Experiment No.
Supplement
Manual
1  3
Ch. 04, 08, 11
Introductory Physics Office, Dept. of Physics, Korea Univ. (Last Update : 20110225)
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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 Spring '11
 drlee
 Physics, Acceleration, Energy, Velocity, Vernier scale, Caliper, mechanical cart

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