Environmental Engineering Reference
In-Depth Information
y
1
y
2
m
1
m
2
Figure 2.16 Two masses attached by a string which passes over a pulley. The device is
known as Atwood's machine.
d
2
y
1
/
d
t
2
twice leads to an equation of constraint between the accelerations: a
1
=
=−
=
a. Since the pulley is massless, it cannot alter the tension, hence
each mass experiences a force T due to the rope (see the free-body diagram in
Figure 2.17). Applying the Second Law to each mass in turn leads to the following
equations of motion:
a
2
m
1
g
−
T
=
m
1
a,
m
2
g
−
T
=−
m
2
a.
Subtraction of the equations eliminates T and yields
(m
1
−
m
2
)g
=
(m
1
+
m
2
)a
or
m
1
−
m
2
a
=
g.
m
1
+
m
2
If the masses are only slightly different a may be small and hence easily measured,
leading to a simple method for the determination of g.
T
T
a
1
a
2
m
1
g
m
2
g
Figure 2.17
Free body diagrams for the masses of Atwood's machine.
