Phys1_06-Conservation_Laws_defb967a-9344-49c1-bde6-034991d433e7

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School

Georgia Institute Of Technology *

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2111

Subject

Electrical Engineering

Date

Apr 3, 2024

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pdf

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Uploaded by ConstableBook10014

Slide 1 Momentum and Energy Objectives: Energy Conservation Learn how energy is transformed from one form to another. Learn what factors can take energy away from the system. Learn what a phase space plot is and apply it to the study of energy conservation. Objectives: Momentum and Impulse Study the relationship between impulse and change in momentum. Derive this relation from Newton's Second Law. Physics Overview Conservation of Energy In an isolated system where there are no external forces acting on the system, energy must be conserved. This means that energy is not leaving or being added to the system. However, energy can be transformed from one form into another. In the case of this lab, you will be looking at the transfer between kinetic energy and spring potential energy. You will once again be looking at a vertical spring system against a vertical table top. By studying the system, you should be able to tell when both the kinetic energy and the spring potential energy are at a maximum. There are also many real world applications, such as friction, in which energy is taken out of the closed system. By plotting the velocity of the device against the distance the spring is compressed or stretched (the position), it is possible to determine if the total energy of the system is conserved. Momentum and Impulse An object is known to have momentum if it has both a mass and a velocity. Therefore, if a massive object has motion, it has momentum. For momentum to be conserved, there must be no external forces acting on the system. Knowing that momentum is conserved can be a very powerful tool. If you know the initial momentum of two colliding objects, it allows you to predict their final momentum after the collision. This has many real-world applications including safety features in vehicle collisions, as well as properties of high-energy single particle collisions. For this lab, you will not be studying an isolated system. You will be bouncing the device off

of a fixed object. Therefore, the momentum of the device will change. However, the force the fixed object exerts on the device occurs so quickly that you will be able to calculate the impulse and compare this to the change in momentum. If you wish to review the topics of energy and momentum you may watch any of these videos: BulletBlock BatmanJoker

Slide 2 Phase Space Plots Oftentimes in physics, the change in a value, such as position or velocity, is plotted versus time in order to see how the motion of an object is changing in time. However, much can be learned using phase space plots as well. A phase space plot represents all possible states of an object, with each point on the plot being a specific state of the object. Most often, the phase space plots use momentum and position as the axes. So in this case, the object has a number of momentum and position states that can be represented in a plot. For the purposes of this lab, we are looking at the position of the iOLab on the x-axis and the velocity on the y-axis. By studying the motion of the device under the influence of the spring force, both the position and the velocity oscillate. Therefore, this lab incorporates the study of energy conservation during this simple harmonic motion. The position can be described using, and the velocity by When plotted against each other, the resulting phase space will be in the shape of a circle. The radius of this circle will remain constant if the energy of the system is conserved. The two types of energy we are looking at for this lab is kinetic energy and spring potential energy. Therefore, at any one point, the total energy is equal to (gravitational potential energy is being ignored). Since both the position and the velocity are squared, x and v can still be utilized for this phase space plot. An example of a phase space plot is shown below:

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