Chapter 33, Problem 023
Someone plans to float a small, totally absorbing sphere 0.514 m
above an isotropic point source of light, so that the upward
radiation force from the light matches the downward gravitational
force on the sphere. The sphere's density is 21.4 g/cm3,
and its radius is 2.08 mm. (a) What power would be
required of the light source? (b) Even if such a
source were made, would the support of the sphere be unstable?
Assume that the speed of light is 2.998*108 m/s.
answer) first we have the condition
W=Fr........................1)
we have intensity I=P/Ar and Ps=I/c
so substituting the value of I
Ps=P/cAr..............2)
now we have the pressure on the sphere Ps=Fs/A
so Fs=PsA and from eqn 2 we have
Fs=PAs/cAr...............3)
we know the relation
W=mg
so eqn 3 becomes
mg=PAs/cAr
P=mgArc/As=Vsg4pid2/pir2=
*(4/3)pir3g4pid2c/pir2=21400*(4/3)pi*(0.00208)3*9.8*4pi*0.5142*2.998*108/pi*(0.00208)2=5.78*1011W
so answer is 5.78*1011W or 5.8*1011 or 6*1011W.
b) yes the support will be unstable because the equal and opposite forces which will be keep the sphere in equilibrium will not be on the same line.
Chapter 33, Problem 023 Someone plans to float a small, totally absorbing sphere 0.514 m above...
Chapter 33, Problem 023 Someone plans to float a small, totally absorbing sphere 0.522 m above an isotropic point source of light, so that the upward radiation force from the light matches the downward gravitational force on the sphere. The sphere's density is 21.2 g/cm3, and its radius is 2.16 mm. (a) What power would be required of the light source? (b) Even if such a source were made, would the support of the sphere be unstable? Assume that the...
Someone plans to float a small, totally absorbing sphere 0.532 m above an isotropic point source of light, so that the upward radiation force from the light matches the downward gravitational force on the sphere. The sphere's density is 20.8 g/cm3, and its radius is 2.34 mm. (a) What power would be required of the light source? (b) Even if such a source were made, would the support of the sphere be unstable? Assume that the speed of light is...
1) One plans to float a small, totally absorbing sphere at a distance of d above an isotrophic point source of light, such that the upward radiation force from the light balances with the downward gravitational force on the sphere. the density of the sphere is p and the radius of the sphere is r. What power of P by the light source to accomplish this?