Chapter 41: Problem 33

Question: Suppose you lie in the sun for $\Delta t~=~2.5~{\rm hr}$, exposing an area of $A~=~1.3~{\rm m^2}$ at 90^o to the sun's rays of intensity $I=1.1~{\rm kW/m^2}$. Assuming complete absorption of the rays, how much momentum is delivered to your body?

Solution: The total energy absorbed by your body is

$$\Delta E~=~I (Delta t) A~=~1.1\times 10^3 1.3 2.5 (60)^2~=~1.29\times 10^7~{\rm J} \ \ \ .$$ (15)

For electromagnetic radiation, its momentum is proportional to its energy, and therefore the absorbed momentum $\vert\Delta p\vert=\Delta E/c=4.3\times 10^{-2}~{\rm Kg m/s}$.