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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View Full Documenta = 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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 Spring '09
 MAMAR
 Physics, Kinetic Energy, Velocity, uniformly motion

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