1_Lista_de_Exerccios_-_2022-_Respostas

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Reologia ESTM 015 
 
ESTM 015 – Reologia 
Prof. Danilo Justino Carastan 
Respostas - Primeira Lista de Exercícios 
 
 
2. 
a) T ∙ v = Tijvj = 321 ˆ7ˆ14ˆ xxx  
b) w ∙ U = wiUij = 321 ˆˆ12ˆ56 xxx  
c) T ∙ U = TijUjk = 












11206
41416
23320
 
d) T : U = TijUji = 3 
e) v ∙ (T ∙ w) = vi (Tij wj) = 50 
f) vv = vivj = 













486
81612
6129
 
g) vw = viwj = 











10122
20244
15183
 
h) (v × w) ∙ T = εijkvjwkTil = 321 ˆ118ˆ38ˆ252 xxx  
 
 
3. 
a) T = 












002
0010
21010
Pa 
|tn| = 11,94 Pa 
σn = 8,67 Pa 
 
b) T = 










010
0110
010
Pa 
|tn| = 6,03 Pa 
σn = 4,33 Pa 
 
 
4. 
a) IT = 7; IIT = 14; IIIT = 8 
b) IT = 1; IIT = -49; IIIT = 68 
 
 
 
 
 
Reologia ESTM 015 
 
5. 
a) T = 












020
200
001
MPa 
b) |f| = √5 N 
c) fn = 1 N 
 d) IT = 1; IIT = -4; IT = -4 
 
6. 
a) 
















000
00
2
0
2
0
3
3
R
M
R
M


 
 
b) 

 cos
4
3
sen
R
M
 




 2
3
2
3
cos
22
R
M
sen
R
M
 
se θ = 0: σ = 0; 
3
2
R
M

  
se θ = 45°: 
3
2
R
M

  ; τ = 0 
se θ = 90°: σ = 0; 
3
2
R
M

  
se θ = 135°: 
3
2
R
M

  ; τ = 0