Recently, the following problem was shared in the Brilliant Community:
My attempt is as follows. Consider the diagram at an arbitrary instant as shown below.
Say the mass is situated at a distance along the X-axis. Then the coordinates of each mass are:
Since no external force acts one the system along the X direction, the momentum along X is conserved. This gives:
The initial momentum of the system is zero. Plugging in all variables above and simplifying gives:
The kinetic energy of this system is:
Simplifying the above expression gives:
Eliminating by using (1) and simplifying gives:
The potential energy of the system is:
Initial potential energy is:
Initial kinetic energy is:
Applying conservation of energy gives:
Now, when the angle between the rods is 30 degrees, then:
This gives the value of at that instant.
The velocity of point at this instant :
The final expression for speed is:
- The cylinders are treated as point masses.