Calculating Momentum and Radiation Pressure

문제)

A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this “solar sail.”

Suppose a sail of area A = 6.00 × 10^5 m^2 and mass m = 6.00 × 10^3 kg.

Ignore all gravitational effects and assume a solar intensity of 1370 W / m^2

 

(a) Calculate the force is exerted on the sail.

(b) Calculate the sail’s acceleration.

(c) Calculate the time interval required for the sail to reach the Moon, 3.84 × 10^8 m away, starting from rest at the Earth.

 

풀이)

sail of area A = 6.00 × 10^5 m^2

mass m = 6.00 × 10^3 kg

solar intensity I = 1370 W / m^2

 

(a)

Calculate the force is exerted on the sail.

Pressure P = I / c = 1370 W / m^2 / 3.00 × 10^8 m/s = 4.57 × 10^-6 N / m^2

Force F = P × A = 4.57 × 10^-6 N / m^2 × 6.00 × 10^5 m^2 = 2.74 N

 

(b)

Calculate the sail’s acceleration.

F = ma

2.74 N = 6.00 × 10^3 kg × a, a = 4.57 × 10^-4 m / s^2

 

(c)

Calculate the time interval required for the sail to reach the Moon, 3.84 × 10^8 m away, starting from rest at the Earth.

S = v0 × t + 1/2 × at^2

S = 4.57 × 10^-4 m / s^2 × t^2 × 1/2 = 3.84 × 10^8 m

t = √{ ( 2 × 3.84 × 10^8 m ) / (4.57 × 10^-4 m / s^2) } = 1.30 × 10^6 s