Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A sail has an area of m² and a total mass of kg. It faces the Sun straight on at of the Earth's distance from the Sun. It reflects a fraction of the light and absorbs the rest. Near the Earth the intensity of sunlight is W/m², and it falls as . Use m/s. Find:
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The intensity there. .
Step 2. The pressure. .
Step 3. The force. .
Step 4. The acceleration. We want , so .
Step 5. The speed. The time is . So .
Answer: ; mN; mm/s²; km/s.
Watch out. The push stays constant only if the sail stays at the same distance. In truth, the sail moves, and the push changes.
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A wave of energy carries the momentum . Light that is absorbed gives the force , and light that is reflected straight back gives twice that. For a beam of power that meets a mirror at an angle to the normal, along the normal.