First slide

Momentum and Radiation pressure

Question

Light with an energy flux of 19 W/ cm² falls on a non-reflecting surface at normal incidence' If the surface has an area of 20cm², the average force exerted on the surface during the span of 30 min is

Moderate

A

$1 \cdot 2 \times 10^{- 6} N$
B

$1 \cdot 5 \times 10^{- 6} N$
C

$2 \times 10^{- 6} N$
D

$3 \times 10^{- 6} N$

Solution

Total energy falling on the surface
$U = (18 W / {cm}^{2}) \times (30 \times 60 s) \times (20 {cm}^{2}) = 6 \cdot 48 \times 10^{5} J Now, momentum p = \frac{U}{c} = \frac{6 \cdot 48 \times 10^{5}}{3 \cdot 0 \times 10^{8}} kg - m / s = 2 \cdot 16 \times 10^{- 3} kg - m / s Average force exerted F = \frac{p}{t} = \frac{2 \cdot 16 \times 10^{- 3}}{30 \times 60} = 1 .2 \times 10^{- 6} N$

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