Aluminized mylar film is a highly reflective, lightweight material that could be

Question

Aluminized mylar film is a highly reflective, lightweight material that could be used to make sails for spacecraft driven by the light of the sun. Suppose a sail with area 1.10 km^2 is orbiting the Sun at a distance o1.52E+11 m. The sail has a mass of 4.90E+03 kg and is tethered to a payload of mass 2.11E+04 kg.
(a) If the intensity of the sunlight is 1.34E+01 W/m^2 and the sail is oriented perpendicular to the incident light, what radial force is exerted on the sail? (N)

(b) About how long would it take to change the radial speed of the sail by 1.00 km/s? Assume that the sail is perfectly reflecting. (s)

(c) Suppose the light were supplied by a large , powerful laser beam instead of the Sun. (Such systems have been proposed.) Calculate the peak electric and magnetic fields of the laser light.

Emax = (N/C)
Bmax = (T)

A laser has a power of 23.8 W and a beam radius of 0.451 mm.
(a) Find the intensity of the laser. (W/m^2)

(b) Suppose you were floating in space and pointed the laser beam away from you. What would your acceleration be? Assume your total mass, including equipment, is 73.0 kg and that the force is directed through your center of mass. Hint: The change in momentum is the same as in the nonreflective case.
(m/s^2)

(c) Calculate your acceleration if it were due to the gravity of a space station with mass 1.14E+06 kg and center of mass 109.3 m away. (m/s^2)

(d) Calculate the peak electric and magnetic fields of the laser.

Emax = (N/C)
Bmax = (T)

If you were planning to use your laser welding torch as a thruster to get you back to the station, don't bother because the force of gravity is stronger. Better yet, get somebody to toss you a line. Aluminized mylar film is a highly reflective, lightweight material that could be used to make sails for spacecraft driven by the light of the sun. Suppose a sail with area 1.10 km^2 is orbiting the Sun at a distance o1.52E+11 m. The sail has a mass of 4.90E+03 kg and is tethered to a payload of mass 2.11E+04 kg.
(a) If the intensity of the sunlight is 1.34E+01 W/m^2 and the sail is oriented perpendicular to the incident light, what radial force is exerted on the sail? (N)

(b) About how long would it take to change the radial speed of the sail by 1.00 km/s? Assume that the sail is perfectly reflecting. (s)

(c) Suppose the light were supplied by a large , powerful laser beam instead of the Sun. (Such systems have been proposed.) Calculate the peak electric and magnetic fields of the laser light.

Emax = (N/C)
Bmax = (T)

A laser has a power of 23.8 W and a beam radius of 0.451 mm.
(a) Find the intensity of the laser. (W/m^2)

(b) Suppose you were floating in space and pointed the laser beam away from you. What would your acceleration be? Assume your total mass, including equipment, is 73.0 kg and that the force is directed through your center of mass. Hint: The change in momentum is the same as in the nonreflective case.
(m/s^2)

(c) Calculate your acceleration if it were due to the gravity of a space station with mass 1.14E+06 kg and center of mass 109.3 m away. (m/s^2)

(d) Calculate the peak electric and magnetic fields of the laser.

Emax = (N/C)
Bmax = (T)

If you were planning to use your laser welding torch as a thruster to get you back to the station, don't bother because the force of gravity is stronger. Better yet, get somebody to toss you a line.
(a) If the intensity of the sunlight is 1.34E+01 W/m^2 and the sail is oriented perpendicular to the incident light, what radial force is exerted on the sail? (N)

(b) About how long would it take to change the radial speed of the sail by 1.00 km/s? Assume that the sail is perfectly reflecting. (s)

(c) Suppose the light were supplied by a large , powerful laser beam instead of the Sun. (Such systems have been proposed.) Calculate the peak electric and magnetic fields of the laser light.

Emax = (N/C)
Bmax = (T)

A laser has a power of 23.8 W and a beam radius of 0.451 mm.
(a) Find the intensity of the laser. (W/m^2)

(b) Suppose you were floating in space and pointed the laser beam away from you. What would your acceleration be? Assume your total mass, including equipment, is 73.0 kg and that the force is directed through your center of mass. Hint: The change in momentum is the same as in the nonreflective case.
(m/s^2)

(c) Calculate your acceleration if it were due to the gravity of a space station with mass 1.14E+06 kg and center of mass 109.3 m away. (m/s^2)

(d) Calculate the peak electric and magnetic fields of the laser.

Emax = (N/C)
Bmax = (T)

If you were planning to use your laser welding torch as a thruster to get you back to the station, don't bother because the force of gravity is stronger. Better yet, get somebody to toss you a line.
(a) Find the intensity of the laser. (W/m^2)

(b) Suppose you were floating in space and pointed the laser beam away from you. What would your acceleration be? Assume your total mass, including equipment, is 73.0 kg and that the force is directed through your center of mass. Hint: The change in momentum is the same as in the nonreflective case.
(m/s^2)

(c) Calculate your acceleration if it were due to the gravity of a space station with mass 1.14E+06 kg and center of mass 109.3 m away. (m/s^2)

(d) Calculate the peak electric and magnetic fields of the laser.

Emax = (N/C)
Bmax = (T)

If you were planning to use your laser welding torch as a thruster to get you back to the station, don't bother because the force of gravity is stronger. Better yet, get somebody to toss you a line.

Explanation / Answer

sol: suppose that, so, we get, B. Since you know I(ave), you save a step. I(peak) = 2I(ave) E = sqrt(I(peak)*Z0) C. H = sqrt(I(peak)/Z0) and B = µ0*H D. Ave. energy density = I(ave)/c J/m^3, where c = velocity of light. Note: Free-space impedance Z0 = sqrt(µ0/e0) = 376.7303 O; µ0 = 4p*1E-7 = 1.256637E-6 N/A^2; e0 = 8.854188E-12 F/M answer

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