Question by Cynthia Gomez: ENGINEERING HELP NEEDED?
solar sails—large sheets of material that would work by reflecting photons. Since the momentum of the photon would be reversed, an impulse would be exerted on it by the solar sail, and—by Newton’s Third Law—an impulse would also be exerted on the sail, providing a force. In space near the Earth, about 3.84 x10^21 photons are incident per square meter per second. On average, the momentum of each photon is 1.30 x 10^-27 kg m/s. For a 1325-kg spaceship starting from rest and attached to a square sail 24 m wide. What is the speed of ship in 1s.
The answer from back of book says 4.333 x 10^ -6 but I keep getting 4.92 x 10^ -6. ANYHELP !!!!
Best answer:
Answer by normally laconic
Photons striking sail in 1 second =3.84e21 m^2/s * (24 m)^2 * 1s = 2.212e24
Their collective change in momentum, assuming that they are reflected back along their incident path, is twice the velocity (since it reverses direction), or
M = 2.212e24*2*1.3e-27 = 5.75e-3
For the ship, the change in momentum is the same, so
v = M / m = 5.75e-3 / (1.325e3) = 4.34e-6 m/s
I agree with the book!
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