ANÁLISIS VECTORIAL
Sea 𝐴= 𝑨𝒙𝒊+𝑨𝒚𝒋+ 𝑨𝒛𝒌,
|𝑨|= √𝑨𝒙𝟐+𝑨𝒚𝟐+ 𝑨𝒛𝟐
𝟏=𝑪𝒐𝒔𝟐𝜶+ 𝑪𝒐𝒔𝟐𝜷+ 𝑪𝒐𝒔𝟐 𝜸
𝑪𝒐𝒔 ∝ = 𝑨𝒙
|𝑨
| 𝑪𝒐𝒔 𝜷 = 𝑨𝒚
|𝑨
| 𝑪𝒐𝒔 𝜸 = 𝑨𝒛
|𝑨
|
𝑨
𝑩
=|𝑨||𝑩| 𝑪𝒐𝒔 𝜽,
donde, 𝐴 𝐵
=𝐴𝑥𝐵𝑥+𝐴𝑦𝐵𝑦+𝐴𝑧𝐵𝑧
Si 𝑨
𝑩
=𝟎 ⇒ 𝑨
𝑩
𝑨
× 𝑩
=|𝑨||𝑩| 𝑺𝒆𝒏 𝜽
𝑨
× 𝑩
= | 𝒊𝒋𝒌
𝑨𝒙𝑨𝒚𝑨𝒛
𝑩𝒙𝑩𝒚𝑩𝒛|=
𝒊|𝑨𝒚𝑨𝒛
𝑩𝒚𝑩𝒛|− 𝒋 |𝑨𝒙𝑨𝒛
𝑩𝒙𝑩𝒛|+ 𝒌
|𝑨𝒙𝑨𝒚
𝑩𝒙𝑩𝒚|
DINÁMICA
∑𝑭=𝒎𝒂
𝒇𝒔,𝒌= 𝝁𝒔,𝒌 𝑵
𝑬𝑷=𝒎𝒈𝒉
𝑬𝒌=𝟏
𝟐𝒎𝒗𝟐
𝑾= 𝑭 𝒅 𝐜𝐨𝐬𝜽
𝑾=∆𝑬𝒌
𝑭= −𝒌𝒙
𝑾= 𝟏
𝟐 𝒌 𝒙𝟐
𝑬𝑷𝒐+ 𝑬𝑪𝒐+ 𝑾𝒐𝒕𝒓𝒂𝒔= 𝑬𝑷+ 𝑬𝑪
CINEMÁTICA
MRU
𝒙= 𝒙𝟎+ 𝒗𝟎𝒕
MRUA
𝒗= 𝒗𝟎+𝒂𝒕
𝒗𝟐= 𝒗𝟎𝟐+𝟐𝒂𝒙
𝒙= 𝒙𝟎+ 𝒗𝟎𝒕+ 𝟏
𝟐 𝒂𝒕𝟐
MC
𝒙=𝑹𝜽, 𝒗 =𝑹𝝎, 𝒂𝑻=𝑹𝜶
𝒂𝒄=𝒗𝟐
𝑹, 𝒇= 𝟏
𝑻, 𝑻=𝟐𝝅
𝝎
MCU
𝜽=𝜽𝟎 + 𝝎𝒕
MCUA
𝝎= 𝝎𝟎+ 𝜶𝒕
𝝎𝟐= 𝝎𝟎
𝟐+ 𝟐𝜶𝜽
𝜽=𝜽𝟎 + 𝝎𝟎 𝒕 + 𝟏
𝟐 𝜶 𝒕𝟐
FLUIDOS
𝝆=𝒎
𝑽
𝑷=𝑭
𝑨
𝑷𝒎𝒂𝒏 =𝝆𝒈𝒉
𝑭𝒃=𝝆𝒇𝒈 𝑽𝒅
𝑷𝒆𝒔𝒐=𝝆𝒐𝒃𝒋𝒈 𝑽𝒐𝒃𝒋
𝝆𝟏𝒗𝟏𝑨𝟏= 𝝆𝟐𝒗𝟐𝑨𝟐
𝒔𝒊 𝝆=𝒄𝒕𝒆 → 𝒗𝟏𝑨𝟏= 𝒗𝟐𝑨𝟐
𝑸= 𝒗𝑨
𝑷𝟏+𝟏
𝟐𝝆𝒗𝟏
𝟐+𝝆𝒈𝒉𝟏=𝑷𝟐+𝟏
𝟐𝝆𝒗𝟐
𝟐+𝝆𝒈𝒉𝟐
𝟏 𝒃𝒂𝒓=𝟏𝟎𝟎 𝟎𝟎𝟎 𝑷𝒂= 𝟎.𝟏 𝑴𝑷𝒂 =𝟏𝟎𝟎𝒌𝑷𝒂
𝟏 𝒂𝒕𝒎 =𝟏𝟎𝟏 𝟑𝟐𝟓 𝑷𝒂=𝟏.𝟎𝟏𝟑𝟐𝟓 𝒃𝒂𝒓 =𝟏𝟒.𝟔𝟗𝟔 𝒍𝒃𝒇
𝒊𝒏𝟐
𝟏 𝒌𝒈𝒇
𝒄𝒎𝟐=𝟗.𝟖𝟏 𝑵
𝒄𝒎𝟐=𝟗.𝟖𝟏 𝒙 𝟏𝟎𝟒𝑵
𝒎𝟐
𝟏 𝒎𝟑=𝟏𝟎𝟎𝟎 𝑳
𝝆𝒓𝒆𝒍=𝝆𝒇
𝝆𝒂𝒈𝒖𝒂
𝜸=𝝆𝒈
CHOQUES
𝒑=𝒎𝒗
𝒎𝟏𝒗𝟏𝒊+𝒎𝟐𝒗𝟐𝒊 =𝒎𝟏𝒗𝟏𝒇+𝒎𝟐𝒗𝟐𝒇
𝒆=𝒗𝟐𝒇−𝒗𝟏𝒇
𝒗𝟏𝒊−𝒗𝟐𝒊
𝟏
𝟐𝒎𝟏𝒗𝟏𝒊
𝟐+𝟏
𝟐𝒎𝟐𝒗𝟐𝒊
𝟐=𝟏
𝟐𝒎𝟏𝒗𝟏𝒇
𝟐+𝟏
𝟐𝒎𝟐𝒗𝟐𝒇
𝟐
∆𝒑=𝒎𝒗𝒇−𝒎𝒗𝒊
