Snowplow model of a supernova remnant

[Tuugii]

Suppose a spherical shell identified as a supernova remnant is observed with radius r and
with outward expansion speed v. Assume the mass density of the ambient medium to have
the uniform value "ro_0". then the supernova remnant must have swept up mass M = ((ro_0)*4pi*r^3)/3.
Let the original mass M_0 be ejected at speed v_0. If we ignore communication between
different parts of the shell (via the thermal pressure of the hot interior), and suppose that
each piece of the shell preserves its outward linear momentum as it sweeps up more material initially at rest, we have the snowplow model.

a) Show that the snowplow model implies
(M +M_0)v = M_0*v_0.

b) The original kinetic energy E_0 of the ejected material equals (M_o*(v_0)^2)/2
0/2. The present
kinetic energy E of the shell equals ((M + M_0)v^2)/2. Show that the ratios E/E_0 and v/v_0 are given by:
E/E_0 = v/v_0 = M_0/(M +M_0).

 

[turbo]

Tuugii! When did you show up, buddy?

 

[Tuugii]

hey Skip! :)

I am a newbie here. Looking for some discussions on some problems related to my astro class.

 

[turbo]

Welcome, Tuugii! If you will post this problem in the Homework section and follow the format for posting, you will likely get some help pretty soon. You're expected to state the problem clearly, with any variables, and take a shot at dissecting/solving the problem so that the homework helpers can figure out where your problem-solving is breaking down.

If you could come to Maine, you wouldn't be missing Mongolia this winter!

 

[Tuugii]

wow that picture looks awesome!

I'll visit your place at some point of this 4 years! :)

Tuugii