During 2004, Japanese scientists successfully tested two solar sails. One had a

Question

During 2004, Japanese scientists successfully tested two solar sails. One had a somewhat complicated shape that we shall model as a disk 9.00m in diameter and 7.50?m thick. The intensity of solar energy at that location was about 1400W/m2

Part A

What force did the sun's light exert on this sail, assuming that it struck perpendicular to the sail and that the sail was perfectly reflecting?

Part B

If the sail was made of magnesium, of density 1.74g/cm3 , what acceleration would the sun's radiation give to the sail?

Part C

Does the acceleration seem large enough to be feasible for space flight? In what ways could the sail be modified to increase its acceleration?

Explanation / Answer

Radiation Pressure = 2 x (Intensity / c)

where c is speed of light in vacuum

Radiation Pressure = 2 x 1400/ 3 x 108 = 9.34 x 10-6 N/m2

Force = pressure x area

= pressure x pi x 4.52

= 5.8 x 10-4 N

as only the top surface of disk will be struck, hence area taken as circular area of top surface with radius = 4.5m.

Part -B

Density = mass / volume

Volume of Disk = Area of circle x height

= pi x 4.5 x 4.5 x 7.50

= 476.88 m3

Mass = density x volume = 1.74 g/cm3 x 476.88 x 106 cm3

= 8.29 x 108g = 8.29 x 105 kg

Acceleration = force / mass

= 5.8 x 10-4/8.29 x 105

= 6.98 x 10-10 m/sec2

Part C

No, it is very less than that reuired for space flight.

Instead of disks, flat panels should be used which have more surface area but less thickness.

This increases the force and decreases the volume,and so mass.   

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