Formulario Primer Parcial Fisica.docx

⃗⃗⃗⃗⃗ de un vector componentes 𝐴𝐵 𝑢 ⃗ ∙ 𝑣 = (𝑥, 𝑦, 𝑧) ⋅ (𝑥, 𝑦, 𝑧)

Modulo |𝑢, ⃗⃗⃗⃗⃗⃗𝑣 | = √(𝑥)2 + (𝑦)2 + (𝑧)2

; ⃗ ∙𝑣 ⃗ 𝑢

⃗ ∙𝑣 ⃗ 𝑢

∝= cos-1|𝑢⃗||𝑣⃗|

Angulo del vector 𝑐𝑜𝑠 ∝= |𝑢⃗||𝑣⃗| ; 𝑖̂ Producto vectorial 𝑢 ⃗ 𝑥𝑣 = |𝑥1 𝑥2

−𝑗̂ 𝑦1 𝑦2

Solución- ∑ 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑒𝑠 𝑒𝑛 𝑋

;

𝑨𝒙 = 𝐴𝑐𝑜𝑠𝜃

𝑘̂ 𝑧1| 𝑧2

;

Proy escalar 𝑝𝑟𝑜𝑦𝑉2 𝑉1 =

∑ 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑒𝑠 𝑒𝑛 𝑌 𝐴𝑦 = 𝐴𝑠𝑒𝑛𝜃

𝐵𝑥 = 𝐵𝑐𝑜𝑠𝜃 𝐶𝑥 = 𝐶𝑐𝑜𝑠𝜃

𝐵𝑦 = 𝐵𝑠𝑒𝑛𝜃 𝐶𝑦 = 𝐶𝑠𝑒𝑛𝜃

∑ 𝐹𝒙 = 𝐴𝒙 + 𝐵𝒙 + 𝐶𝑥 𝐹𝑅 = √𝐹𝑥2 + 𝐹𝑦2

⃗⃗⃗⃗⃗ = (𝑥2 − 𝑥1 , 𝑦2 − 𝑦1 ) 𝐴𝐵

∑ 𝐹𝒚 = 𝐴𝑦 + 𝐵𝑦 + 𝐶𝑦 ∑ 𝐹𝑦

; 𝜃 = tan−1 ∑ 𝐹

𝒙

𝑉1 ∙𝑉2 |𝑉2 |

TORQUE.

⃗ 𝒐 = 𝒓 ⋅ ⃗𝑭 (𝑵 ⋅ 𝒎) ⃗𝑭 = 𝝉

⃗𝒐 𝝉 𝒓

𝑖̂ 𝜏𝑜 = 𝑟𝑥𝐹 = | 𝑥 𝐹𝑥

;

𝐹1 = 𝑢𝑥 (𝐹1 𝑐𝑜𝑠𝜃) + 𝑢𝑦 (𝐹2 𝑠𝑒𝑛𝜃) 𝐹2 = 𝑢𝑥 (𝐹2 𝑐𝑜𝑠𝜃) + 𝑢𝑦 (𝐹2 𝑠𝑒𝑛𝜃) 𝐹3 = 𝑢𝑥 (𝐹3 𝑐𝑜𝑠𝜃) + 𝑢𝑦 (𝐹3 𝑠𝑒𝑛𝜃) 𝐹4 = 𝑢𝑥 (𝐹4 𝑐𝑜𝑠𝜃) + 𝑢𝑦 (𝐹4 𝑠𝑒𝑛𝜃) La magnitud 𝐹𝑅 𝑅 = √𝐹𝑥2 + 𝐹𝑦2

𝑐𝑜

angulo 𝑡𝑔𝜃 = 𝑐 𝑎𝑑𝑦

𝐹𝑦

𝜃 = 𝑡𝑔−1 𝐹

𝑥

𝑗̂ 𝑦 𝐹𝑦

𝑘̂ 𝑧| 𝐹𝑧