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gibson:teaching:spring-2018:math445:lab11

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 gibson:teaching:spring-2018:math445:lab11 [2018/04/26 08:59]gibson gibson:teaching:spring-2018:math445:lab11 [2018/05/01 06:20]gibson Both sides previous revision Previous revision 2018/05/01 06:23 gibson 2018/05/01 06:20 gibson 2018/04/26 08:59 gibson 2018/04/26 05:57 gibson created 2018/05/01 06:23 gibson 2018/05/01 06:20 gibson 2018/04/26 08:59 gibson 2018/04/26 05:57 gibson created Last revision Both sides next revision Line 18: Line 18: $dy/dt = v_y$ $dy/dt = v_y$ - $dv_x/dt = -\frac{\mu}{m} v_x \sqrt{v_x^2 + v_y^2}$ ​ + $dv_x/dt = -\frac{\alpha}{m} v_x \sqrt{v_x^2 + v_y^2}$ ​ - $dv_y/dt = -\frac{\mu}{m} v_y \sqrt{v_x^2 + v_y^2} - g$ + $dv_y/dt = -\frac{\alpha}{m} v_y \sqrt{v_x^2 + v_y^2} - g$ - The constant $g = 9.81 m/s^2$ is the acceleration due to gravity. The constant $\mu = \rho_{air} C_D A/2$ in the air resistance term depends on physical characteristics of the projectile and the air. The following code will calculate $\mu$ for a standard baseball, given either value of $\rho_{air}$. + The constant $g = 9.81 m/s^2$ is the acceleration due to gravity. The constant $\alpha = \rho_{air} C_D A/2$ in the air resistance term depends on physical characteristics of the projectile and the air. The following code will calculate $\alpha$ for a standard baseball, given either value of $\rho_{air}$. <​code>​ <​code>​ Line 34: Line 34: m = 0.145; ​      % mass of baseball in kg (145 gm m = 0.145; ​      % mass of baseball in kg (145 gm - mu = rho_air*C_D*A/​2;​ % coefficient of nonlinear |v|^2 term, in mks units + alpha = rho_air*C_D*A/​2;​ % coefficient of nonlinear |v|^2 term, in mks units