Question

You've recently read about a chemical laser that generates a 20-cm-diameter, 25.0 MW laser beam. One day, after physics class, you start to wonder if you could use the radiation pressure from this laser beam to launch small payloads into orbit. To see if this might be feasible, you do a quick calculation of the acceleration of a 20-cm-diameter,
100 kg,perfectly absorbing block. What speed would such a block have if pushed horizontally 100 m along a frictionless track by such a laser?

Answer 1

Answer:

0.408m/s

Explanation:

To develop this problem it is necessary to take into account the concepts related to the radiation pressure applied by an electromagnetic wave on a surface of perfect absorption. Radiation pressure can be viewed as a consequence of the conservation of momentum given the momentum attributed to electromagnetic radiation. According to Maxwell's theory of electromagnetism, an electromagnetic wave carries momentum, which will be transferred to an opaque surface it strikes.

The pressure is experienced as radiation pressure on the surface:

$P= \frac{I}{c}$

Where,

P = Pressure

I = Incident irrandiance

c= Speed of light in vacuum

For definition we know that Incident irradiance is defined as,

$I = \frac{\dot{P}}{A}$

Where $\dot{P}$ is the Power required and A the area (For a circle in this case)

Then replacing,

$P = \frac{\dot{P}}{Ac}$

$P = \frac{\dot{P}}{\pi r^2 c}$

Substituting our values we have,

$P = \frac{25*10^6}{\pi (0.2/2)^2 (3*10^8)}$

$P = 2.652N/m^2$

With the pressure we can now calculate the Force and the Acceleration to find finally the velocity, that is

$F = PA$

$F = 2.652*\pi*(\frac{0.2}{2})^2$

$F = 0.083N$

The acceleration then would be expressed as indicate the Second Newton's Law

$a = \frac{F}{m}$

$a = \frac{0.083}{100}$

$a = 8.33*10^{-4}m/s^2$

The velocity is:

$v = \sqrt{2ad}$

$v = \sqrt{2*8.33*10^{-4}*100}$

$v = 0.408m/s$

Therefore the speed would such a block have if pushed horizontally 100m along a frictionless track by such a laser is 0.408m/s