fisica1-youn-e-freedman-exercicios-resolvidos

5.70:
It’s interesting to look at the string’s angle measured from the perpendicular to the top of
the crate. This angle is of course 90 ° —angle measured from the top of the crate. The
free-body diagram for the washer then leads to the following equations, using Newton’s
Second Law and taking the upslope direction as positive:
− m g sin θ + T sin θ = m a
− m
Dividing the two equations:
w
w
g cosθ
slope
slope
tanθ
+ T cosθ
T sin θ
T cosθ
string
string
string
string
string
= 0
= m
= m
w
w
w
a + g sinθ
=
g cos0
slope
( a + g sinθ
g cosθ
For the crate, the component of the weight along the slope is − mc g sinθslope
and the
normal force is m g θ . Using Newton’s Second Law again:
c
cos slope
− m g sin θ
c
slope
+ µ m g cosθ
k
c
slope
slope
= m a
c
slope
a + g sin θ
µ
k
=
g cosθ
which leads to the interesting observation that the string will hang at an angle whose
tangent is equal to the coefficient of kinetic friction:
µ = θ = tan(90° − 68°
) = tan 22°
0.40
k
tan string
=
slope
slope
slope
)