Cambridge Pre-U 9792/03/M/J/22
Examination question: What is the total energy E of the binary star system?
Given: The kinetic energy of star X is $E_x = \frac {2GM^2}{9D}$
Working:
$E_Y = \frac{GM^2}{9D}$
Using potential energy formula $E_p$ = $\frac{-GMm}{r}$, the potential energy of both stars is $\frac{-2GM^2}{3D}$
E = $E_k$ + $E_y$ + $E_p$
E = $\frac{2GM^2}{9D}$ + $\frac{GM^2}{9D}$ – $\frac{6GM^2}{9D}$ = $\frac{–3GM^2}{9D}$
This gives the correct answer as in the marking scheme.
My question:
This isn't very intuitive to me because we're subtracting the potential energy. Rather, what makes more sense to me is adding the magnitude of both. Maybe my understanding of potential energy is limited. I can slightly see how it would make sense -- is it because the potential energy is work got out? -- but I want a clearer understanding.
