Exercícios - Incerteza Padrão - Cálculo Diferencial e Integral 2 - 2023-2

Desenvolve a expressão para a incerteza padrão relativa para os seguintes fenômenos físicos: a) \quad D = f(m,l,d) = \frac{4 \cdot m}{l \cdot \pi \cdot d^2}\ ; b) \quad V = f(V_1,V_2) = V_1 - V_2\ ; D = \frac{4m}{l \cdot \pi \cdot d^2} \Delta D = \left(\frac{\partial D}{\partial l}\right) dl + \left(\frac{\partial D}{\partial d}\right) dd + \left(\frac{\partial D}{\partial m}\right) dm \Delta D = \frac{4m}{l^2 \pi d^2} \Delta l + \frac{4m}{l \cdot \pi} \left(-\frac{2}{d^3}\right) \Delta d + \frac{4}{l \pi d^2} \Delta m \frac{\Delta D}{D} = \left(\frac{4m}{l^2 \pi d^2 \cdot \frac{l \pi d^2}{4m}}\right) \Delta l + \left(\frac{8m}{l \pi d^3 \cdot \frac{l \pi d^2}{4m}}\right) \Delta d + \left(\frac{4}{l \pi d^2 \cdot \frac{l \pi d^2}{4m}}\right) \Delta m \frac{\Delta D}{D} = \frac{\Delta l}{l} + \frac{2 \Delta d}{d} + \frac{\Delta m}{m} . \Delta V = \left(\frac{\partial V}{\partial V_1}\right) \Delta V_1 + \left(\frac{\partial V}{\partial V_2}\right) \Delta V_2 \Delta V = 1 \cdot \Delta V_1 + ( -1 ) \Delta V_2 \boxed{\Delta V = \Delta V_1 + \Delta V_2}