manual1 - Contents > Lab 4 - Conservation of Mechanical...

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Contents > Lab 4 - Conservation of Mechanical Energy Lab 4 - Conservation of Mechanical Energy Introduction When a body moves, some things—such as its position, velocity, and momentum—change. It is interesting and useful to consider things that do not change. The total energy is a quantity that does not change; we say that it is conserved during the motion. There are several forms of energy with which you may be familiar, such as solar, nuclear, electrical, and thermal energies. In this experiment you will investigate two kinds of mechanical energy : kinetic energy and potential energy . You will carry out an experiment that demonstrates the conservation of the total mechanical energy of a system. Discussion of Principles Conservation of Mechanical Energy The total mechanical energy E of a system is defined as the sum of the kinetic energy K and potential energy U of the system. ( 1 ) E = K + U In the absence of non-conservative forces, such as friction or air drag, the total mechanical energy remains a constant and we say that mechanical energy is conserved. If K 1 , U 1 , K 2 , U 2 are the kinetic and potential energies at two different locations 1 and 2 respectively, then the conservation of mechanical energy leads to the following mathematical expression
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( 2 ) K 1 + U 1 = K 2 + U 2 This can also be expressed in terms of the changes in kinetic and potential energies ( 3 ) Δ K + Δ U = 0 where Δ K = K 2 K 1 and Δ U = U 2 U 1 . Conservation of Mechanical Energy is one of the fundamental laws of physics that is also a very powerful tool for solving complex problems in mechanics. Kinetic Energy Kinetic energy K is the energy a body has because it is in motion . When work is done on an object, the result is a change in the kinetic energy of the object. Energy of motion can be translational kinetic energy and/or rotational kinetic energy . Translational kinetic energy K T
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is the energy an object has because it is moving from place to place, regardless of whether it is also rotating; K T is related to the mass m and velocity or speed v of the object by ( 4 ) K T = 1 2 mv 2 Rotational kinetic energy K R is the energy an object has because it is rotating, regardless of whether the body as a whole is moving from place to place. K R is related to the moment of inertia I and angular velocity ω of the object by ( 5 ) K R = 1 2 I ω 2 The angular velocity of a rolling sphere that is not slipping is the velocity (relative to the center of the sphere) of a point on the circumference, divided by the radius R of the sphere. ( 6 ) ω = v R Just as the mass m of a body is a measure of its resistance to a change in its (translational) velocity, the moment of inertia I of an object is a measure of that object's resistance to a change in its angular velocity. The moment of inertia of a solid sphere (of uniform density) is given by ( 7 ) I =
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2 5 MR 2 where M and R are the mass and radius of the sphere, respectively. The total kinetic energy K total
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This note was uploaded on 08/21/2011 for the course PY 211 taught by Professor Owen during the Spring '07 term at N.C. State.

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manual1 - Contents > Lab 4 - Conservation of Mechanical...

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