Download - Lista 8 Solucão
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7/25/2019 Lista 8 Soluco
1/5
8, 0N
5, 0N
0, 7m
W =F.d. cos = (8, 0N).(0, 70m).(cos 0o) = 5, 6J
Et= Fat.d= (5, 0N).(0, 70m) = 3, 5J
27kg
9, 2m
32o
0, 20
F. cos 32o
Fat = c.N
P =N+ F. sin(32o)
F = c.N
cos 32o F = 55, 5N
W =F.d. cos = (55, 5N).(9, 2m). cos 32o = 433J
Fat= c.(mg F. sin32o)
Et= Fat.d= (27.9, 8 55, 5. sin32o).0, 2.9, 2 = 433J
3, 57kg
4, 06m
7, 68N 15o
W =F.d. cos = (7, 68N).(4, 06m). cos 15o = 31, 1J
f
f =F. cos 15o
f= 7, 42N
Et= f.d= (7, 42N).(4, 06m) = 30, 1J
F. cos 15o f= 0 N+ F. sin 15o mg= 0,
m
F
f
N
f= 7, 42N
N=mgF. sin15o = (3, 75kg)(9, 8m/s2)(7, 68N). sin15o = 33, 0N
f =c.N c = f
N =
(7, 42N)
(33, 0N) = 0, 225
35, 0N 4, 00kg
0, 600
3, 00m
40, 0J
W =F.d. cos = (35, 0N)(3, 00m). cos0o = 105J
Et= Fat.d= c.N.d= c.m.g.d= (0, 600)(4, 00kg)(9, 80m/s2)(3, 00m)
40, 0J
(70, 640, 0)J= 30, 6J 70, 6J (105 70, 6)J = 34, 4J
520Kg
500m 300m
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7/25/2019 Lista 8 Soluco
2/5
0.25
U
U
U
U=m.g.h
U= (520)(9, 8)(300) = 1, 53.106J
fk =k.N =k.m.g. sin(2 ) =k.m.g. cos
Eat= fk.d= k.m.g.d. cos d
d= 500
cos
cos = xd
x = 400m
Eter = k.m.g.d. cos = k.m.g.d.xd
=k.m.g.x= (0.25)(520)(9.8)(400) = 5, 1.10
5J
Kf =Ki+Ui UfEter
Kf= 0 + 1, 53.106 0 5, 1.105
Kf= 0 + 1, 02.106J
Kf = 12mv
2 v =
63m/s
vo 6, 0m/s
h 1, 1m e k= 0, 60 d
Ki = U+ Eter = m.g.(h+.d),
Ki = 12mv
2
m
1
2 v
2
=g(h+.d) = d=
v2i2g
h
= 1, 2m
5, 29N
20m/s
0., 65N
h
Eter = f .h
Kf+ Uf+ Eter = Ki+Ui
0 +m.g.h+f.h = 1
2.m.v2o
h
h = m.v2o2(m.g+f) m = 5,299,8
= 0, 54Kg
h= m.v2
o
2(m.g+f) = (0,54)(20)
2
2(0,54.9,8+0,265) = 19, 4m
Eter = 2.f.h
Kf+ Eter = Ki
1
2m.v2 + 2.f.h=
1
2m.v2o
1
2
m.v2 = 1
2
m.v2o 2.f. m.v2o
2(m.g+f)
v2 =v2o(1 2.f
(m.g+f))
v2 = (20)2(1 2.0, 265
5, 29 + 0, 265) =
361, 836 = 19m/s
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7/25/2019 Lista 8 Soluco
3/5
4.0Kg
30o
128J
0, 30
N =m.g. cos
fk = k.m.g. cos
Ki = Kf+ U+ Eter
Ki = 0 +m.g.d. sin +k.m.g.d. cos
d
d= Kim.g(sin +k. cos )
= 1284.9, 8.(sin 30o + 0, 3. cos 30o)
= 4, 3m.
25J
7, 5cm
E= 12 .k.x2
k= 89N/cm.
m = 2kg h= 40cm
k= 1960n/m
Ki+Ui = Kf+ Uf
0 = m.g(h+x) +1
2.k.x2
M.g = 19, 6N, h= 0, 4m e k= 1960n/m
x= 0, 10m
t = 0
1kg
v = (18m/s)i+ (24m/s)j
U
t= 0 t= 6s
y = voy .t1
2.g.t2
y = 32m
U=m.g.y= 318J= 3, 2.102J
25cm
15g
dx
x
Du = (dx)gx = = m
h
0 h
U=
du=
gx.dx=
1
2.g.h2 =
1
2.m.g.h
m= 15g
h= 25cm
U= 0, 018J
U(x) U(x) x
U(x)
U(x) =F dx
F(2) = x 3, F(x) = 0
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7/25/2019 Lista 8 Soluco
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3 x 2, F(x) = 1
2 x 1, F(x) = 2(x+ 1, 5)
1 x 1, F(x) = 1
1 x 2, F(x) = 2(x 1, 5)
2 x 3, F(x) = 1
x 3, F(x) = 0
U(x)
x 3
x 3 = U(x) = U(0) = 0
0 x 1 = U(x) = x
0 dx= xx= 1 U(1) = 1
1 x 2 = U(x) = 1
x1
(2x 3)dx=1(x2 3x)
x1
=
x2 3x+ 1x= 1 U(1) = 1 3 + 1 = 1x= 2 U(2) = 4 6 + 1 = 1
2 x 3 = U(x) = 1 +
x2
dx= 1 +x 2 = x 3
x= 2 U(2) = 1x= 3 U(3) = 0
U(x) = 3x2 x3 [x] =metros [U] =J oules
U(x)
2 x 2
3x2
x3
= 0
x = 0 ou x = 3
U(x) = 6x 3x2 x = 0 ou x = 2 U(0) = 0 ou U(2) = 4
U(x)
x
F(x) = dU(x)dx
= 6x 3x2
100g
U() = 1, 6sin
U()
3 =
3
1, 6m
= 2
F() = dU(L)dL
= dU(R)d(R)
= 1R
dU()d
F() = 1
1, 6.1, 6. cos
cos = 0, 1a
U()
dF
d = 0 sin = 0
a= cos(
3)
0, 1 = 5m/s2
75kg 7, 0m
12m 7, 0m
W =m.g. cos W= (75kg)(9, 80m/s2)(7, 0m)(cos 180o) = 5100J
W = 75.9, 8.7. cos0 = 5100J
90o
W = 0
Wt= 0
10kg
0, 250 2, 00m 4, 00m
= 180 W =m.g..2r
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7/25/2019 Lista 8 Soluco
5/5
W = (0, 250)(10)(9, 80)(2)(2) = 308J
W = 616J
0, 6kg
1, 2N
3, 0m
3, 0m
(1, 2N)(3, 0m) = 3, 6J 3, 6J 7, 2J
1, 5kg
0, 25
W1 = W2= (3, 675).(8, 0) = 29, 4J e Wt = W1+W2 = 59J
W = (3, 675).d
d= 11, 3m (diagonal).W = 42J
F.d = (3, 675).(8, 0) = 29, 4J
59J