Question

One possible means of achieving space flight is to place a perfectly reflecting aluminized sheet into Earth

Answer 1

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One possible means of achieving space flight is to place a perfectly reflecting aluminized sheet into Earth 's orbit and to use the light from the Sun to push this solar sail. Suppose such a sail, of area 5.20 104 m2 and mass 6500 kg, is placed in orbit facing the Sun. Ignore all gravitational effects, and assume a solar intensity of 1340 W/m2.
(a) What force is exerted on the sail?
F = __?__ N

(b) What is the sail's acceleration?
a = __?__ m/s2

(c) How long does it take for this sail to reach the Moon, 3.84 108 m away?
t = __?__ days

Given:

      The area of the sail, A = 5.20x10⁴ m²

      The mass of the sail, m = 6500 kg

      The solar intensity, I = 1340 W/m²

      The speed of the light, c = 3x10⁸ m/s

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Solution:

a)

      The radiation pressure is

                     P = 2I/c

                        = (2)(1340 W/m²)/(3x10⁸ m/s)

                        = 893.33x10^-8 N/m²

      The force F realated with the The radiation pressure P is

                     F = PA

                         = (893.33x10^-8 N/m²)(5.20x10⁴ m²)

                         = 0.46453 N

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b)

      According to Newton's second law of motion, the force

      can be deffined as

                       F = ma
      Therefore, the acceleration of the sail's is

                        a = F/m

                           = (0.46453 N)/(6500 kg)

                           = 7.1467x10^-5 m/s²

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c)

      The distance, s = 3.84x10⁸ m

      Using the kinematic relation,

                           s = ut + (1/2)at²    

                           s = 0 + (1/2)at²  

      Therefore, the time taken by the sail to reach the moon is

                           t = ?2s/a

                              = ?(2)(3.84x10⁸ m)/(7.1467x10^-5 m/s²)

                              = 3278150.188 s

                              = (3278150.188 s)(1 day/86400 s)

                              = 37.94 days

                              = 38.00 days (nearly)