2.1.55. Two small spheres, each of mass $m$, connected by a thread of length $l$, are moving with a velocity $v$ on a horizontal table in a direction perpendicular to the connecting thread (the thread is taut). The middle of the thread hits a nail. What is the tension force of the thread immediately after this?
Solution
Forces acting on the system
Since the thread is taut:
$$T_1 = T_2 = T$$
As soon as the thread hits the nail, both bodies continue to move with velocity $v$ along a new trajectory with radius $r=\frac{l}{2}$:
$$T=ma_n$$
$$T=m\frac{v^2}{\frac{l}{2}}$$
We obtain the tension force of the thread immediately after this:
