Dynamics | Part IA, 2008

Two particles of masses m1m_{1} and m2m_{2} have position vectors r1(t)\mathbf{r}_{1}(t) and r2(t)\mathbf{r}_{2}(t) at time tt. The particle of mass m1m_{1} experiences a force f\mathbf{f} and the particle of mass m2m_{2} experiences a force f-\mathbf{f}. Show that the centre of mass moves at a constant velocity, and derive an equation of motion for the relative separation r=r1r2\mathbf{r}=\mathbf{r}_{1}-\mathbf{r}_{2}.

Now suppose that f=kr\mathbf{f}=-k \mathbf{r}, where kk is a positive constant. The particles are initially at rest a distance dd apart. Calculate how long it takes before they collide.

Typos? Please submit corrections to this page on GitHub.