Lista 8 Solucão

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


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


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


4/5

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


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

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Lista 8 Solucão