A pulsed laser fires a `1000 MW` pulse that has a `200 ns` duration at a small object that has a mass equal to `10.0 mg` and is suspended by a fine fiber that is `4.00 cm` long. If the radiation is completely absorbed by the object, what is the maximum angle of deflection of this pendulum?

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The attached diagram shows the displacement of the pendulum bob, through an angle theta, as a consequence of the complete absorption of the incident radiation. Now use conservation of mechanical energy.

`Delta K +Delta U=0`


In this case, set the initial potential energy of the pendulum to zero and since the final state of the pendulum comes to a complete stop, `K_f=U_i=0` .





Solve for `theta` .

`eq. (1) :->` `theta=cos^-1(1-P_i^2/(2m^2gL))`

Now use conservation of momentum between the laser and the initial momentum of the pendulum, `p_i` .


Use the momentum relation for light. Then relate energy to the laser power `P` .

`p_i=E_(laser)/c=(P delta t)/c`

Now substitute for `p_i` in `eq. (1)` .

`theta=cos^-1(1-(P^2(Delta t)^2)/(2m^2c^2gL))`

Substitute numerical values and evaluate `theta` .

`theta=cos^-1(1-((1000 MW)^2(200 ns)^2)/(2(10.0 mg)^2(2.998*10^8 m/s)^2(9.81 m/s^2)(0.0400 m)))=6.10^@`

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