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M o d e l N o . M E - 9 5 0 2 E x p . 1 6 : M o d i f i e d A t w o o d ’ s M a c h i n e
0 1 2 - 1 2 8 7 6 B 85
Exp. 16: Modified Atwood’s Machine
Equipment Needed
Theory
The acceleration of an object depends on the net applied force and the
object’s mass. In an Atwood’s Machine, the difference between two hang-
ing masses determines the net force acting on the system of the two
masses. The net force accelerates both of the hanging masses; the heaver
mass is accelerated downward and the lighter mass is accelerated upward.
The Atwood’s Machine was invented in 1784 by the Reverend George
Atwood to demonstrate the principles of acceleration and net force. In an
ideal Atwood’s Machine, two unequal masses are attached to a flexible,
massless string which passes over a frictionless, massless pulley. A real
Atwood’s Machine is not as simple as its ideal counterpart. Strings and
pulleys are not massless and pulleys are not frictionless. The rotational
inertia of the pulley complicates the demonstration.
In the free body diagram (FBD) of the Atwood’s Machine, T is the tension in the string, Mass
2
is greater than
Mass
1
, and g is the acceleration due to gravity. Using the convention that up is positive and down is negative, the
net force equations for the two masses are:
Ideally (where the string is massless and doesn’t stretch and the pulley is massless and frictionless), the tension, T ,
is the same for both hanging masses. Let T
1
= T
2
and solve for the theoretical acceleration, a :
The theoretical acceleration is the difference in the two forces (M
2
g - M
1
g) divided by the sum of the two masses.
In this experiment you will investigate the acceleration of the masses in an Atwood’s Machine. You can determine
the acceleration,
a , by measuring the time, t , it takes for one of the masses to fall a known distance, d .
Compare your measured acceleration to the theoretical acceleration.
Item Item
Statics Board Small Pulley (2)
Mass and Hanger Set Thread
Stopwatch Dry-erase Marker Pen or Pencil
Mass
2
Mass
1
M
2
g
M
1
Pulley
Thread
Fig. 16.1: Atwood’s FBD
T
T
M
1
g
M
2
T
1
M
1
g – F
net
M
1
a = =
T
2
M
2
g – F
net
M
2
a –
 
= =
a g
M
2
M
1
–
M
2
M
1
+
---------------------
=
a
2 d
t
2
------
=