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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

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Educational Text: Solar Sail Space Flight** A possible means of space flight involves deploying a perfectly reflecting aluminized sheet, known as a "solar sail," into orbit around Earth. This sail utilizes sunlight for propulsion. Suppose a solar sail with an area \( A = 6.30 \times 10^5 \, \text{m}^2 \) and a mass \( m = 7200 \, \text{kg} \) is oriented to face the Sun. For simplicity, ignore all gravitational effects and assume a solar intensity of \( 1370 \, \text{W/m}^2 \). **Problem Analysis:** **(a) Force Exerted on the Sail:** - **Question:** What force (in N) is exerted on the sail? (Enter the magnitude.) - **Prompt:** Consider the intensity of the light and the concept of radiation pressure. **(b) Sail's Acceleration:** - **Question:** What is the sail's acceleration? (Enter the magnitude in \(\mu\text{m/s}^2\).) - **Prompt:** Use the net force from part (a) and the mass of the sail. **(c) Time to Reach the Moon:** - **Question:** Assuming the acceleration remains constant, find the time interval (in days) needed for the sail to reach the Moon, which is \( 3.84 \times 10^8 \, \text{m} \) away, starting from rest at Earth. - **Prompt:** Review methods for solving constant acceleration problems. **(d) Gravitational Field Analysis:** - **Scenario:** Determine if a solar sail initially in Earth orbit at an altitude of \( 400 \, \text{km} \) could escape Earth’s gravity, regardless of size. - **Result:** Calculated gravitational field is \( 8.64 \, \text{m/s}^2 \). **(e) Solar Sail Mass Density:** - **Question:** What must the mass density (in \(\text{kg/m}^2\)) of the solar sail be to achieve the same initial acceleration as in part (b)? - **Prompt:** Solve for the required mass density using previous calculations. This exercise involves applying concepts of physics, such as force, acceleration, and gravitational fields, to innovative space travel methods.
Transcribed Image Text:**Educational Text: Solar Sail Space Flight** A possible means of space flight involves deploying a perfectly reflecting aluminized sheet, known as a "solar sail," into orbit around Earth. This sail utilizes sunlight for propulsion. Suppose a solar sail with an area \( A = 6.30 \times 10^5 \, \text{m}^2 \) and a mass \( m = 7200 \, \text{kg} \) is oriented to face the Sun. For simplicity, ignore all gravitational effects and assume a solar intensity of \( 1370 \, \text{W/m}^2 \). **Problem Analysis:** **(a) Force Exerted on the Sail:** - **Question:** What force (in N) is exerted on the sail? (Enter the magnitude.) - **Prompt:** Consider the intensity of the light and the concept of radiation pressure. **(b) Sail's Acceleration:** - **Question:** What is the sail's acceleration? (Enter the magnitude in \(\mu\text{m/s}^2\).) - **Prompt:** Use the net force from part (a) and the mass of the sail. **(c) Time to Reach the Moon:** - **Question:** Assuming the acceleration remains constant, find the time interval (in days) needed for the sail to reach the Moon, which is \( 3.84 \times 10^8 \, \text{m} \) away, starting from rest at Earth. - **Prompt:** Review methods for solving constant acceleration problems. **(d) Gravitational Field Analysis:** - **Scenario:** Determine if a solar sail initially in Earth orbit at an altitude of \( 400 \, \text{km} \) could escape Earth’s gravity, regardless of size. - **Result:** Calculated gravitational field is \( 8.64 \, \text{m/s}^2 \). **(e) Solar Sail Mass Density:** - **Question:** What must the mass density (in \(\text{kg/m}^2\)) of the solar sail be to achieve the same initial acceleration as in part (b)? - **Prompt:** Solve for the required mass density using previous calculations. This exercise involves applying concepts of physics, such as force, acceleration, and gravitational fields, to innovative space travel methods.
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