Part A Estimate the radiation pressure due to a bulb that emits 25 W of EM radia

Question

Part A

Estimate the radiation pressure due to a bulb that emits 25 W of EM radiation at a distance of 4.5 cm from the center of the bulb. Assume that light is completely absorbed.

Express your answer to two significant figures and include the appropriate units.

Part B

Estimate the force exerted on a fingertip at this point. Suppose that the area of the fingertip is 1.2 cm^2 . Assume that light is completely absorbed.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

here,

Assuming all the energy is emitted as EM-radiation .. W = 25.0J/s

Energy radiates outwards over the surface area of a sphere

Energy absorbed per 1m^2 of the surface at radius R

E = W / (4* pi * R^2) .. .. ..(J/s) per m^2 ----- (1)

The mass equivalent of this energy .. M = E/c^2 (Einstein) .. so ..

M = W / (4* pi * R^2 c^2) .. (kg/s) per m^2 ----- (2)

For an absorbing area, A (m^2) .. equ (2) becomes .. A.W / (4* pi * R^2 c^2) .. kg/s ---- (3)

From Newton L2 .. F = rate of change of momentum of absorbed mass (m/t * v)

F = M (kg/s ) * c .. .. F = A.W / (4* pi * R^2 c) ---- (4)

Radiation pressure .. p = F/A .. .. p = W / (4* pi * R^2 c) ----- (5)

a)

Using (5)

p = 25 / (4* pi * [0.045 m]^2 * 3.0 * 10^8)

p = 3.27 * 10^-6 N/m^2

the pressure due to bulb is 3.27 * 10^-6 N/m^2

b)

F = p * area

F = 3.27 * 10^-6 * 1.2 * 10^-4

F = 3.92 * 10^-10 N

the force exerted the finger tip is 3.92 * 10^-10 N

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