Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

Statement

$1.3.23.$ A small body moves at a constant velocity $v$ along a trajectory consisting of two smoothly connected arcs of circles of radius $R$ and $\frac{R}{3}$. Plot the acceleration vectors at the marked points of the trajectory.

Solution

Direction of acceleration

Acceleration is directed along the radius-curvature of the trajectory and is equal to

$$ \fbox{$ a = \frac{v^2}{r}$} $$

Answer

See figure