Phys1_06-Conservation_Laws_defb967a-9344-49c1-bde6-034991d433e7
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Georgia Institute Of Technology *
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Course
2111
Subject
Electrical Engineering
Date
Apr 3, 2024
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14
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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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A
P KN
Refer to the figure.
d₁
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