Relatório de Física A Lei de Hooke

7/31/2019 Relatrio de Fsica A Lei de Hooke

1/11

ALAN MELO

DOUGLAS MENEZES

EDUARDO FARANI

HERALDO DDA

HUGO VILLANOVA

RAPHAEL CALAZANS

LEI DE HOOKE

SO CRISTOVO

2010


2/11

ALAN MELO

DOUGLAS MENEZES

EDUARDO FARANIHERALDO DDA

HUGO VILLANOVA

RAPHAEL CALAZANS

LEI DE HOOKE

Relatrio de laboratrio apresentado Universi-

dade Federal de Sergipe, Centro de Cincias Exa-

tas e Tecnologia, Departamento de Fsica, como

um dos pr-requisitos para a concluso da disciplina

Laboratrio de Fsica A.

Orientador: Professora Rafaela Dantas

SO CRISTOVO

2010


3/11

SUMRIO

1 INTRODUO_____________________________3

2 OBJETIVOS________________________________5

3 MATERIAIS E METODOLOGIA_______________5

4 RESULTADOS______________________________ 6

5 DISCUSSO________________________________7

6 CONCLUSO_______________________________10

7 BIBLIOGRAFIA_____________________________11


4/11

1-Introduo:

Em 1678 o cientista ingls Robert Hooke formulou a Lei de Hooke.Essa lei afirma que o alongamento ou a contratao de um material elstico(normalmente uma mola),quando sendo submetido a uma fora deformadora,gera uma outra fora de reao chamada de restauradora.

Hooke descobriu que quanto maior fosse o peso de um corpo suspenso auma das extremidades de uma mola (cuja outra extremidade era presa a umsuporte fixo) maior era a deformao (no caso: aumento de comprimento)sofrida pela mola. Analisando outros sistemas elsticos, Hooke verificou queexistia sempre proporcionalidade entre fora deformante e deformaoelstica produzida. Essa lei regida pela seguinte equao:

Onde:

F a fora restauradora;

K a constate elstica (que depende do material da mola);

x a deformao da mola.A fora elstica uma fora negativa, ou seja, conclui-se que ela atua no

sentido contrrio a fora aplicada na mola.

Quando o sistema est em equilibro, o mdulo da fora peso (P) ser igualao mdulo da fora elstica: || ||

Assim sendo, podemos afirmar que:

Onde:

m a massa utilizada na experincia.

g gravidade.


5/11

2-Objetivos:

Estudar e compreender as equao que regem a Lei de Hooke pormeio da deformao de uma mola.

Comparar dados calculados a partir de valores tericos e condiesreais do sistema.

Determinar o valor da constante elstica da mola a partir dos dadosexperimentais.

3-Materiais e Metodologia

3.1-Materiais

Suporte com escala graduada (dinammetro); 2 molas; 3-Porta peso (10 g); 4-Pesos de 10 g e 50 g.

Figura 1: Dinammetro Figura 2: Mola

Figura 3: Porta peso Figura 4: Massas Aferidas

3.2-Metodologia

Para cada mola, inicialmente, determinamos o seu comprimento semnenhuma fora aplicada a ela. Aps esse procedimento, medimos trsvezes a deformao da mola apenas com o porta peso inserido. Depoisrefez-se esse procedimento com oito valores de massa diferentes sempremedindo trs vezes para cada valor de massa, com objetivo de eliminar oerro.

Foi elaborada uma tabela com os pesos e medidas obtidas nesseexperimento:


6/11

4-Resultados

Mola: Pequena X0 (m) = 0,085

M

(kg)

Peso

(N)

X (m) X

(m)a

(m)

b

(m)

c

(m)

x

(m)x

(m)Resultado de x

Medida 1 Medida 2 Medida 3

Massa 1 0,01 0,0978 0,087 0,088 0,087 0,0873 3,33x10-4

0,0005 6,01x10-4

2,33x10-3

7,07x10-4

(2,33x10-3 7,07x10

-4)

Massa 2 0,02 0,1956 0,092 0,089 0,090 0,0903 8,82x10-4

0,0005 1,01x10-3

5,33x10-3

7,07x10-4

(5,33x10-3 7,07x10

-4)

Massa 3 0,03 0,2934 0,093 0,093 0,093 0,0930 0 0,0005 5x10-4 8x10-3 7,07x10-4 (8x10-3 7,07x10-4)Massa 4 0,04 0,3912 0,096 0,094 0,094 0,0947 6,67x10

-40,0005 8,33x10

-49,67x10

-37,07x10

-4(9,67x10

-3 7,07x10

-4)

Massa 5 0,05 0,4890 0,097 0,099 0,098 0,0980 5,77x10-4

0,0005 7,64x10-4

13,33x10-3

7,07x10-4

(13,33x10-3 7,07x10

-4)

Massa 6 0,06 0,5868 0,099 0,099 0,098 0,0987 3,33x10-4

0,0005 6,01x10-4

13,67x10-3

7,07x10-4 (13,67x10

-3 7,07x10

-4)

Massa 7 0,07 0,6846 0,102 0,102 0,101 0,1017 3,33x10-4

0,0005 6,01x10-4

16,67x10-3

7,07x10-4

(16,67x10-3 7,07x10

-4)

Massa 8 0,08 0,7824 0,103 0,104 0,103 0,1033 3,33x10-4

0,0005 6,01x10-4

18,33x10-3

7,07x10-4

(18,33x10-3 7,07x10

-4)

Mola: Grande X0 (m) = 0,102

M

(kg)

Peso

(N)

X (m) X

(m)a

(m)

b

(m)

c

(m)

x

(m)x

(m)

Resultado de x

Medida 1 Medida 2 Medida 3

Massa 1 0,01 0,0978 0,108 0,107 0,108 0,1077 3,33x10-4

0,0005 6,01x10-4

5,67x10-3

7,07x10-4

(5,67x10-3 7,07x10

-4)

Massa 2 0,02 0,1956 0,114 0,114 0,115 0,1143 3,33x10-4

0,0005 6,01x10-4

12,4x10-3

7,07x10-4

(12,4x10-3 7,07x10

-4)

Massa 3 0,03 0,2934 0,119 0,120 0,118 0,1190 5,77x10-4

0,0005 7,64x10-4

17x10-3

7,07x10-4

(17x10-3 7,07x10

-4)

Massa 4 0,04 0,3912 0,126 0,126 0,127 0,1263 3,33x10-4

0,0005 6,01x10-4

24,33x10-3

7,07x10-4

(24,44x10-3 7,07x10

-4)

Massa 5 0,05 0,4890 0,131 0,132 0,134 0,1323 1,76x10-4

0,0005 3,33x10-4

30,33x10-3

7,07x10-4

(30,33x10-3 7,07x10

-4)

Massa 6 0,06 0,5868 0,137 0,137 0,138 0,1373 5,77x10-4 0,0005 7,64x10-4 36x10-3 7,07x10-4 (36x10-3 7,07x10-4)

Massa 7 0,07 0,6846 0,145 0,143 0,145 0,1443 6,67x10-4

0,0005 8,33x10-4

42,33x10-3

7,07x10-4

(42,33x10-3 7,07x10

-4)

Massa 8 0,08 0,7824 0,150 0,150 0,149 0,1497 3,04x10-4

0,0005 5,85x10-4

47,67x10-3

7,07x10-4

(47,67x10-3 7,07x10

-4)

b (M) = 0,001 kg b (Peso)= 9,78x10

-3N


7/11

5-Discusso

Primeiramente calculamos a mdia das medidas () para ento calcular aincerteza delas. Ento calculamos a incertezas do tipo A (), do tipo B ()ea incerteza combinada (

) a partir das frmulas seguintes:

=

A partir das medidas obtidas no experimento, e pela definio de incerteza,calculamos:

( )Sabendo que g uma constante, ento:


8/11

1)Os grficos assumem um comportamento linear,pois o coeficiente angular uma constante e nesses representado pela constante elstica,justamente,poresse motivo diz-se que uma mola obedece a lei de Hooke. (Os grficos foramentregues hoje pela manh).

2)A constate elstica determinada graficamente pelo coeficiente angular dareta.Pegando dois pontos da reta,P1(x,y) e P2(a,b), representada nogrfico,calcula-se o coeficiente angular da seguinte forma

Aplicando essa equao com dados dos grficos, temos:

Mola fina:P1(6x10

-3 ; 0,25) e P2(16,6x10-3 ; 0,69) , substituindo na formula tem-

se: Mola Grossa:

P1(0; 0) e P2(45x10

-3 ; 0,72) , substituindo na formula tem-se:

Entretanto, esses resultados so acompanhados de incertezas, para isso foramfeitos os clculos com o intuito de determin-los da seguinte forma:

1. Traa-se um retngulo que contenha a reta do grfico;2. Traam-se suas diagonais;3. Calculam-se os coeficientes angulares das diagonais;4. Determinar a incerteza atravs da frmula abaixo.


9/11

Aplicando essa equao com dados obtidos, temos:

Mola fina:

Mola Grossa:

3)A partir dos coeficientes angulares determinados acima,foi observado quequanto menor for o dimetro da mola maior ser a constante elstica e vice-versa.

4)Como provado anteriormente a constante elstica corresponde aocoeficiente angular que no grfico de fora deformadora X deformao a

tangente da reta de acordo com a seguinte equao:

|| Logo, observa-se que a mola obedece a Lei de Hooke, por que:

5) Houve dificuldades quanto aos clculos das incertezas, j que ocorrevariao nos instrumentos de medio durante o processo experimental.

6) No.Por que no foi ultrapassado o limite de deformao suportado pelamola.


10/11

6-Concluso

Nesse documento foram esclarecidas questes a cerca da Lei deHooke, analisando a variao de uma mola qualquer sob ao de uma foracontrolada.

Durante as experincias foi trabalhado de perto com os princpios daLei de Hooke, com o dinamismo da prtica foi imensamente facilitado oabsorvimento do aprendizado pelos alunos. Foi observada e notificada avariao causada na mola por cada um dos pesos, quando contrastados osvalores em grfico, encontramos o coeficiente de elasticidade da mola (K)como sendo o coeficiente angular da reta expressa no grfico.


11/11

7-Bibliografia

http://www.google.com.br/imgres?imgurl=http://1.bp.blogspot.com/_sGWqTz-au00/R1A3qjj0YPI/AAAAAAAAAR0/51wC-ncQGTw/s400/dinamometro.jpg&imgrefurl=http://fjsousa.blogspot.com/2007/11/dinammetro.html&usg=__xZ4RvmkZyDkIJTJli4nFRiX

Xx0M=&h=369&w=171&sz=54&hl=pt-BR&start=15&zoom=1&um=1&itbs=1&tbnid=IycyIQPoCtUZOM:&tbnh=122&tbnw=57&prev=/images%3Fq%3Ddinam%25C3%25B4metro%26um%3D1%26hl%3Dpt-BR%26rlz%3D1T4ADSA_pt-BRBR338BR339%26tbs%3Disch:1

http://www.fisica.net/mecanicaclassica/a_lei_de_hooke.pdf http://www.google.com.br/imgres?imgurl=http://www.nunesbrasil.co

m.br/redima/admin/fotos/26mola.jpg&imgrefurl=http://www.nunesbrasil.com.br/redima/produtos.php%3Fver%3D2%26titulosub%3DDiversas&usg=__7YL1PETRYS1L2-Ou_bYBFStUPCo=&h=400&w=400&sz=18&hl=pt-

BR&start=9&zoom=1&um=1&itbs=1&tbnid=QUFfQ17TENRRBM:&tbnh=124&tbnw=124&prev=/images%3Fq%3Dmola%26um%3D1%26hl%3Dpt-BR%26sa%3DN%26rlz%3D1R2ADSA_pt-BRBR338%26tbs%3Disch:1

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