Translations

Code	Language		Translator	Run
ta	ta	ta

Credits

This email address is being protected from spambots. You need JavaScript enabled to view it.; annecox; tinatan

http://iwant2study.org/lookangejss/02_newtonianmechanics_7energyworkpower/ejss_model_SHMxvapendulumjc/SHMxvapendulumjc_Simulation.xhtml

Briefing Document: Energy Pendulum Model

1. Introduction

This document analyzes an online educational resource focused on an energy pendulum model. The resource, part of the "Open Educational Resources / Open Source Physics @ Singapore" project, provides an interactive simulation of a pendulum to teach concepts related to energy, specifically potential energy (PE) and kinetic energy (KE), and the principle of conservation of energy. The resource aims to bridge understanding from primary school concepts to secondary level physics.

2. Main Themes

• Energy Transformation: The primary theme revolves around the continuous transformation between potential and kinetic energy within the pendulum system. The simulation visually demonstrates this process, with PE at its maximum when the pendulum is at its highest point and KE at its maximum when the pendulum passes through its lowest point.
• Conservation of Energy: The resource emphasizes the principle that energy is neither created nor destroyed, but rather converted from one form to another. This is illustrated by the constant total mechanical energy of the pendulum system when frictional forces are not considered. As stated in the document:
• “Total energy te is equal to the sum of pe and ke”
• and
• “energy can be converted from one form to another but cannot be created or destroyed.”
• Factors Influencing Energy: The interactive nature of the simulation allows users to explore how different parameters affect PE and KE. This includes:
• Initial Angle (θ): Increasing the initial angle leads to a higher maximum PE and KE.
• “a larger θ will result in a larger maximum potential and kinetic energies.”
• Length of Pendulum (L): Increasing the length of the pendulum also results in a larger maximum PE and KE.
• “a larger L will result in a larger maximum potential and kinetic energies as consequence of a larger change in height due to larger L.”
• Work and Power: The document briefly touches on work as a means of energy transfer, noting that work is done when a force moves an object over a distance. Power is introduced as the rate at which work is done.
• Conceptual Understanding: The resource is designed to address common misconceptions about energy, such as the idea that energy is "used up" or "lost" during interactions. It emphasizes that energy is transferred during interactions and not just "stored" in a body.
• Inquiry-Based Learning: The use of a simulation encourages exploration and inquiry. Students are prompted to manipulate the pendulum and observe the effects on energy graphs. The resource also provides guiding questions, which further promote analysis and critical thinking.

3. Important Ideas and Facts

• Simulation Tool: The core of the resource is an interactive simulation accessible through an iframe embed or directly through a provided URL (http://tinyurl.com/ast2016-4). This simulation allows users to:
• Visualize energy changes with "E bars" (bar graphs of PE and KE).
• Track energy over time using "E vs t" graphs.
• Adjust the initial angle (θ) and length (L) of the pendulum.
• Potential Energy (PE):
• Defined as the energy stored in a body due to its position, specifically gravitational potential energy in the case of a pendulum.
• Mathematically represented as Ep = mgh where m is the mass, g is acceleration due to gravity and h is the height above the lowest point. The resource sets m= 1kg and g = 9.81 m/s².
• Kinetic Energy (KE):
• Defined as the energy a body possesses due to its motion.
• Mathematically represented as Ek = ½ mv² , where m is mass and v is velocity.
• Key Questions: The resource poses several guiding questions that include:
• "At what point of the pendulum’s swing is the potential energy the highest?" (Answer: At the extreme ends of the swing.)
• "At what point of the swing is the kinetic energy the highest?" (Answer: At the middle of the swing where the velocity is max)
• "What happens if you change θ (but leave L the same)?" (Answer: A larger θ results in larger PE and KE.)
• "What happens if you change L (but leave initial θ the same)?" (Answer: A larger L results in larger PE and KE)
• Prior Knowledge: The resource considers prior knowledge of students at primary and lower secondary levels:
• Primary: Students are already aware of different forms of energy, including kinetic and potential energy, and that the sun is our primary source of light and heat.
• Lower Secondary: Students are introduced to the concept of work, defined as force multiplied by distance, and the conservation of energy.
• Misconceptions: The resource addresses the following common misconceptions:
• Students often think of energy as a substance that flows or as a force rather than understanding energy as the capacity to do work
• Students do not understand that the work done is the energy transferred during the interaction and not energy stored in a body
• Students think energy is "used up" or "lost" instead of understanding that it transforms from one form to another.
• Supporting Materials: The resource is accompanied by worksheets, videos, and other materials to support learning and teaching. It also links to various other open-source physics resources available from the site, including models for:
• projectile motion
• rotational motion
• wave properties
• electrostatics
• atomic physics

4. Key Quotes

• “Total energy te is equal to the sum of pe and ke”
• “energy can be converted from one form to another but cannot be created or destroyed.”
• “a larger θ will result in a larger maximum potential and kinetic energies.”
• “a larger L will result in a larger maximum potential and kinetic energies as consequence of a larger change in height due to larger L.”
• "Work done is defined as the force x distance moved in the direction of the force."
• "When we do work, energy is ‘used up’. The amount of work is equal to the energy transferred or used."
• "Power is the rate of doing work and is given by: power = work done / time taken (P = W/t)."

5. Conclusion

The "Energy Pendulum Model" is a valuable educational resource for teaching fundamental physics concepts related to energy transformation and conservation. Its interactive simulation and guided inquiry approach make it an effective tool for addressing common misconceptions and promoting deeper understanding of energy principles. The resource is well-structured, builds upon prior knowledge, and offers a variety of supporting materials to enhance the learning experience. The sheer number of linked resources shows the breadth of the projects available at this site.

 

Energy Pendulum Study Guide

Quiz

Instructions: Answer the following questions in 2-3 sentences each.

1. According to the simulation, where is a pendulum's potential energy the highest during its swing?
2. According to the simulation, where is a pendulum's kinetic energy the highest during its swing?
3. How does increasing the initial angle (θ) of the pendulum affect its maximum potential and kinetic energies?
4. How does increasing the length (L) of the pendulum affect its maximum potential and kinetic energies if the initial angle remains the same?
5. What is the relationship between work done and energy transferred?
6. What is the definition of kinetic energy and what formula can be used to calculate it?
7. What is the definition of potential energy and what formula can be used to calculate gravitational potential energy?
8. What is the principle of conservation of energy?
9. According to the source, how do students often mistakenly think about energy in terms of substance or force?
10. What is one common student misconception about energy and its conservation?

Quiz Answer Key

1. The potential energy is highest at the extreme ends of the pendulum's swing, where its vertical height (h) is at its maximum. At these points the pendulum is momentarily at rest, and the energy is stored as gravitational potential energy.
2. The kinetic energy is highest at the middle of the swing, where the angle (θ) of the mass with the vertical line is 0 degrees, and the pendulum's velocity is at its maximum. At this point, potential energy is at its minimum as it is converted to kinetic.
3. A larger initial angle (θ) results in a larger maximum potential and kinetic energies as the pendulum will reach a greater height in its swing, and a correspondingly greater velocity.
4. A larger length (L) will also result in a larger maximum potential and kinetic energies, due to the greater change in height that occurs as the pendulum swings. This assumes a constant initial angle (θ).
5. The amount of work done is equal to the amount of energy transferred or used. Therefore, work is directly related to changes in energy within a system.
6. Kinetic energy is the energy possessed by an object due to its motion. It can be calculated using the formula Ek = ½ mv², where 'm' represents mass, and 'v' represents velocity.
7. Potential energy is energy stored in an object due to its position, state, or shape. Gravitational potential energy, specifically, is the energy an object has due to its position relative to the ground and is calculated using Ep = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity, and 'h' is the height above a reference point.
8. The principle of conservation of energy states that energy can be transformed from one form to another, but it cannot be created or destroyed. The total amount of energy in a closed system remains constant over time.
9. Students commonly think of energy as a physical substance that flows from one thing to another, or as a force, which is not accurate. Rather than a flowing substance, energy is a property that can be transferred and transformed.
10. A common misconception is that energy is "used up" or "lost" during interactions and is not conserved. In reality, the energy is transformed into different forms, but the total energy in a closed system remains constant.

Essay Questions

Instructions: Answer each of the following essay questions in a well-organized, multi-paragraph essay.

1. Explain the relationship between potential energy, kinetic energy, and the conservation of energy within the context of a swinging pendulum. Use the simulation described in the source material as a reference for your explanation.
2. Discuss how changing the initial angle (θ) and length (L) of a pendulum affects its energy, and relate these changes to the concepts of potential and kinetic energy.
3. Describe the different forms of energy mentioned in the source, and give examples of how energy can transform from one form to another in everyday situations beyond the context of the pendulum.
4. How do students' common misconceptions about energy affect their understanding of physics concepts, and what strategies can be used to address these misconceptions?
5. Explain the concept of work done and how it relates to energy transfer, using real-world examples to illustrate your point.

Glossary of Key Terms

Kinetic Energy (Ek): The energy an object possesses due to its motion. Calculated as Ek = ½ mv², where m is mass and v is velocity.

Potential Energy (Ep): The energy stored in an object due to its position, state, or shape. Gravitational potential energy, specifically, is calculated as Ep = mgh, where m is mass, g is the acceleration due to gravity, and h is the height.

Conservation of Energy: The principle that states energy can be converted from one form to another, but it cannot be created or destroyed. The total energy of an isolated system remains constant.

Work (W): The energy transferred when a force moves an object over a distance. It is defined as force x distance moved in the direction of the force.

Power (P): The rate at which work is done, calculated as work done divided by time taken (P = W/t).

Angle (θ, Theta): In the context of the pendulum simulation, it refers to the initial angular displacement of the pendulum from its resting, vertical position.

Length (L): In the context of the pendulum simulation, it is the length of the string connecting the mass to the pivot point.

Total Mechanical Energy: The sum of an object's kinetic and potential energy. In a system with no frictional forces, the total mechanical energy is conserved.

Energy Transformation: The process of changing energy from one form to another, such as potential energy to kinetic energy.

 

 

Sample Learning Goals

[text]

For Teachers

INVESTIGATE

Go to the following website to access a simulation about energy of a pendulum: http://tinyurl.com/ast2016-4 

The left panel shows a pendulum—a mass on a string that can oscillate back and forth.

The right panel allows you to plot one of two types of graphs:

• E bars gives bar graphs that shows the amount of potential and kinetic energy (pe and ke) at any specific moment.
• E vs t graphs the pe and ke of the pendulum over time.

Remember that you can play (►) the simulation by clicking the appropriate button and the pause button ( ▌▌) to pause it.

1. Run several trials with the pendulum, watching the E bars and the E vs t graphs. Note you can have to choose the E bars or the E vs t graphs; you cannot show both at the same time.
   1. You can drag the pendulum’s bob to change its position. This changes the initial angle (indicated by the Greek letter θ, theta, and the blue sliding bar at the bottom).
   2. You can also change the length (L) of the pendulum using the slider at the bottom of the simulation. 
2. Let the pendulum oscillate for a while. Answer the following questions by looking at the E vs t graphs.
3. At what point of the pendulum’s swing is the potential energy the highest?
   • Suggested Answer:  at the extreme ends where vertical height of pendulum mass, h is maximum.
4. At what point of the swing is the kinetic energy the highest? 
   • Suggested Answer: at the middle where the angle of mass with vertical line θ is 0 degree where velocity of mass is maxmum
5. What happens if you change θ (but leave L the same)? 
   • Suggested Answer: a larger θ will result in a larger maximum potential and kinetic energies.
6. What happens if you change L (but leave initial θ the same)? 
   • Suggested Answer: a larger L will result in a larger maximum potential and kinetic energies as consequence of a larger change in height due to larger L.

MODEL

The potential energy pe depends on the height above the lowest point h. Set up the applet to show the E bars on the right. Pause the applet at various points. Try to fill up the table below for various values of h. Note that the mass of the bob is 1 kg and that the acceleration of free fall is g = 9.81 m/s²

Height h in m	Weight m g in N	Potential energy pe in J
	9.81

Time for some more modelling rules!

1. Write down some rules for the pe and ke in the pendulum’s motion. Consider rules in general, and some rules involving θ and L. Here’s an example of a general rule:

“Total energy te is equal to the sum of pe and ke”

The first rule, given above, is a consequence of the principle of conservation of energy. It states that

“energy can be converted from one form to another but cannot be created or destroyed.”

In our oscillating pendulum, energy is converted from potential to kinetic and back again all the time. But energy cannot be destroyed, so the total amount remains fixed.

APPLY

This figure shows the E-t graph for a few swings of a pendulum. 

1. Can you reproduce this figure? Try adjusting the initial angle and the length of the pendulum to see if you can re-recreate it perfectly. 

 

 Energy transfers and transformations Key inquiry question:

How can we account for the ‘appearance’ and ‘disappearance’ of energy when objects interact with each other?

1. & 2.Work and power

• Work done is defined as the force x distance moved in the direction of the force.

• When we do work, energy is ‘used up’. The amount of work is equal to the energy transferred or used.

• Power is the rate of doing work and is given by: power = work done / time taken (P = W/t).

3. Potential energy and kinetic energy

• Kinetic energy is the energy a body possesses due to its motion.

• Kinetic energy Ek = ½ mv2 .

• Potential energy is the energy stored in a body due to its position, state or shape (e.g. elastic, gravitational, chemical). Gravitational potential energy is the energy which a body possesses due to its position relative to the ground. Gravitational potential energy Ep = mgh.

• The total mechanical energy (Ek and E p) is conserved if no frictional forces are present in a moving system.

4. Energy conversion and conservation

• Energy is defined as the capacity to do work. Energy is transferred when work is done.

• There are different forms of energy e.g. kinetic energy, elastic potential energy, gravitational potential energy, chemical potential energy and thermal energy.

• Energy can be transformed from one form to another but cannot be destroyed or created (principle of conservation of energy).

Students’ prior knowledge of Energy

Primary level:

Students learn that energy:

• is required to make things work or move and energy from most of our energy resources is derived in some ways from the Sun, our primary source of light and heat energy.

• exist in different forms e.g. kinetic energy (movement energy), gravitational potential energy (objects above the ground), elastic potential energy (spring, elastic band), light energy, electrical energy, sound energy, heat energy and chemical energy (as a form of stored energy: food, batteries, fuels).

Students do simple experiments to investigate energy conversion from one form to another e.g. in an electric circuit; learn about sources of energy such as wind, water and fuels, and the need to reduce energy usage in our everyday lives.

Lower secondary level:

Students learn that:

• work is the use of a force to move an object.

• work done by a force is defined as force x distance moved in the direction of the force and, based on this definition of work, there are situations involving forces where work is done and where work is not done (calculation only for force parallel to direction of motion) (unit: joule).

• energy is the ability (or capacity) to do work or to produce change (work done = energy used) and there are different forms of energy e.g. kinetic, potential, light and sound.

• energy is conserved and can only change from one form to another (the total amount of energy before and after the change is exactly the same).

• sources of energy include fossil fuels (coal, oil, gas), kinetic energy from water and wind, nuclear, solar, and biomass.

Students’ common misconceptions and learning difficulties in Energy

Forces between masses, charges and magnets:

Students often think of energy either as a physical substance that flows out of one thing to another or as a kind of force. Work done on a body: Students have difficulty understanding that the work done on a body represents the energy transferred during the interaction between the body and another system, and does not represent energy stored in a body.

Energy is conserved:

Students often think that energy is used up or lost (disappears) during interactions

Worksheet

1. ejss_model_projectileprimary Energy - student worksheet (2017).docx
2. Energy - student worksheet (final).docx
3. Energy - student worksheet (gwf-dl 2).docx

Research

[text]

Video

 Energy Pendulum Model - Secondary & JC by Dave Lommen

 Version:

1. http://weelookang.blogspot.sg/2016/03/energy-pendulum-model-with-modeling.html 
2. http://weelookang.blogspot.sg/2014/11/ejss-primary-school-pendulum-energy.html

Other Resources

[text]

Project related:

Understanding Teacher Learning Community as Support for Implementation of Open Source Physics for Conceptual Instruction
Project Number: OER 10/15 GWF
Project Duration: 01 July 2015 - 30 April 2017

http://weelookang.blogspot.sg/2015/07/understanding-teacher-learning.html

FAQ: Understanding the Energy of a Pendulum

• What are the two main types of energy involved in a pendulum's motion?
• A pendulum's motion primarily involves two types of energy: potential energy (PE) and kinetic energy (KE). Potential energy is the energy an object possesses due to its position relative to a reference point. In the case of a pendulum, gravitational potential energy is determined by the height of the pendulum bob above its lowest point. Kinetic energy is the energy of motion, which is determined by the pendulum's velocity as it swings back and forth.
• At what points in its swing does a pendulum have the most potential and kinetic energy, respectively?
• A pendulum's potential energy is highest at the extreme ends of its swing where the pendulum's height (h) is at its maximum, relative to its lowest point. This is because the bob has reached the peak of its upward displacement. Conversely, the kinetic energy is at its maximum at the middle of the swing, where the pendulum's bob is at its lowest point and has its highest velocity. At this point the angle with the vertical line is 0.
• How does changing the initial angle of the pendulum's swing affect its energy?
• Increasing the initial angle (θ) of the pendulum will result in higher maximum potential energy and consequently, a higher maximum kinetic energy. This is because a larger initial angle means the pendulum bob starts at a greater height, thus increasing the initial potential energy of the system.
• How does changing the length of the pendulum affect its energy?
• Increasing the length (L) of the pendulum also results in a higher maximum potential energy and thus a higher maximum kinetic energy. A longer pendulum travels a greater distance from its highest point to its lowest point, resulting in a greater change in vertical height, consequently increasing the maximum potential energy.
• What is the principle of conservation of energy, and how does it apply to a pendulum?
• The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another. In a pendulum, this means the total amount of energy (the sum of its potential and kinetic energy) remains constant throughout its motion, provided there are no energy losses due to forces like friction or air resistance. Energy is continuously being transformed between potential and kinetic energy as the pendulum swings, but the total amount of mechanical energy of the system remains the same.
• How are work and energy related, and what is power?
• Work is defined as the transfer of energy that occurs when a force acts upon an object to cause displacement. Energy is, in essence, the capacity to do work. When we perform work on an object, we transfer energy to it or from it. The amount of work done is equivalent to the amount of energy transferred. Power, on the other hand, is the rate at which work is done, measured by dividing the amount of work performed by the time it takes to do the work.
• What is a common misconception about energy and what should we understand instead?
• A common misconception about energy is that it is lost or disappears when interactions occur. Instead, we need to understand that energy is transformed from one form to another and that the total amount of energy in a closed system remains constant. This means that energy may be converted into different forms, including less obvious forms like thermal energy (often from friction), but is never truly "lost".
• What are some practical applications of understanding the energy of a pendulum?
• Understanding the energy of a pendulum is fundamental in physics and has various practical applications. It helps in the development of understanding simple harmonic motion, which is crucial in many areas such as clock mechanisms, the tuning of musical instruments, or even understanding the motion of many other physical systems. Furthermore, studying the energy transformations in a pendulum can help in developing a greater understanding of how energy is transferred and conserved in real-world systems.