fisica1-youn-e-freedman-exercicios-resolvidos

11.93: a) Taking torques about the left edge of the left leg, the bookcase would
(1500 Ν)(0.90
m)
tip when F = = 750 Ν,
and would slip when F = ( µ s
)(1500 Ν)
= 600 Ν,
so
(1.80 m)
the bookcase slides before tipping. b) If F is vertical, there will be no net
horizontal force and the bookcase could not slide. Again taking torques about the
(1500 Ν)(0.90
m)
left edge of the left leg, the force necessary to tip the case is
= 13.5 kN.
(0.10 m)
c) To slide, the friction force is f = µ
s
( w + F cos θ ), and setting this equal
to F sin θ and solving for F gives
µ
sw
F =
.
sin θ − µ
s
cos θ
To tip, the condition is that the normal force exerted by the right leg is zero, and
taking torques about the left edge of the left leg,
F sin θ (1.80 m) + F cos θ(0.10 m) = w(0.90 m), and solving for F gives
w
F =
.
( 1 9) cos θ + 2 sin θ
Setting the expression equal gives
µ
s(( 1 9) cos θ + 2 sin θ)
= sin θ − µ
s
cos θ,
and solving for θ gives
⎛ (10 9) µ ⎞
s
θ = arctan
⎜ = 66°
.
(1- 2
s)
⎟
⎝ µ ⎠