fisica1-youn-e-freedman-exercicios-resolvidos

7.80: (a) Stored energy = mgh = ( ρ V ) gh = ρ A(1
m)
gh
3
6
= (1000 kg m )(3.0 × 10
= 4.4 × 10
12
J.
2
m )(1 m)(9.8
m
2
s
)(150
m)
(b) 90% of the stored energy is converted to electrical energy, so
(0.90) ( mgh)
= 1000 kW h
(0.90) ρ V gh = 1000 kW h
3600 s
(1000 kW h) (
1 h
)
V =
3
(0.90)(1000 kg m ) (150 m) (9.8 m
= 2.
7 × 10
3
m
3
s
2
)
Change in level of the lake:
A∆h
= V
∆h
=
V
A
water
.7 × 10
=
3.0 × 10
3 3
2 −4
= 9.0 × 10
6 2
m
m
m
7.81: The potential energy of a horizontal layer of thickness dy, area A, and height y is
dU = ( dm)
gy . Let ρ be the density of water.
dm = ρ dV = ρA dy, so dU = ρAgy
dy.
The total potential energy U is
h
h
1 2
U = ∫ dU = ρAg∫
ydy =
2
ρAh
.
0
A = 3.0 × 10
6
m
2
0
and h = 150 m, so U
= 3.3×
10
14
J = 9.2 × 10
7
kWh.
7.82: a) Yes; rather than considering arbitrary paths, consider that
r
F
⎡ ∂ ⎛ Cy
= −⎢
⎜ −
⎣∂y
⎝ 3
3
⎞⎤
⎟⎥ ˆ. j
⎠ ⎦
b) No; consider the same path as in Example 7.13 (the field is not the same). For this
force, F r = 0 along Leg 1, F
r ⋅ d l
r
= 0 along legs 2 and 4, but F
r ⋅ d l
r
≠ 0 along Leg 3.