PHYS 252

Always hand in:
  1. written solutions to any questions
  2. a paper print-out of well-commented code. Include a multiline comment at the top of your code with (i) the assignment name, (ii) your name, and (iii) the date you handed in all elements of the assignment
  3. paper print-out of output (graph or text)
  4. also, e-mail me (y-lithwick@northwestern.edu) the code with your name and the exercise number in the subject line

Assignment #5
[5 pts, due 2pm, April 12]

    1. Solve the equation for a cyclist, dv/dt=P/(mv) with the following parameters: m=70kg, P=400W, initial velocity=4m/s, timestep=0.1s, and plot v(t).
    2. Add the friction term to the right hand side, -(B2/m) v2, where B2=(1/2)Cρ A, ρ=1.4 kg/m3, A = 0.33 m2, and drag coefficient C=1. You should reproduce the curve in Fig 2.2.
    3. How does the terminal velocity scale with (a) P and (b) m. [The following is not for credit: can you figure out the formula for the terminal speed in terms of m, P, and B2, and if so what is it? ]
    4. Consider swimming instead of biking. How does the equation for a swimmer differ from the equation for the biker used in part ii? Be quantitative. [You may use google to find any physical parameters you might need.] Now run a numerical integration, and plot the result. Compare the terminal speed with the world record speed in the 1.5km freestyle.

  2. Reproduce the two curves Figure 2.5 in Computational Physics without density correction, with parameters as detailed in the text.
  3. [This question is not for credit:] You are travelling in an airplane, throwing rocks out the window. Plot the speed of the rock when it hits the ground versus the size of the rock. Include even ridiculously small and large sizes so that you map out all the behaviour. Explain very briefly the reasoning you used in your code (including the equations, initial conditions, and parameters you're using). You may use equations 2.9 and 2.23 in the book. You may also use google again for physical parameters. These don't have to be exact, but your final plot should be correct to within an order of magnitude.
    Very large rocks don't slow down at all. Can you derive approximately how large a rock has to be in order not to slow down, and give a simple intuitive explanation for what sets this critical size?