Homework 5 Due February 13 2007
 1 
1) A stone of mass
m
is attached to a light
string of length
L
describes a circular path
at an angle
θ
as shown.
a)
Indicate the direction of the total
acceleration vector of the stone on
the figure.
b)
What is the radius
R
of the circle in
terms of
θ
and
L
?
c)
Find the tension in the string.
d)
Find the angular velocity
ω
of the
motion in terms of
g, L
and
θ.
2) On a winter's day in Maine, warehouse workers are pushing boxes of mass
m
down a
rough plank inclined at an angle
α
above the horizontal. The plank is partially covered
with ice, more ice near the bottom of the plank than near the top, so that the coefficient of
friction increases with the distance
x
from the bottom of the plank according to
µ
s
=
µ
k
=
Ax
where
A
is a positive constant and the bottom of the plank is at
x
=0 (note that we assume
that kinetic and static friction coefficients are the same). Suppose that initially a box is
resting at a position
x
0
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 Spring '08
 HerreraSiklody
 Acceleration, Force, Mass, Work, Light, mg sin, mg F, mg cos, mL sin cos

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