Problem 4.56, Giancoli
I have gotten several questions about problem 4.56 in Giancoli, which is on the homework, so I
am writing this document to help you out a little bit. Normally, the approach we would take with
a force problem would be: (1) Draw a free body diagram, (2) write
F
=
ma
equations for each
FBD, (3) substitute in any known or related quantities, (4) solve for any unknown quantities. In
step 3, you would do things like replace the force of friction with
μN
. In Lab 3, for example, we
used the fact that the cart and the hanging mass had the same acceleration because they were tied
together. Here, there is clearly a relationship between the various accelerations, but it is not easy
to immediately identify like in Lab 3. We will use a more formal approach to ﬁnd the “kinematic
constraint” on this problem.
Figure 1: Problem 4.56, Giancoli, with Established Coordinate Systems
Kinematic Constraint.
Looking at ﬁgure 1, we see the problem presented in Giancoli, but I
have included some coordinates to measure the various positions. The vector
y
c
, drawn in black,
represents the position of block C as measured from the center of the top pulley. We measure the
other two blocks, as shown in blue, from that same point, and we call these
y
a
and
y
b
. Since the
bottom pulley also moves, we measure its position (measured from the top pulley as well) and call
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 Spring '11
 wallace
 Acceleration, Force

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