This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Hey captain, good to see you again. To find the center of gravity (CG) location of the loaded aeroplane in MAC%, we need to calculate the total mass, total moment, the overall CG in inches, and then convert it to a percentage of the Mean Aerodynamic Chord (MAC). Step 1: Calculate the moment for each component. The moment is calculated as mass multiplied by its arm (station). Basic Empty Mass (BEM) moment: M_1 = 1000 kg × 92 inches = 92000 kg-inches Pilot's mass moment: M_2 = 80 kg × 100 inches = 8000 kg-inches Fuel mass moment: M_3 = 120 kg × 130 inches = 15600 kg-inches Step 2: Calculate the total mass of the loaded aeroplane. Total Mass = 1000 kg + 80 kg + 120 kg = 1200 kg Step 3: Calculate the total moment of the loaded aeroplane. Total Moment = 92000 kg-inches + 8000 kg-inches + 15600 kg-inches = 115600 kg-inches Step 4: Calculate the overall Center of Gravity (CG) in inches. CG_inches = Total MomentTotal Mass = 115600 kg-inches1200 kg = 96.333... inches Step 5: Convert the CG location to a percentage of MAC. The 0% MAC is at station 80 inches, and the length of the MAC is 60 inches. CG_\%MAC = CG_inches - Station of 0% MACLength of MAC × 100\% CG_\%MAC = 96.333... inches - 80 inches60 inches × 100\% CG_\%MAC = (16.333...)/(60) × 100\% CG_\%MAC = 0.27222... × 100\% CG_\%MAC ≈ 27.2\% Comparing this to the given options, the closest answer is D. The final answer is D) 27.2% MAC. Send me the next one 📸