p08_033.pdf

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Chapter 8 - 8.33
33. The work required is the change in the gravitational potential energy as a result of the chain being pulled
onto the table. Dividing the hanging chain into a large number of infinitesimal segments, each of length
dy , we note that the mass of a segment is ( m/L ) dy and the change in potential energy of a segment when
it is a distance
|
below the table top is dU =( m/L ) g
|
y
|
dy =
−
mg
L
0
ydy = 1
2
mg
L ( L/ 4) 2 = mgL/ 32 .
∆ U =
−
− L/ 4
The work required to pull the chain onto the table is therefore W =∆ U = mgL/ 32.
( m/L ) gy dy since y is negative-valued
(we have + y upward and the origin is at the tabletop). The total potential energy change is
|
y

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