Physics 243
Assignment #2

Date Due: February 12, 2018

Please solve the following problems. (6 marks)

From Moore: Q2R.2, Q3M.12, Q4M.2, Q4R.1

1. The photograph below shows a soap film created by dipping a circular ring (about 10 cm diameter) in a soap solution and then withdrawing and it holding it vertically.
   
   1. Look at the soap film shown below. Why is the top of the film black (or very dark)?
   2. Why do the colour bands appear as they do? In particular, why does the colour of each band change and eventually becomes a series of green-pink bands that get progressively narrower as you go down.
   3. Why does the film eventually become a "dirty" white colour?
   4. Sketch a model of what the soap film would look like physically - ie - how does width of the film vary from top to bottom? Include some estimates for the thickness of the soap film at various locations.
      

2. Our Sun emits 3.99 X 10²⁶ J/s. At the same time it also creates a "solar wind" of high energy protons that blow outward from the Sun. The solar wind is responsible for, among other things, the northern lights. This wind creates a typical pressure of about 2 nPa. Please answer the following questions:
   1. What is the Solar Intensity in W/m² (sometimes called the Solar Constant) at the top of the atmosphere?
   2. Light can also exert pressure - which would be bigger (and by how much) - the pressure of sunlight at the top of Earth's atmosphere or the solar wind?
   3. NASA engineers want to propel a 1000 kg spacecraft by creating a solar sail that is 1km by 1 km and made from a highly reflective mylar sheet (almost 100% reflective). Calculate the acceleration of such a craft due to pressure from the Sun
   4. How fast would the spacecraft be travelling 1 week after deploying the sail? Explain any simplifications that you have made.
      
      
3. Fun With Fourier! Use Excel to combine 10 waves related by the expression y(x) = a_nsin(nx) where n =1,3,5.. (odd) .and a_n = -1^(n-1)/2/n² and x ranges from x = 0 to x = +14. What function do you think this "represents"?
   
   
4. In classical physics the emission of electrons from metals when illuminated by light should take a long time but should not depend as much on wavelength as on frequency (opposite of what really happens!)! Suppose a metal has a work function of 2 eV and is illuminated by a light beam (shown below) of diameter 1cm and intensity 1 W/m2. Estimate how long it will take for the metal to emit an electron. Consider the following in your solution:

1. The diameter of each atom in the metal is 5 x 10^-10 m
2. Estimate how much of the light energy any one atom can absorb in a second if any light falling on the atom is absorbed.