The video illustrates this with examples such as a projectile, skier, pendulum, roller coaster, and ski jumper. Additionally, it discusses how real-life factors like friction and air resistance affect energy conservation by converting mechanical energy to non-mechanical forms. It wraps up by providing additional resources for further learning.

Highlights

• Total mechanical energy stays constant when only conservative forces act on a system. 🚀
• Examples include projectiles, where initial and final kinetic plus potential energies are equal. 🏹
• The skier model explains energy conversion during upward and downward motion. ⛷️
• Pendulums demonstrate energy trade-offs between kinetic and potential forms. 🕰️
• Illustrations like bar chart diagrams show how energy types vary over time, yet total remains the same. 📊
• External factors like air resistance influence energy distributions in real life. 🌬️

Key Takeaways

• Mechanical energy is conserved when only conservative forces, like gravity, do work. 🎢
• Potential energy can be converted to kinetic energy and vice versa while keeping the total energy constant. ⚖️
• External non-conservative forces (like friction) lead to a decrease in mechanical energy by converting it to thermal or vibrational energy. 🔄
• Understanding mechanical energy conservation helps in analyzing the motion of objects like projectiles, pendulums, and roller coasters. 🎯
• Real-life scenarios include factors that slightly alter theoretical conservation due to dissipative forces. 🌍

Overview

In the world of physics, understanding the conservation of mechanical energy is paramount. This concept rests on the pivotal role of conservative forces—like gravity—that command the motion of objects such as projectiles or pendulums. When only these forces act, the total mechanical energy (sum of potential and kinetic energy) remains unchanged, a principle vital for analyzing motion in an idealized setting.

Consider the dynamic journey of a roller coaster car, illustrating energy transformation. As the car descends, it forsakes potential energy for kinetic energy, augmenting its speed. Conversely, climbing ramps sees kinetic energy translated back into potential energy, exemplifying energy conservation principles where the total energy tally remains untouched by non-conservative forces.

Despite the ideal scenarios in educational settings, real-world complexity arises via non-conservative forces like friction and air resistance. These agents transform mechanical energy into non-mechanical forms (e.g., heat), implicitly nudging physicists to approximate ideal models. Nonetheless, these exercises in theory help anyone grasp the foundations of mechanical energy conservation and its utility in describing natural phenomena.

Chapters

• 00:00 - 00:30: Introduction to Mechanical Energy Conservation The chapter introduces the concept of mechanical energy conservation, posing questions about the conditions under which mechanical energy is conserved and the meaning of conservation of mechanical energy. It refers back to previous content about non-conservative external forces and provides a link for further review.
• 00:30 - 01:00: Effect of Non-conservative Forces The chapter discusses the impact of non-conservative forces on a system's total mechanical energy. It explains that when these external forces do work on a system, they can transfer energy across its boundary. Positive work, where force aligns with motion, increases a system's energy, while negative work, where force opposes motion, decreases the system's energy. An equation is provided to support these principles.
• 01:00 - 01:30: Conservation with Zero Work by Non-conservative Forces The chapter discusses the relationship between the initial and final total amount of energy within a system, specifically kinetic and potential energy.
• 01:30 - 02:30: Illustration: Projectile Motion The chapter discusses the concept of mechanical energy conservation, particularly focusing on projectile motion. It explains that when gravity or a spring force is the only force acting on a system, the total mechanical energy, which includes potential and kinetic energy, is conserved. The text illustrates this with the example of a projectile, where gravity is the only acting force, and begins with the launch having zero joules of mechanical energy.
• 02:30 - 03:30: Example: Skiing Uphill and Downhill This chapter discusses the concept of mechanical energy, specifically potential and kinetic energy, using an example. Initially, there is 100 joules of mechanical energy, divided into kinetic and potential energy. At the peak of its trajectory, the kinetic energy reduces to 20 joules while potential energy becomes 80 joules, maintaining a total of 100 joules. As it returns to its original height, the potential energy goes back to zero, conserving mechanical energy.
• 03:30 - 05:00: Example: Pendulum Motion The chapter 'Pendulum Motion' discusses the conservation of mechanical energy in systems where only conservative forces, such as gravity, are doing work. It mentions that, despite the interchange between kinetic and potential energy, the total mechanical energy remains constant throughout the pendulum's trajectory. This principle highlights the idea that energy can change forms but the total quantity remains unchanged in isolated systems.
• 05:00 - 07:30: Example: Roller Coaster Motion The chapter titled 'Roller Coaster Motion' focuses on the concept of total mechanical energy conservation, particularly in systems where non-conservative work (W_nc) is zero. This scenario simplifies the equation to show that the sum of initial kinetic and potential energy equals the sum of final kinetic and potential energy. As an example, it discusses a skier traveling uphill, who loses kinetic energy while gaining potential energy.
• 07:30 - 09:00: Example: Ski Jumper and Real Situations The chapter discusses the concept of mechanical energy through the example of a ski jumper. Initially, the ski jumper has a lot of kinetic energy and little potential energy. As they reach the top of the hill, the kinetic energy decreases while potential energy increases. As the skier descends the hill, potential energy is converted back into kinetic energy. Despite these energy transformations, the total mechanical energy remains constant throughout the process.
• 09:00 - 10:30: Conclusion and Further Resources In this final chapter, the example of a pendulum is used to illustrate the principle of mechanical energy conservation. A pendulum is described as a small object, or bob, attached to a fixed point by a string, moving in a circular arc. It experiences two forces: gravity, which acts downwards, and tension, acting in the direction of the string. Despite tension being a non-conservative force, it doesn't perform work on the pendulum bob as it swings. This chapter concludes the series of explanations and may provide additional resources for further exploration into the topic.

Mechanical Energy Conservation Transcription

• 00:00 - 00:30 welcome to the physics classrooms video tutorial on work in energy the topic of this video is mechanical energy conservation and we want to know under what conditions is mechanical energy conserved and what is meant when we say mechanical energy is conserved mr h let's get started in a previous video this one i discuss what happens when non-conservative external forces do not work upon an object i've left a link to the video in the description section of this one if you need to review it in the video i
• 00:30 - 01:00 mentioned that when non-conservative external forces do not work upon a system it causes the total mechanical energy of the system to change these types of forces can transfer energy across the system boundary when the work that's done is positive work the force is in the direction of the motion then the energy of the system increases but if the work is negative work and that force is in the opposite direction of the motion then it causes the total mechanical energy of the system to decrease in both cases we'll use this equation to
• 01:00 - 01:30 relate the total amount of energy initially kinetic plus potential to the total amount that is finally present within the system the w and c in this equation is the work done by non-conservative forces we'll be using the same equation in this video except we'll be making a small adjustment to it as you'll soon see in this video i'll be discussing what happens when the work done by non-conservative external forces is zero joules when conservative forces such as
• 01:30 - 02:00 the force of gravity or the spring force are the only forces doing network upon the system then the total mechanical energy of the system is conserved potential energy can be converted to kinetic energy or vice versa kinetic converted to potential but the sum of these two forms of energy remains constant as an illustration let's consider a projectile an object upon which the only force is gravity w and c would be zero for a projectile let's assume that at launch it has zero joules
• 02:00 - 02:30 of potential energy that's on the ground in 100 joules of kinetic energy the total mechanical energy is 100 joules when it reaches the peak of its trajectory it's run out of all of its vertical speed and its kinetic energy would have decreased to say 20 joules potential energy would be 80 joules in order for the total to be 100 joules when it reaches its original height its launch height it would be back to zero joules of potential energy so just before striking the ground it would have
• 02:30 - 03:00 to have 100 joules of kinetic energy again the total is 100 joules all along the course of its trajectory we would notice that the potential energy would be decreasing in the kinetic increasing or vice versa but the total amount remains 100 joules so in such situations when the only forces doing work are conservative forces such as gravity the total mechanical energy remains constant so when we say that mechanical energy is conserved we mean that the total amount
• 03:00 - 03:30 of it is constant you might remember from a few slides back this equation total mechanical energy is conserved whenever the w in c term in that equation is zero in effect it cancels out of the equation and the equation becomes this one the kinetic plus the potential initially is equal to the kinetic plus potential energy finally to illustrate let's consider a skier that's traveling uphill it would lose its kinetic energy and gain potential energy as it travels uphill it would start
• 03:30 - 04:00 initially with a lot of kinetic and a little potential but by the time it reaches the top of the hill it would have very little kinetic and a lot of potential and as the skier skis down the hill it would lose its potential energy but gain its kinetic energy it would start with a lot of potential in a little kinetic but would finish with a lot of kinetic energy and a little potential energy but the amount of total mechanical energy initially is equal to the amount it has finally in both of these cases
• 04:00 - 04:30 the motion of a pendulum provides another example of mechanical energy conservation a pendulum is a small object known as a bob attached by a string to a fixed point as the bob moves along its circular arc there's always two forces that act upon the bob there's the force of gravity acting downwards and there's the tension force that acts along the direction of the string tension is a non-conservative force but it does not do work upon the pendulum bob because as the bob moves along its
• 04:30 - 05:00 circular arc the force of tension is always directed perpendicular to the motion of the bob such forces cannot do work upon objects when the angle between f in the direction of motion is a 90 degree angle so the only force doing work upon the pendulum is the force of gravity a not a conservative force and thus mechanical energy is conserved numerically we could represent the situation by a diagram like this at position one the highest location the pendulum bob has zero joules of kinetic
• 05:00 - 05:30 energy in eight joules of potential energy the total is eight joules as it moves to position two it has lost some potential energy and gain some kinetic energy but the total energy remains eight joules at the lowest location position three it has run out of all of its potential energy it has all kinetic energy eight joules but the total is still eight when it moves upward it begins to lose some of this kinetic energy and gain some potential energy as it moves along its circular
• 05:30 - 06:00 arc downwards it's losing potential and gaining kinetic and as it moves upwards it's losing kinetic and gaining potential this concept is often illustrated by a bar chart diagram bar chart shows the relative amount of kinetic and potential energy over the course of motion and it often shows the total amount of energy you'll notice in this animation again as the pendulum moves downwards it's losing its potential energy in gaining its kinetic energy and as it moves upwards it's
• 06:00 - 06:30 losing its kinetic energy and gaining its potential energy but the total mechanical energy of a pendulum bob remains constant over the course of its motion the up and down motion of a roller coaster car demonstrates the same idea of mechanical energy conservation on a roller coaster car there are two forces the force of gravity a conservative force directed downwards and the normal force a non-conservative force directed perpendicular to the track at all locations and as such it's always at a
• 06:30 - 07:00 90 degree angle to the direction of motion and whenever a normal force in the direction of motion or a 90 degree angle that normal force does not do work upon the object so we expect mechanical energy conservation so that means that as the roller coaster car moves downwards it loses its potential energy and gains kinetic energy and as it moves upwards it would gain potential energy and lose kinetic energy there's this conservation of total mechanical energy
• 07:00 - 07:30 while the potential energy is converted to kinetic energy and vice versa as we notice here in the animation the speeds are always greatest at the lowest location where the kinetic energy is greatest and the speeds are always smallest at the highest location where the potential energy is the greatest and the kinetic energies the smallest as a final example of mechanical energy conservation let's consider a ski jumper the normal force on the ski jumper is perpendicular to the surface and as such can't do work upon the ski jumper
• 07:30 - 08:00 mechanical energy is conserved since the only force doing work is a conservative force the force of gravity so as the ski jumper moves downwards its potential energy begins to decrease and its kinetic energy begins to increase when it has finally reached its lowest potential lowest position where the potential energy is zero its kinetic energy is the maximum and it's now traveling the fastest if you've been around the physics course for a while you may have noticed some terms in problems like ignore air
• 08:00 - 08:30 resistance assume negligible friction assuming mechanical energy is concerned these terms don't represent reality they represent idolizations or approximations to reality the fact is there really is some air resistance and some friction acting on objects as they move and these forces are non-conservative forces and do negative work on objects so as to remove some of their mechanical energy these are dissipative forces that change the mechanical energy into non-mechanical forms such as thermal energy and vibrational energy
• 08:30 - 09:00 here's a table showing what we just saw with the ski jumper with the potential in the kinetic energy being shown this is the ideal kinetic energy when we assume negligible friction and air resistance but if we were to add a column for the real kinetic energy when friction and air resistance are considered we'd have a different situation for instance at 60 meters we might notice sixteen thousand joules of kinetic energy instead of the twenty thousand joules of the ideal situation four thousand joules of mechanical
• 09:00 - 09:30 energy being converted to the non-mechanical forms like thermal and vibrational energy at forty meters we might notice 24 000 joules of kinetic energy instead of the 30 000 joules of kinetic energy in the ideal situation once more a dissipation of energy from mechanical to non-mechanical forms and at 20 meters it might be 30 000 joules of kinetic energy instead of 40 000 joules of kinetic energy and so forth so the fourth column represents the real situation with dissipated energy energy
• 09:30 - 10:00 being transformed from mechanical to non-mechanical form but the third column is an idolization or approximation to reality which we often use to illustrate a concept it's at this time in every video that i like to help you out with an action plan a series of next steps for making the learning stick but before i help you out could you help us out by giving us a like subscribing to the channel or leaving a question or comment in the comment section below now for your action plan here are four resources that you'll find on our website i've left
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