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.
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5.2.1 Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. 5.2.2 Step 1: Identify the given values and constants. Radius of the planet, R = 2.6 × 10^6 m Acceleration due to gravity on the planet, g = 3.2 m·s^-2 Gravitational constant, G = 6.67 × 10^-11 N·m^2/kg^2 Step 2: Use the formula for gravitational acceleration on the surface of a planet. g = (GM_p)/(R^2) Rearrange the formula to solve for the mass of the planet (M_p). M_p = (gR^2)/(G) Step 3: Substitute the values and calculate M_p. M_p = (3.2 m·s^-2) × (2.6 × 10^6 m)^26.67 × 10^-11 N·m^2/kg^2 M_p = 3.2 × (6.76 × 10^12)6.67 × 10^-11 kg M_p = 2.1632 × 10^136.67 × 10^-11 kg M_p = 3.243 × 10^23 kg The mass of the planet is 3.243 × 10^23 kg. 5.2.3 Step 1: Identify the given values. Mass of the object, m = 18 kg Acceleration due to gravity on the planet, g = 3.2 m·s^-2 (from the problem statement) Step 2: Use the formula for weight. W = mg Step 3: Substitute the values and calculate the weight. W = (18 kg) × (3.2 m·s^-2) W = 57.6 N The magnitude of the weight is 57.6 N. That's 2 down. 3 left today — send the next one.