   Chapter 29, Problem 86PE

Chapter
Section
Textbook Problem

Integrated ConceptsSunlight above the Earth's atmosphere has an intensity of 1.30kW/m2. If this is reflected straight back from a mirror that has only a small recoil, the light's momentum is exactly reversed, giving the mirror twice the incident momentum. (a) Calculate the force per square meter of mirror. (b) Very low mass mirrors can be constructed in the near weightlessness of space, and attached to a spaceship to sail it. Once done, the average mass per square meter of the spaceship is 0.100 kg. Find the acceleration of the spaceship if all other forces are balanced. (c) How fast is it moving 24 hours later?

To determine

(a)

The force per square meter of mirror.

Explanation

Given Data:

Given that the sunlight above the Earth's atmosphere has an intensity of1.30kW/m2 . If this is reflected straight back from a mirror that has only a small recoil, the light's momentum is exactly reversed, giving the mirror twice the incident momentum.

Formula Used:

Force is calculated as follows:

F=ΔPΔt

WhereΔP= Change in Momentum

Δt= Change in time

Calculation:

Momentum of photon is calculated as

P=2Ec

We havec=3×108m/s andE=1.30×103J/m2

Substituting the values in above equation, we get

P=2×1.30×103J/m23×108m/s

P=8

To determine

(b)

The acceleration of the spaceship if all forces are balanced.

To determine

(c)

How fast is it moving24hours later.

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