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**Physics, Astronomy & Cosmology / Re: How much force does a torch or flashlight beam apply to a dust particle?**

« **on:**11/11/2018 01:02:12 »

The pressure is going to fall off the further away from the light you are, so I'll assume a best case scenario where we are looking at the pressure the light is producing right at the face of the flashlight.

The equation for calculating radiation pressure is P = I

P is pressure in pascals

I

c is the speed of light in meters per second

If I have a 5 watt flashlight with a lens radius of 2.5 centimeters (0.025 meters, 0.0019634954 square meters), then the irradiance will be about 2,546.48 watts per square meter. This assumes that 100% of those watts are going into the creation of electromagnetic radiation, which we know it wouldn't be. The actual efficiency might run anywhere from 10% to 90% depending on the kind of bulb used.

So now we put the relevant numbers into the equation:

P = 2,546.48 watts per square meter/299,792,458 meters per second

P = 0.00000849414 pascals (newtons per square meter)

Multiply that number by a value from 0.1 to 0.9 depending on how efficient the lightbulb is to get a better estimate.

EDIT: According to Engineering Toolbox, household dust particles range in size from 0.05 to 100 microns across. For the sake of convenience, I'll assume they are spherical, resulting in cross-sectional areas of 0.0019634954 square microns (1.9634954 x 10

F = 0.00000849414 newtons per square meter x 1.9634954 x 10

F = 1.6678205 x 10

F = 0.00000849414 newtons per square meter x 7.85398163397 x 10

F = 6.671282 x 10

To find the acceleration that the light imparts on these particles, their mass will need to be known. If I assume that they are made of organic matter, then a density similar to water might not be far off the mark (if it is, we can modify this later). A sphere 0.05 microns across has a volume of 6.54 x 10

m = 6.54 x 10

m = 6.54 x 10

m = 5.24 x 10

m = 5.24 x 10

Now for the acceleration:

A = F/m

A = 1.6678205 x 10

A = 0.255 meters per second squared (for 100% efficient light)

A = 0.23 meters per second squared (for 90% efficient light)

A = 0.0255 meters per second squared for (for 10% efficient light)

A = F/m

A = 6.671282 x 10

A = 0.00127 meters per second squared (for 100% efficient light)

A = 0.00114 meters per second squared (for 90% efficient light)

A = 0.000127 meters per second squared (for 10% efficient light)

The equation for calculating radiation pressure is P = I

_{f}/c, where:P is pressure in pascals

I

_{f}is the irradiance in watts per square meterc is the speed of light in meters per second

If I have a 5 watt flashlight with a lens radius of 2.5 centimeters (0.025 meters, 0.0019634954 square meters), then the irradiance will be about 2,546.48 watts per square meter. This assumes that 100% of those watts are going into the creation of electromagnetic radiation, which we know it wouldn't be. The actual efficiency might run anywhere from 10% to 90% depending on the kind of bulb used.

So now we put the relevant numbers into the equation:

P = 2,546.48 watts per square meter/299,792,458 meters per second

P = 0.00000849414 pascals (newtons per square meter)

Multiply that number by a value from 0.1 to 0.9 depending on how efficient the lightbulb is to get a better estimate.

EDIT: According to Engineering Toolbox, household dust particles range in size from 0.05 to 100 microns across. For the sake of convenience, I'll assume they are spherical, resulting in cross-sectional areas of 0.0019634954 square microns (1.9634954 x 10

^{-15}square meters) and 7,853.98163397 square microns (7.85398163397 x 10^{-8}square meters) respectively. Now to calculate the force on these particles:F = 0.00000849414 newtons per square meter x 1.9634954 x 10

^{-15}square metersF = 1.6678205 x 10

^{-20}newtonsF = 0.00000849414 newtons per square meter x 7.85398163397 x 10

^{-8}square metersF = 6.671282 x 10

^{-13}newtonsTo find the acceleration that the light imparts on these particles, their mass will need to be known. If I assume that they are made of organic matter, then a density similar to water might not be far off the mark (if it is, we can modify this later). A sphere 0.05 microns across has a volume of 6.54 x 10

^{-5}cubic microns (6.54 x 10^{-23}cubic meters). A sphere 100 microns across has a volume of 5.24 x 10[/sup]5[/sup] cubic microns (5.24 x 10^{-13}cubic meters). The density of water is 1,000 kilograms per cubic meter, so:m = 6.54 x 10

^{-23}cubic meters x 1,000 kilograms per cubic meterm = 6.54 x 10

^{-20}kilogramsm = 5.24 x 10

^{-13}cubic meters x 1,000 kilograms per cubic metersm = 5.24 x 10

^{-10}kilogramsNow for the acceleration:

A = F/m

A = 1.6678205 x 10

^{-20}newtons / 6.54 x 10^{-20}kilogramsA = 0.255 meters per second squared (for 100% efficient light)

A = 0.23 meters per second squared (for 90% efficient light)

A = 0.0255 meters per second squared for (for 10% efficient light)

A = F/m

A = 6.671282 x 10

^{-13}newtons / 5.24 x 10^{-10}kilogramsA = 0.00127 meters per second squared (for 100% efficient light)

A = 0.00114 meters per second squared (for 90% efficient light)

A = 0.000127 meters per second squared (for 10% efficient light)

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