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Fascheue
Homework Statement
A coin stands vertically on a table. It is projected forward (in the plane of itself) with speed v and angular speed w. The coefficient of kinetic friction between the coin and the table is u. What should v and w be so that the coin comes to rest (both translationally and rotationally) a distance d from where it started.
Homework Equations
I = 1/2mr^2
T = r x f
Ff = uFn
F = ma
T = Iw’
The Attempt at a Solution
For v:
Ff = uFn
Ff = umg
Fnet = umg
ma = umg
a = ug
v - ug(t) = 0
v - ug(d/v) = 0
v = (ugd)/v
v^2 = ugd
v = sqrt(ugd)
For w:
T = r x f
T = umgr
T = Iw’
umgr = 1/2mr^2w’
w’ = 2ug/r
w - (2ug/r)(t) = 0
w = (2ug/r)(d/v)
w = (2ug/r)(d/(sqrt(ugd)))
w = 2sqrt(ugd)/r
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