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Light with an energy flux of $18 \;W / cm ^{2}$ falls on a nonreflecting surface at normal incidence. If the surface has an area of $20\; cm ^{2},$ find the average force exerted on the surface during a $30$ minute time span.
$4.8 \times 10^{-7} \;N$
$8.7 \times 10^{-6} \;N$
$2.8 \times 10^{-5} \;N$
$1.2 \times 10^{-6} \;N$
Solution
The total energy falling on the surface is
$U=\left(18\,W / cm ^{2}\right) \times\left(20 \,cm ^{2}\right) \times(30 \times 60\,s)$
$=6.48 \times 10^{5} \,J$
Therefore, the total momentum delivered (for complete absorption) is
$p=\frac{U}{c}=\frac{6.48 \times 10^{5} \,J }{3 \times 10^{8} \,m / s }=2.16 \times 10^{-3}\, kg\, m / s$
The average force exerted on the surface is
$F=\frac{p}{t}=\frac{2.16 \times 10^{-3}}{0.18 \times 10^{4}}=1.2 \times 10^{-6} \;N$
