Question about supernova kinetic energy

[lr1]

A9: Supernova Remnants
Consider a supernova explosion in the outer 4M⊙ of a dying star, ejected at a speed of 5000 km/s.
a ◮ What is the kinetic energy of the expanding ejecta?
b ◮ The ejecta are slowed by sweeping up the local interstellar gas. Assuming the density of the interstellar gas
is ig = 2 × 10−19 kg/m3, how large a volume will be swept up by the time the outflow velocity has decreased
to 10 km/s? HINT: Assume the KE of the expansion is conserved.
A10:

 

[tiny-tim]

welcome to pf!

hi lr1! welcome to pf!

(try using the X² button just above the Reply box )

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[lr1]

Part a I used virial theorem for kinetic energy 3mv^2 and for part b I used mass= density / volume but am confused with swept volume

 

[Chronos]

Virial theorem is only useful on large scales, for a region near a supernova event you still need to use kinematical models.

 

[pmacias]

The kinetic energy of the expanding ejecta can be calculated using the equation KE = 1/2 mv^2, where m is the mass of the ejecta and v is its velocity. Assuming the mass of the ejecta is 4M⊙ and the velocity is 5000 km/s (or 5,000,000 m/s), the kinetic energy would be approximately 2 × 10^44 joules.

To calculate the volume of interstellar gas swept up by the ejecta, we can use the equation V = m/ρ, where m is the mass of the ejecta and ρ is the density of the gas. In this case, the mass of the ejecta is still 4M⊙, but the density of the gas is 2 × 10^-19 kg/m^3. Plugging these values into the equation, we get a volume of approximately 2 × 10^71 m^3.

However, it should be noted that the conservation of kinetic energy assumption may not hold true in this scenario, as the ejecta will lose some of its kinetic energy due to interactions with the interstellar gas. This could result in a slightly smaller swept up volume. Further calculations and observations would be needed to accurately determine the exact volume of gas swept up.