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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?

Respuesta :

davidlcastiblanco

Answer:

[tex]v_f=0.408m/s[/tex]

Explanation:

The radiation pressure creates a force on the block

[tex]F_r=_{pr}A[/tex]

Where A is the area of the beam so using the force the creates can determinate the acceleration

[tex]F=m*a[/tex]

[tex]a=\frac{Fr}{m}=\frac{_{pr}A}{m}[/tex]

The acceleration is constant so can find the velocity using the equation for a uniform motion, also that the force can be the power of the laser plugging in the number so:

[tex]_{pr}A=\frac{P}{c}=\frac{25.0MW}{3x10^8}[/tex]

[tex]v_f^2=v_i^2+2*a*x_t[/tex]

The initial velocity is zero:

[tex]v_f^2=2*a*x_t[/tex]

[tex]v_f=\sqrt{2*a*x_t}[/tex]

replacing a'

[tex]v_f=\sqrt{\frac{2*P*x_t}{m*c}}[/tex]

[tex]v_f=\sqrt{\frac{2*25x10^6W*100m}{100kg*(3x10^8)}}[/tex]

[tex]v_f=\sqrt{0.166 m^2/s^2}=0.408m/s[/tex]

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