fisica1-youn-e-freedman-exercicios-resolvidos

11.46: a) Denote the weight per unit length
as α , so w1 = α(10.0 cm), w2
= α(8.0 cm), and w3
= αl.
The center of gravity is a distance xcm
to the right of point O where
x
cm
=
w1
(5.0 cm) + w2
(9.5 cm) + w3
(10.0 cm − l
w + w + w
1
2
3
2)
(10.0 cm)(5.0 cm) + (8.0 cm)(9.5 cm) + l(10.0 cm − l
=
(10.0 cm) + (8.0 cm) + l
2)
.
Setting x 0 gives a quadratic in l , which has as its positive root cm.
cm =
l = 28.8
b) Changing the material from steel to copper would have no effect on the length l
since the weight of each piece would change by the same amount.
r r v
11.47: Let ′
i
=
i
− R ,where R r is the vector from the point O to the point P.
r r r
The torque for each force with respect to point P is then τ ′ =
′× F , and so the net torque
is
∑
r
τ
i
=∑
= ∑
= ∑
r
r
r
( i
− R) × Fi
r r r r
i
× Fi
− ∑ R × Fi
r r r r
i
× Fi
− R × ∑Fi.
In the last expression, the first term is the sum of the torques about point O, and the
second term is given to be zero, so the net torques are the same.
i
i
i
11.48: From the figure (and from common sense), the force F r 1
is directed along the
length of the nail, and so has a moment arm of (0.0800 m) sin 60°
. The moment arm of
F r 2
is 0.300 m, so
(0.0800 m) sin 60°
F
2
= F1
= (500 N)(0.231) = 116 N.
(0.300 m)