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
Welcome back — missed you this week. 5.1 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 The displacement vector represents the change in position from the starting point to the current point. Assuming the parachutist is falling downwards towards the Earth, the displacement vector will point vertically downwards. 5.3 Step 1: Identify the given values and constants. Mass of parachutist, m_1 = 60 kg Height above Earth's surface, h = 3630 m Radius of Earth, R = 6371 km = 6371 × 10^3 m Gravitational constant, G = 6.67 × 10^-11 N·m^2/kg^2 Mass of Earth, M_2 = 5.972 × 10^24 kg Step 2: Calculate the total distance from the center of the Earth to the parachutist. r = R + h r = 6371 × 10^3 m + 3630 m r = 6371000 m + 3630 m r = 6374630 m Step 3: Apply Newton's Law of Universal Gravitation formula. F = (G m_1 M_2)/(r^2) F = (6.67 × 10^-11 N·m^2/kg^2) × (60 kg) × (5.972 × 10^24 kg)(6374630 m)^2 F = 2.3888 × 10^16 N·m^24.0636 × 10^13 m^2 F = 587.86 N The magnitude of the gravitational force is 587.86 N. 5.4.1 The weight of the parachutist when wearing suit A compared to suit B is EQUAL TO. The problem states that the suits are of equal mass and the combined mass of the parachutist and suit is 60 kg for both. Weight depends only on mass and gravitational acceleration, which are the same in both cases. 5.4.2 He would hit the earth first with suit A. Suit A experiences a very small frictional force, meaning less air resistance. Less air resistance results in a greater net downward force and thus a greater acceleration, causing him to reach the ground faster. 5.4.3 Yes, the mass of the parachutist affects his acceleration when wearing suit A. Reason: The net force acting on the parachutist is the gravitational force minus the air friction. Equation: F_net = ma mg - F_friction = ma a = g - F_frictionm Since the air friction (F_friction) is not directly proportional to the mass (m) in the same way gravity is, a change in mass will alter the acceleration. For a given air friction, a larger mass will experience a smaller reduction in acceleration from g. 5.4.4 The gravitational acceleration will be SMALLER THAN. Explanation: Gravitational acceleration (g) is inversely proportional to the square of the distance from the center of the Earth. Equation: g = (GM)/(r^2) Where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth. When jumping from 10 000 m, the distance r from the center of the Earth is greater than when jumping from 3 630 m (R + 10000 m > R + 3630 m). Since g is inversely proportional to r^2, a larger r results in a smaller g. Send me the next one 📸