A plane is in level flight at constant speed | vedclass

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(D) The total area of the two wings is $A = 2 	imes 40 \,m^2 = 80 \,m^2$.Convert the air speeds from $km/h$ to $m/s$:$V_1 = 180 \,km/h = 180 	imes \

Vedclass · Accepted Answer

$9600$

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(D) The total area of the two wings is $A = 2 	imes 40 \,m^2 = 80 \,m^2$.Convert the air speeds from $km/h$ to $m/s$:$V_1 = 180 \,km/h = 180 	imes \frac{5}{18} = 50 \,m/s$ (lower surface)$V_2 = 252 \,km/h = 252 	imes \frac{5}{18} = 70 \,m/s$ (upper surface)According to Bernoulli's principle,the pressure difference $\Delta P = P_1 - P_2$ between the lower and upper surfaces provides the lift force $F_L$:$F_L = (P_1 - P_2) A = \frac{1}{2} ho (V_2^2 - V_1^2) A$For level flight,the lift force must balance the weight of the plane:$mg = \frac{1}{2} ho (V_2^2 - V_1^2) A$Substitute the given values:$m 	imes 10 = \frac{1}{2} 	imes 1 	imes (70^2 - 50^2) 	imes 80$$10m = 40 	imes (4900 - 2500)$$10m = 40 	imes 2400$$10m = 96000$$m = 9600 \,kg$.

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