Calculating Speed & Acceleration of Banelings

[grave]

Homework Statement

In space two banelings are separated by a distance of 1x10^10. Baneling-A has 5 solar mass and a radius of 2.5 billion meters. Baneling-B has 1 solar mass with a radius of 1.5 billion. They are initially at rest from each other. Measured at a rest frame, (a)how fast are they moving when their separation is half of the initial value? (b)What is d(speed)/d(separation)?

Homework Equations

(1/2) (M) (vf)^2 - (GMm/distace final) = (1/2) ( M) (vi)^2 - (GMm/distace inital)

The Attempt at a Solution

(1/2) (1x10^31) (Vf^2) - ((6.67x10^-11) (1x10^31) (2x10^30)) / (1x10^10/2) =
(0) - ((6.67x10^-11) (1x10^31) (2x10^30)) / (1x10^10)

vf= 163340
is it right? did i use the right mass? do i need to convert solar mass to kgs?

 

[gneill]

Homework Statement

In space two banelings are separated by a distance of 1x10^10. Baneling-A has 5 solar mass and a radius of 2.5 billion meters. Baneling-B has 1 solar mass with a radius of 1.5 billion. They are initially at rest from each other. Measured at a rest frame, (a)how fast are they moving when their separation is half of the initial value? (b)What is d(speed)/d(separation)?

Homework Equations

(1/2) (M) (vf)^2 - (GMm/distace final) = (1/2) ( M) (vi)^2 - (GMm/distace inital)

The Attempt at a Solution

(1/2) (1x10^31) (Vf^2) - ((6.67x10^-11) (1x10^31) (2x10^30)) / (1x10^10/2) =
(0) - ((6.67x10^-11) (1x10^31) (2x10^30)) / (1x10^10)

vf= 163340
is it right? did i use the right mass? do i need to convert solar mass to kgs?

Yes, it would be best to convert everything to consistent units before beginning your calculations. So converting the masses to kg would be a good idea. Note that you could do most of the work symbolically and then you won't need to convert the masses, simply plug in the mass of the Sun in one spot at the end. But if you're more comfortable banging away at the calculator, then you should do the conversion

Note also that there are TWO objects, and that it looks like you should calculate a speed for each. They give a hint by suggesting that these speeds are measured in a rest frame. That suggests a center of momentum frame, especially since they both start out with zero velocity.

 

[Morgoth]

each time you want to make calculations and give up the final number, you must be careful in what you measure everything (is it kg,m,sec, cm, ... ?)

eg, if we say that you have m=1gr, v=2 cm/hr you can still say that the kinetic energy is:
KE= m v^2 /2 = 2 gr cm/hr
This is as true as saying
KE= 5.5 E-09 kg m/s
Of course you cannot use the SI system and say that the KineticEnergy is 2Joule.

Everytime it is always good when doing the numerical calculations to do the calculations considering your measurments.