Sunlight above the Earth\'s atmosphere has an intensity of 1.36 kW/m 2 . If this

Question

Sunlight above the Earth's atmosphere has an intensity of 1.36 kW/m2. If this is reflected straight back from a mirror that has only a small recoil, the light's momentum is exactly reversed, giving the mirror twice the incident momentum.

a) Calculate the force per square meter of mirror (in N/m2).

b) Very low mass mirrors can be constructed in the near weightlessness of space, and attached to a spaceship to sail it. Once done, the average mass per square meter of the spaceship is 0.147 kg. Find the acceleration (in m/s2) of the spaceship if all other forces are balanced.

c) How fast (in m/s) is it moving 24 hours later? (Assume the spaceship started from rest.)

Explanation / Answer

Force Due to total reflection is

F = 2 IA/C

where A is area and C is speed of light

so

Force/area = F/A = 2I/c

F/A = 2 * 1360 /(3*10^8)

F/A = 9.06 *10^-6 N/m^2

----------------------------

part B:

since Force F = m a

F/A = (m/A)* a

a = 9.06 * 10^-6/(0.147)

a = 6.16 *10^-5 m/s^2

------------------------

part C:

use Velocity V = u + a t

so

V = 0 + (6.16 *10^-5 * 24* 60 * 60)

V = 5.322 m/s

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