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Unformatted text preview: 12. (a) From Eqs. 353 and 354, we obtain i = pf /(p − f ) = pr/(2p − r). Diﬀerentiating both sides with
respect to time and using vO = −dp/dt, we ﬁnd
vI = di
d
=
dt
dt pr
2p − r = −rvO (2p − r) + 2vO pr
=
(2p − r)2 r
2p − r (b) If p = 30 cm, we obtain
vI = 2 15 cm
2(30 cm) − 15 cm (5.0 cm/s) = 0.56 cm/s . (c) If p = 8.0 cm, we obtain
vI = 15 cm
2(8.0 cm) − 15 cm 2 (5.0 cm/s) = 1.1 × 103 cm/s . (d) If p = 1.0 cm, we obtain
vI = 15 cm
2(1.0 cm) − 15 cm 2 (5.0 cm/s) = 6.7 cm/s . 2 vO . ...
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 Fall '08
 SPRUNGER
 Physics

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