Consider a space sail such as mentioned in Example 29.5. Construct a problem in which you calculate the light pressure on the sail in N/m² produced by reflecting sunlight. Also calculate the force that could be produced and how much effect that would have on a spacecraft. Among the things to be considered are the intensity of sunlight, its average wavelength, the number of photons per square meter this implies, the area of the space sail, and the mass of the system being accelerated.

Data from Example 29.5

(a) Calculate the momentum of a visible photon that has a wavelength of 500 nm.

(b) Find the velocity of an electron having the same momentum. 

(c) What is the energy of the electron, and how does it compare with the energy of the photon?

Strategy

Finding the photon momentum is a straightforward application of its definition: p = h/λ . If we find the photon momentum is small, then we can assume that an electron with the same momentum will be nonrelativistic, making it easy to find its velocity and kinetic energy from the classical formulas.