Question

Sunlight above the Earth's atmosphere has an intensity of 1.40 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 0.116 kg. Find the acceleration (in m/s2) of the spaceship if all other forces are balanced. ____m/s2

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

Answer 1

(a) The momentum of photon is, 2E P= с (2)(1.40x109) 3x108 =9.33x10 kg-m/sm? The force per square meter is, F = 4p At 9.33x10-6 1.0 = 9.33x100 N/m (b) The force is, F = ma The acceleration is, F a=— m 9.33x10-6 0.116 = 8.0x10-5 m/s2 (c) The time is. t=24 hr =(24)(3600) = 86400 S Using equation v=U + at V=0+ +(8.0x10-^)(86400) = 6.91 m/s