GCSE Physics - Elastic Potential Energy and F = ke Equations

Summary

In this video, viewers are introduced to two fundamental equations related to elasticity in GCSE Physics: F equals ke and elastic potential energy equals 1/2 ke². F equals ke describes the relationship between the force applied to an object and its resulting extension, with K representing the spring constant. Elastic potential energy, on the other hand, quantifies the energy transferred when an object is stretched. The presenter uses practical examples, such as calculating spring constants and elastic potential energy from given scenarios, to elucidate these concepts. Important insights include understanding the role of the spring constant, and how force-extension graphs can delineate the elastic limit that otherwise marks the boundary of Hooke's Law applicability.

Highlights

• Learn about the F = ke formula to link force, extension, and the spring constant. 🔍
• Discover why elastic potential energy = 1/2 ke² is like saving energy for a bouncy payback. 💥
• Follow examples solving for spring constants and energy scenarios for practical application. 🎓

Key Takeaways

• Understanding the spring constant! It tells you how easy or hard it is to stretch something. 📏
• Elastic potential energy is the energy stored when you stretch an object. Think of it like a spring piggy bank! 🐷
• Force vs. extension graphs can show you the spring constant and energy transferred. Visuals help! 📉

Overview

Let's dive into elasticity in the realm of GCSE Physics! This video gets hands-on with two critical equations - F equals ke and elastic potential energy equals 1/2 ke². The focus is on understanding how force affects an object's extension, with the spring constant (K) playing a star role in the stiffness narrative! 📏

We then unravel elastic potential energy, which captures the energy proceedings during stretching. Imagine storing energy in a spring as you pull it, and when released, the energy bounces back - illustrating why it's half the product of k and e squared! 🤓

Plus, the practical journey through calculative examples for spring constants and elastic potential energy makes it all the clearer. Force-extension graphs will unveil the elastic limit and show you the energy transfer as areas under the curve - superb for visual learners! 🧠

Chapters

• 00:00 - 00:30: Introduction to Elasticity Equations This chapter introduces the basic equations of elasticity, focusing primarily on the equation F = k * e. This equation describes the relationship between the force applied to an object and the extent to which the object is stretched, with 'k' representing the spring constant, a measure of the object's firmness or elasticity. The discussion sets the groundwork for understanding how different materials respond to force applications.
• 00:30 - 01:00: Explanation of Spring Constant The chapter titled 'Explanation of Spring Constant' discusses the concept of spring constant. A lower spring constant indicates that an object is more elastic and easier to stretch, whereas a higher spring constant means the object is stiffer and harder to stretch. The chapter also covers the equation for elastic potential energy, which is 1/2 ke squared, where 'k' represents the spring constant and 'e' represents the extension.
• 01:00 - 01:30: Elastic Potential Energy Equation The chapter explores the concept of elastic potential energy, emphasizing the importance of understanding that only the extension component is squared in its calculation. It describes elastic potential energy as the energy transferred to an object when it is stretched. This principle is illustrated using the example of a spring, where if 100 joules of energy are employed to stretch the spring, these 100 joules are stored as elastic potential energy. When the spring is released, the stored energy causes it to revert to its original state.
• 01:30 - 02:00: Energy Transfer in Springs The chapter focuses on energy transfer within springs, including the conversion of energy into different forms such as light and kinetic energy. It also covers practical examples to illustrate these concepts, like determining the spring constant when given the natural length of a spring, the amount of force applied, and the new length of the spring.
• 02:00 - 02:30: Example: Calculating Spring Constant The chapter titled 'Calculating Spring Constant' involves understanding the process of determining the spring constant by analyzing the extension of a spring. It begins with identifying the initial and final lengths of the spring, which are 0.6 meters and 0.8 meters, respectively, to calculate the extension, resulting in a difference of 0.2 meters. The chapter seems to aim at applying known equations to find the spring constant using this information, though it ends abruptly before completing the explanation.
• 02:30 - 03:30: Example: Calculating Elastic Potential Energy In the chapter titled 'Calculating Elastic Potential Energy,' the discussion revolves around determining the spring constant using Hooke's Law. The formula F = k * e is rearranged to solve for the spring constant k, yielding a result of 17 Newtons per meter. This calculation is based on given values of 14 (force) and 0.2 (extension). Following this, the chapter introduces the concept of elastic potential energy, indicating that another equation will need to be used to calculate it based on the previous findings.
• 03:30 - 04:00: Understanding Force-Extension Graphs The chapter 'Understanding Force-Extension Graphs' explains how to calculate energy using the formula energy = 1/2 ke². It breaks down the method by illustrating how the spring constant and extension are used in the equation. By plugging the given values into the equation, the calculation is demonstrated: 1/2 or 0.5 times 70 times 0.2 squared equals 1.4 joules.
• 04:00 - 04:30: Conclusion and Recap This chapter concludes by discussing the interpretation of a force versus extension graph. The straight part of the line on this graph indicates the spring constant. The area under the curve represents the energy transferred to the spring, known as elastic potential energy. The chapter also reminds us about the elastic limit point on the graph.

GCSE Physics - Elastic Potential Energy and F = ke Equations Transcription

• 00:00 - 00:30 in today's video we're going to look at the two equations you need to know about elasticity the first F equals ke links the force that you apply to an object - how much it extends by when you apply that force with K being a spring constant which is specific to each object and as a measure of how firm or elastic the object is a lowest spring
• 00:30 - 01:00 constant means that the object is more elastic and so easier to stretch while a higher spring constant means that the object is more stiff and so harder to stretch the other equation is the elastic potential energy equals 1/2 ke squared where K and E are the spring constant and extension again and importantly it's
• 01:00 - 01:30 only the extension as being squared not the whole thing you can think of elastic potential energy as the energy transferred to an object as its stretched so if you used 100 joules of energy to stretch a spring then the 100 joules would be transferred to the springs elastic potential energy store and then when you let it go and it springs back it would transfer that 100
• 01:30 - 02:00 joules back out to a different form light kinetic energy you to see how these equations work let's try a couple of examples imagine this spring has a natural length of 0.6 meters but when we apply a force of 14 Newtons it stretches to 0.8 meters what's the spring constant of the spring
• 02:00 - 02:30 well first we need to figure out what's going on as the spring has stretched from 0.6 to 0.8 meters we can find this extension by subtracting 0.6 from 0.8 which gives us zero point 2 meters so we now know the force and the extension and we want to find the spring constant if we look at our two equations we can see
• 02:30 - 03:00 that we would have to use F equals K E and then rearrange it to get F over e equals K which if we plug in 14 divided by 0.2 gives us 17 Newton's per meter at our spring constant you now using the same scenario what would the elastic potential energy of the spring now be this time we're gonna have to use the other equation so elastic potential
• 03:00 - 03:30 energy equals 1/2 ke squared and it's a bit simpler because we've already worked out the spring constant and extension so all we have to do is plug the values into the equation so we get 1/2 or 0.5 times 70 times 0.2 squared which gives us one point four joules
• 03:30 - 04:00 the last thing we want to point out is that if you have a graph of force against extension like this one then as long as we only look at the straight part of the line the gradient of the line will be the spring constant and the area under the curve is equal to the energy transferred to the spring so the elastic potential energy and just to recap remember that this point here is known as the elastic limit or the limit
• 04:00 - 04:30 of proportionality and it's when the object stopped to obeying Hookes law you anyway that's everything for this video so hope you found it useful if you did then give us a like and subscribe and I'll see you next time