Answer:
(a) F = 6.14 *10⁻⁴ N
(b) P = 6.14* 10⁻¹⁰ Pa
(c) t = 27.2 min
Explanation:
Area of sail A = 1.0 km² = 1.0 * 10⁶m²
Wavelength of light λ = 650 nm = 650 * 10⁻⁹ m
Rate of impact of photons R = 1 mol/s = 6.022 * 10²³ photons/s
(a)
Momentum of each photon is Ρ = h/λ = 6.625 * 10⁻³⁴ / 650 * 10⁻⁹
= 1.0192 * 10⁻²⁷ kg.m/s
Since the photons are absorbed completely, in every collision the above momentum is transferred to the sail.
Momentum transferred to the sail per second is product of rate of impact of photons and momentum transferred by each photon.
dp/dt = R * h/
λ
This is the force acting on the sail.
F = R * h/λ = 6.022 * 10²³ * 1.0192 * 10⁻²⁷ = 6.14 *10⁻⁴ N
F = 6.14 *10⁻⁴ N
b)
Pressure exerted by the radiation on the sail = Force acting on the sail / Area of the sail
P = F/A = 6.14 * 10⁻⁴ / 1.0 * 10⁶ = 6.14* 10⁻¹⁰ Pa
P = 6.14* 10⁻¹⁰ Pa
c)
Acceleration of spacecraft a = F/m = 6.14 * 10⁻⁴ /1.0 = 6.14 * 10⁻⁴m/s²
As the spacecraft starts from rest, initial speed u=0,m/s ,
final speed is u = 1.0 m/s after time t
v = u+at
t = 1.0 - 0/ 6.14 * 10⁻⁴ = 1629s = 27.2 min
t = 27.2 min
