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GenPhyLab_Manual_1_3

# GenPhyLab_Manual_1_3 - Experiment No 1 3 Supplement Ch 04...

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Experiment No. Supplement Manual 1 - 3 Ch. 04, 08, 11 Introductory Physics Office, Dept. of Physics, Korea Univ. (Last Update : 2011-02-25) PAGE 1/7 Measurement of the Motion of Objects in the Inclined Plane and Understanding of the Conservation Law of Mechanical Energy 1. Objective The acceleration and the velocity of the objects moving in the inclined plane will be measured in this experiment. In addition, the conservation law of mechanical energy will be considered for the objects in the translational motion and the rotational motion simultaneously. 2. Theory (1) Motion with the constant acceleration Assume that the object at rest initially starts to move with the constant acceleration in the inclined plane. If the initial velocity of the object is   and the object moves downward in the inclined plane by the distance during the time , the velocity and the acceleration of the object at the time are given as the following.        ,    (Eq. 1)        ,    (Eq. 2) (2) Motion of the object in the inclined plane Assume that the object with the mass and the rotational inertia moves in the inclined plane with the angle and no friction as shown in Fig. 1. Fig. 1. Motion of the object in the inclined plane. 1) Case of sliding without rolling Consider the case that the object slides without rolling. If the object moves downward in the inclined plane by the distance , the height of the object decreases by    sin and the potential energy of the object changes by     sin . Instead, the velocity and the angular speed of the object increase by and respectively, and the kinetic energy due to the translational motion and the rotational motion change by  and  respectively. Therefore, the change of the mechanical energy is given as the following.          sin (Eq. 3) Since the mechanical energy keeps constant in the case of no friction (   ) and the object slides without rolling (    ), the following result is obtained from Eq. 3.  sin    (Eq. 4) Differentiating Eq. 4 with respect to the time , the acceleration of the object can be determined as the following.    sin    ,       sin (Eq. 5) Here, the velocity     of the object is used.

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GenPhyLab_Manual_1_3 - Experiment No 1 3 Supplement Ch 04...

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