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
Step 1: Identify the formula for free fall acceleration. The free fall acceleration g on the surface of a celestial body is given by the formula: g = (GM)/(R^2) where G is the gravitational constant, M is the mass of the celestial body, and R is its radius. Step 2: List the given values and the gravitational constant. • Mass of the moon, M = 7.40 × 10^22 kg • Radius of the moon, R = 1.76 × 10^6 m • Gravitational constant, G = 6.674 × 10^-11 N · m^2/kg^2 Step 3: Substitute the values into the formula. g = (6.674 × 10^-11 N · m^2/kg^2) × (7.40 × 10^22 kg)(1.76 × 10^6 m)^2 Step 4: Calculate the square of the radius. (1.76 × 10^6 m)^2 = (1.76)^2 × (10^6)^2 m^2 = 3.0976 × 10^12 m^2 Step 5: Perform the multiplication in the numerator. (6.674 × 10^-11) × (7.40 × 10^22) = (6.674 × 7.40) × (10^-11 × 10^22) = 49.3876 × 10^11 N · m^2/kg Step 6: Divide the numerator by the squared radius. g = 49.3876 × 10^11 N · m^2/kg3.0976 × 10^12 m^2 g = (49.3876)/(3.0976) × 10^1110^12 m/s^2 g ≈ 15.943 × 10^-1 m/s^2 g ≈ 1.5943 m/s^2 The free fall acceleration on the surface of the moon is approximately: 1.59 m/s^2 Send me the next one 📸