Please provide answers One propulsion method that is currently being studied for

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Please provide answers

One propulsion method that is currently being studied for interstellar travel uses a large sail. The intent is that sunlight striking the sail will create a force that pushes the ship away from the sun (see figure), much as the wind propels a sailboat. Some scientists have suggested that spacecraft with sails of the kind described above could be propelled by lasers. Suppose that such a sail is constructed of a highly reflective material thin enough so that one square meter of the sail has a mass of just 2.70 10-3 kg. The sail is to be propelled by an ultraviolet laser beam (wavelength = 244 nm) that will strike its surface perpendicularly. (a) Use the impulse-momentum theorem to determine the number of photons per second that must strike each square meter of the sail in order to cause an acceleration of 9.80 10-6 m/s2, which is one million times smaller than the gravitational acceleration at the earth's surface. Assume that no other forces act on the sail, and that all the incident photons are reflected. photons (b) Determine the intensity (power per unit area) that the laser beam must have when it strikes the sail. W/m2 Please provide answers

Explanation / Answer

a.)

p = h/
p = 6.62607095e-34 J*s / 244nm
p = 6.62607095e-34 J*s / 2.44e-7m =2.7156e-27 m*kg/s

p final is in opposite direction
p = pi - pf

pf = -pi

p = 2*pi = 2 * 2.7156e-27 m*kg/s

p = 5.4312e-27 m*kg/s per photon

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Momentum required to cause acceleration of 9.80e-6 m/s^2

p = Ft = m*a*t

m = .0027 kg/m^2

p = .0027 kg/m^2 * 9.80e-6 m/s^2 * t

p/sec = 2.646e-8 m*kg/s per second per square meter

2.646e-8 m*kg/s*s*m^2 / 5.4312e-27 m*kg/s*photons = 4.8718512e18 photons / s -m^2

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energy is equal to p*v = 5.4312e-27 m*kg/s per photon * (Speed of light)

E = 1.6282328 × 10-18 kg*m^2 / s^2 per photon

Power = E/t

Power = E per photon * Number of Photons per second

Intensity = Power per m^2

Intensity = 1.6282328 × 10-18 kg*m^2 / s^2 per photon * 4.8718512e18 photons / s -m^2

Intensity = 7.932W/m^2

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