Introduction to Classical Mechanics by David Morin

Author:David Morin
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2013-06-14T16:00:00+00:00

For β → 0, no energy is lost, which makes sense. And for β → ∞ (a spool sliding on its axle), all the energy is lost, which also makes sense, because we essentially have a sliding block which can’t rotate.

(b)Let’s first find t. The friction force is Ff = −μmg, so F = ma gives −μg = a. Therefore, ΔV = at = −μgt. But Eq. (8.150) says that ΔV ≡ Vf − V0 = −V0β/(1 + β). Therefore,

For β → 0, we have t → 0, which makes sense. And for β → ∞, we have t → V0/(μg), which equals the time a sliding block would take to stop.

Let’s now find d. We have d = V0t+(1/2)at2. Using a = −μg, and plugging in the t from Eq. (8.152), we obtain

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