This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
ScanSolve AI Answer
Here is the solution to the physics problem. Given data: • Satellite mass, m = 60 kg • Orbital radius, r = 3R, where R is the mean radius of the Earth • Gravitational field strength at Earth's surface, g = 9.8 N/kg • Mean radius of the Earth, R = 6400 km = 6.4 × 10^6 m a) Calculate the centripetal force acting on the satellite. The centripetal force required to keep the satellite in orbit is provided by the gravitational force between the Earth and the satellite. The gravitational force F_g is given by Newton's Law of Universal Gravitation: F_g = (G M m)/(r^2) where G is the gravitational constant and M is the mass of the Earth. The gravitational field strength at the Earth's surface is g = (G M)/(R^2). From this, we can deduce that G M = g R^2. Step 1: Substitute G M into the gravitational force equation. The centripetal force F_c is equal to the gravitational force F_g: F_c = ((g R^2) m)/(r^2) Step 2: Substitute the orbital radius r = 3R. Since r = 3R, then r^2 = (3R)^2 = 9R^2. F_c = (g R^2 m)/(9R^2) Step 3: Simplify the expression and calculate the centripetal force. The R^2 terms cancel out: F_c = (g m)/(9) F_c = 9.8 N/kg × 60 kg9 F_c = (588)/(9) N F_c = 65.33 N b) Calculate the period of the satellite in orbit. The centripetal force can also be expressed in terms of the satellite's mass m, its orbital speed v, and the orbital radius r: F_c = (m v^2)/(r) The orbital speed v is related to the period T by the relation v = (2 r)/(T). Step 1: Substitute the expression for v into the centripetal force equation. F_c = (m (2 r)/(T))^2r = (m (4 ^2 r^2 / T^2))/(r) = (4 ^2 m r)/(T^2) Step 2: Equate the two expressions for centripetal force (F_c = (g m)/(9) and F_c = (4 ^2 m r)/(T^2)). (4 ^2 m r)/(T^2) = (g m)/(9) We can cancel m from both sides: (4 ^2 r)/(T^2) = (g)/(9) Step 3: Solve the equation for T^2. T^2 = (4 ^2 r × 9)/(g) = (36 ^2 r)/(g) Step 4: Substitute r = 3R into the expression for T^2. T^2 = (36 ^2 (3R))/(g) = (108 ^2 R)/(g) Step 5: Calculate the period T. T = sqrt((108 ^2 R)/(g)) = sqrt((108 R)/(g)) Using R = 6.4 × 10^6 m and g = 9.8 m/s^2: T = sqrt(108 × 6.4 × 10^6 m)9.8 m/s^2 T = sqrt((691.2 × 10^6)/(9.8)) T = sqrt(70530612.24) T ≈ 3.14159 × 8398.25 T ≈ 26384.80 s 3 done, 2 left today. You're making progress.