ME 261  Spring 2008  Test 1
Problem 1
Two identical pendulums consist of a mass of 500 g at the end of a
1.5 m long string.
At rest, the two strings are vertical and the two
masses are touching.
Pendulum A is then released from rest at an
angle of 60
o
.
Find the maximum angle B will reach after impact.
The coefficient of restitution is 0.8.
Solution:
The entire event consists of three phases: (1) A will swing
down by an angle of 60
o
; (2) A will impact B; (3) B will swing out
until it stops and starts moving back.
During the first phase, A starts from rest and moves down following a
circular path as shown in Figure 1.b.
When it reaches the vertical, its
velocity will be V
A
.
The velocity V
A
can be determined applying the
workenergy principle
1
2
12
T
T
U

=
to mass A.
To determine
12
U
, the work done by the external forces, we
consider the free body diagram (Fig. 1.c) which shows two
forces: the weight mg and T, the tension in the string.
As mass
A moves on a circle, the tension T is always directed in the
radial direction.
Since the tension is always perpendicular to
the direction of the motion, it does not do any work.
The work
done by the weight mg is equal to mg(LL’).
The initial
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 Spring '08
 SERGEABRATE
 Force, Friction, Mass, Fig.

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