A Classical Approach of Newtonian Mechanics

4 NEWTON’S LAWS OF MOTION 4.7 Strings, pulleys, and inclines

(^1) T
m (^2)
m
T
m
2
g
Figure 30: Block sliding over a smooth table, pulled by a second block
wrong in this assumption then we will simply obtain a negative acceleration for
this mass. The first mass is subject to an upward force T, due to the tension in the
string, and a downward force m 1 g, due to gravity. These forces cause the mass
to move upwards with acceleration
a =
T
− g. (4.18)
m 1
The second mass is subject to a downward force m 2 g, due to gravity, and an
upward force T, due to the tension in the string. These forces cause the mass to
move downward with acceleration
a = g −
T

. (4.19)
m 2

Now, the upward acceleration of the first mass must match the downward accel-

eration of the second, since they are connected by an inextensible string. Hence,

equating the previous two expressions, we obtain

T =

2 m 1 m 2

m 1 + m 2

g, (4.20)

a =

m 2 − m 1

g. (4.21)

m 1 + m 2

As expected, the first mass accelerates upward (i.e., a > 0 ) if m 2 > m 1 , and vice
versa. Note that the acceleration of the system is less than the full acceleration

due to gravity, g, since both masses contribute to the inertia of the system, but