Problem 4.7 Comments
Regarding the note at the end of the problem: To "show that"
you get their result, you must make this assumption. It
is still possible (and quite simple) to solve the problem
when this assumption isn't valid. In that case, the
mud leaves the wheel at the top of the wheel...it gets its
height from being stuck to the wheel, not from projectile
motion.
Solve this problem using conservation of energy and be
careful. Draw a good picture and don't oversimplify the
problem. If you do, you won't get the right answer.
Find the initial height (is not zero), the initial velocity
(is not zero), and
(assuming projectile motion) the "final" velocity
(you guessed it, this isn't zero either). With
these, you can solve for the "final" height.
A most common mistake is to assume the velocity on
the edge of the wheel is tangent to the wheel. You
might find it helpful to refer to figure 1.10.6 in the text.
Note that the velocity at a point on the rolling wheel is
NOT tangent to the wheel (except at the top).
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