Unimonte, Engenharia.Física Mecânica, prof. SimõesAplicações de vetores

F 800 X cos350 0 FI 655 N

Fy 800 x Sen350 13 Fig 459 N

IE t.FI F 1 1655 N

arc tan 1500 D 0 650700

F 1,66 103n 0 650

Por coordenadas cartesian asPsc 40 Cos D Px _37,6N

Py 40 Sen200 1 Py 13,7 N

Qsc 60 cos450 1 Qsc 42,4 NQy 60 Sen 45 DQy 42,4 N

Fsc D Ex 37,6 42,4 F x 80,0NEiFy D Fy 13,7142,4 Fy 56,1 N

Diagrama da resultante

56 ftp.T.IE97,7 N80

D arc tan 56,1 0 35,00

F 97,7N 0 35,00

Peta regra dos cossenos

z

I pIg4z pxgx cos 250I F 402 602 2 40 Xbox cos250

IFI 97,7N

97 Senf 60 54155Sen1550 Senp 97,7

t Sen f 0,260 D p 15,00

i 0 20 115,0 D 0 35 F 97,7N 0 3

Lei dos cossenos

120GEO F 64842 6 8 65600

F 12,2N8 Seno 8XSeul2 Seno 0,568

Sen1200 Sen O 12,2

T0 34,60 i F l2,2N o 34

Pet as componentes Cartesian asFix F G N

Fly O N

Fz 8 X cos 600 DFz x 4,0N

Fz y 8 x seu 68 Fay 6,9N

Ig 6 4 Ex ION 6a f E9

Fy Ot 6,9 Ey 6,9NIO

F T1046,92 F 12,1N

arctan6,01 p0 34,60 i E l2iN o 34

35 F

E

a P1 4 450 F Ez

Fi x Fi Cos 35 D Fix 0,866 F

F if Fi Sen 35 Fay 0,5 F

Fax Fz Cos 45 D Fax 0,707 Fz

Fay Fz Sen450 D Fay 0,707 Fz

FI FTI tax p 22250 0,866 F t 0,707 E l

Fy y Ely 0 0,5 Fi 0,707Fz Z

Z D 0,5 F O 707 Fz D F 0,70712 1,414Fz95

Em l D 22250 0,866 1,414Fz 10,707 Fz22250 1,224 Fz t 0,707 Fz22250 1,931 Fz222 50 Fz DFz 11523 N D

1,9311Fz l l5X1

F 1,414Fz D F 1,414 11523 D F 16293N

IF_1,63 104Nl

FTI 150 cos 35 D Fix 130 Ny 150 x Sen 35 D F'y 75 N

Fax 80 Cos 75 Fix 27,4 N

Fly 80 Sen 75 D Fzy 7512N

F3x O

Esg Fs p Easy 110N

x 100 65150 1 F yx 96,6N

tug 100 Sen is D Ely 25,9

Fsc 130 27,4 01 96,6 1 Fsc 199 N

Fyi 75 175,2 110 25,9 D Fry 14,3N

14,3 I199

IET T1992 14,32 D I 1 199 N

D arc tan 0 4,110

199

Coordenadas polares E 199N 0 4,110

Coordenadasvetangulares 199 e 14,3J Ni

F FT Fi cos 65 Fx 120 0565

65 1150FIX 50,7 N

Ey F seu 65 Ey 120 xsen 65

Fig 109 N

iFz Fix Fz cosy

Fay Fz send

FTytty _160N109 1 Fz Sen 2 160 D Fz send 160 109

Fz Sen 2 51 D 1 2 51 l

Tena1 x O D 50,7 1 Fz 652 0 D Fz cost 50,7

12 50,72 2

Cosa

it _14 51 50.72send cost 50,7 Cosa

tan 2 51 4 L arc tan 2 45,2050,7 50,7

F 2 50,70

1 2 72 N Ez 72N Q 45

0545,2

550 I 1650i FI 360 Cos 550

FI 20 GNF t v p

a Ey 360 Sen55 0 E'y 295 N

Pfc P cos 65 D Fsc 0,422PBy P Sen650 D Fly 0,906P

Rsc o 206 10 42210 0 D 0,422P 206 DP 206_ 488N01422

b Fx O 422 x 488 D Fsc 206 N

Fy 0,906 488 By 442 N

RI tic 152 Fsc 206 206 p Rx o N

Tty Ej Pig R y 295 442 DBy 737N

it Entity Titty R 737 f N ou

TIT 737 N 0 270

90NT3 Fy o p 90 Sen300 63 Sen 2 0

45 63 send63N

send 4563

7a arcsen 4 1245,60

13 8Fsc I 90 65300 63 6545,60 0 13 122 IN 1

a P1 4 300 calcular F j R Ez t

F x 100 Cos 35 86,6 N

F y 100 Seu300 50,0N Em x i

RI 86,6 175,0 173

fi in

E m YFs 200 6535 173 N y 50,0 130 100

3 y Zooxsen 35 100N R y 280N

11,4NTB 280 I I 8oT 1171 280 N

zoo4 are tan 4 87,70 0 180187,7011,4 0 268

280N 0 2680

b Valor de X pl que sega vertical D Rfc o

RI sat so Fsx i

Fix 100 cost

tix 150 Cos 4 130 150 Los X Cos 30 Sea x Sen300

130 Cos x 75,0 Sen x

x 200 Cos q

Substituindo em i

0 100 Cos 130 cos 75 Sen x 200 cos

D 30,0 cos 75,0 Sena

7 5,0 Send 30,06 S

Sent 3 D tan 2 0,400cos x 75,0

2 arctan 0,400 p 4 Z

c Valor de IE R x o IF R y Ey t y y

Fly too x Sen 21,8 37 I N

n I I a nF3y

R 229 N 0 2701