Lab2 - Lab. No.2. Study of kinematics and dynamics on the...

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Lab. No.2. Study of kinematics and dynamics on the Atwood’s machine Objective: to acquire skills in investigation of kinematical equations for straight line and uniformly accelerated motions; to study main dynamics equation of point particle and translational motion of rigid body. Main tasks: 1. Straight line velocity determination of the load using Atwood’s machine. 2. Determination of acceleration for the uniformly accelerated motion of the load. 3. Newton’s second law verification. 1. Theory of experiment Motion of mechanical system (Fig.1) is described by the laws of Newtonian’s classical mechanics. The mechanical system consists of two loads with masses and ± ² ³ , which are connected by unstretchable line. ´ is radius of pulley, moment of inertia is µ and ³ is mass of overload. The potential energy of the mechanical system does not depend on the loads position if the masses of the loads are equal. It comes from the fact that the loss of the potential energy of the first body results the correspondent potential energy increase of the second one. If the loads have different masses, variation of the mechanical system’s potential energy is defined by changing position ¶·± of overload ± ³ : ∆Е р = m 1 g ∆h. (1) Potential energy of the system transforms into kinetic energy of translational and circular motion of the system (work to overcome the gravity can be neglected): m 1 g ∆h = [ mv 2 /2 + (m + m 1 )v 2 /2 + Jω 2 /2], (2) where mv 2 /2 is kinetic energy of the left load (without overload); (m + m 1 )v 2 /2 is kinetic energy of the right load (with overload); Jω 2 /2 is kinetic energy of pulley’s circular motion. Taking into account, that ∆h = a t 2 /2 and angular velocity is ω = v/r, linear velocity is v = a t, radius of the rotating disc is r, it is possible to get expression for the determination of acceleration of the system in the following form:
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a = m 1 g / (2m + m 1 + J/r 2 ). (3) If we neglect pulley’s moment of inertia J, The formula for the acceleration has the
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This note was uploaded on 10/15/2011 for the course PHYSICS 0207239 taught by Professor Mamar during the Spring '09 term at Jordan University of Science & Tech.

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Lab2 - Lab. No.2. Study of kinematics and dynamics on the...

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