Question

A powerful 0.54-W laser emitting 670-nm photons shines on a black sail of a tiny 0.10-g cart that can coast on a frictionless track.

Part A Determine the force of the light on the sail. Assume that the light is totally absorbed by the sail. Express your answer to two significant figures and include the appropriate units. F = SubmitMy AnswersGive Up Part B What time interval is needed for the cart's speed to increase from zero to 2.0 m/s? Express your answer using two significant figures. t =   s   SubmitMy AnswersGive Up

Answer 1

energy of the photons is E = h*c/lamda

h is planck's constant

c is speed of light

lamda is the wavelength of light

then E = (6.625*10^-34*3*10^8)/(670*10^-9) = 2.96*10^-19 J

but this is completely absobed by the sail to move

hence E = 0.5*m*v^2 = 0.5*0.1*10^-3*v^2 = 2.96*10^-19

v = 7.69*10^-8 m/s

then we know that Power P = F*v

then Force F = P/v = 0.54/(7.69*10^-8) = 7.01*10^6 N

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B) P = W/t

but W = change in kinetic energy = 0.5*m*v^2 = 0.5*0.1*10^-3*2*2 = 0.2*10^-3 J

time t = W/P = 0.2*10^-3 / 0.54 = 0.37*10^-3 S = 0.37 milli S