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A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this "solar sail." Suppose a sail of area A = 6.30 x 105 m² and mass m = 7,200 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1,370 W/m². (a) What force (in N) is exerted on the sail? (Enter the magnitude.) If you know the intensity in a beam of light, how do you determine the radiation pressure? N (b) What is the sail's acceleration? (Enter the magnitude in µm/s².) X If you know the net force from part (a) and the mass from the problem statement, how do you find the acceleration? μm/s² (c) Assuming the acceleration calculated in part (b) remains constant, find the time interval (in days) required for the sail to reach the Moon, 3.84 x 108 m away, starting from rest at the Earth. X This is a constant acceleration situation. It might be a good opportunity to review solution methods for problems involving constant acceleration. days (d) If the solar sail were initially in Earth orbit at an altitude of 400 km, show that a sail of this mass density could not escape Earth's gravitational pull regardless of size. (Calculate the magnitude of the gravitational field in m/s².) 8.64 m/s² (e) What would the mass density (in kg/m²) of the solar sail have to be for the solar sail to attain the same initial acceleration as that in part (b)? x kg/m²

A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this "solar sail." Suppose a sail of area A = 6.30 x 105 m² and mass m = 7,200 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1,370 W/m². (a) What force (in N) is exerted on the sail? (Enter the magnitude.) If you know the intensity in a beam of light, how do you determine the radiation pressure? N (b) What is the sail's acceleration? (Enter the magnitude in µm/s².) X If you know the net force from part (a) and the mass from the problem statement, how do you find the acceleration? μm/s² (c) Assuming the acceleration calculated in part (b) remains constant, find the time interval (in days) required for the sail to reach the Moon, 3.84 x 108 m away, starting from rest at the Earth. X This is a constant acceleration situation. It might be a good opportunity to review solution methods for problems involving constant acceleration. days (d) If the solar sail were initially in Earth orbit at an altitude of 400 km, show that a sail of this mass density could not escape Earth's gravitational pull regardless of size. (Calculate the magnitude of the gravitational field in m/s².) 8.64 m/s² (e) What would the mass density (in kg/m²) of the solar sail have to be for the solar sail to attain the same initial acceleration as that in part (b)? x kg/m²

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter24: Electromagnetic Waves
Section: Chapter Questions
Problem 32P
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A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this "solar sail." Suppose a sail of area A = 6.30 x 105 m² and mass m = 7,200 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1,370 W/m². (a) What force (in N) is exerted on the sail? (Enter the magnitude.) X If you know the intensity in a beam of light, how do you determine the radiation pressure? N (b) What is the sail's acceleration? (Enter the magnitude in µm/s².) If you know the net force from part (a) and the mass from the problem statement, how do you find the acceleration? μm/s² (c) Assuming the acceleration calculated in part (b) remains constant, find the time interval (in days) required for the sail to reach the Moon, 3.84 × 108 m away, starting from rest at the Earth. X This is a constant acceleration situation. It might be a good opportunity to review solution methods for problems involving constant acceleration. days (d) If the solar sail were initially in Earth orbit at an altitude of 400 km, show that a sail of this mass density could not escape Earth's gravitational pull regardless of size. (Calculate the magnitude of the gravitational field in m/s².) 8.64 m/s² (e) What would the mass density (in kg/m²) of the solar sail have to be for the solar sail to attain the same initial acceleration as that in part (b)? X kg/m²
Transcribed Image Text:A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this "solar sail." Suppose a sail of area A = 6.30 x 105 m² and mass m = 7,200 kg is placed in orbit facing the Sun. Ignore all gravitational effects and assume a solar intensity of 1,370 W/m². (a) What force (in N) is exerted on the sail? (Enter the magnitude.) X If you know the intensity in a beam of light, how do you determine the radiation pressure? N (b) What is the sail's acceleration? (Enter the magnitude in µm/s².) If you know the net force from part (a) and the mass from the problem statement, how do you find the acceleration? μm/s² (c) Assuming the acceleration calculated in part (b) remains constant, find the time interval (in days) required for the sail to reach the Moon, 3.84 × 108 m away, starting from rest at the Earth. X This is a constant acceleration situation. It might be a good opportunity to review solution methods for problems involving constant acceleration. days (d) If the solar sail were initially in Earth orbit at an altitude of 400 km, show that a sail of this mass density could not escape Earth's gravitational pull regardless of size. (Calculate the magnitude of the gravitational field in m/s².) 8.64 m/s² (e) What would the mass density (in kg/m²) of the solar sail have to be for the solar sail to attain the same initial acceleration as that in part (b)? X kg/m²
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