In the diagrma, a particle (A, mass 0.6kg) is moving in a vertical circle. The question is: When it gets to the lowest point, what is the tension in the light rod that is between the center of the circle (B) and the mass A?
At that point the particle is not moving vertically, so why doesn't the tension = the weight (0.6g)? The tension in the rod is providing the centripetal force so it's not like the tension and the centripetal force have to equal 0.6g?
Best Answer
Assume that at the moment of interest (mass at the very bottom of its circular path), the mass is travelling at a velocity $V (m/s)$.
Then the total force acting on the mass, at that moment, $F_{Total}$, must be sufficient to keep the mass moving in a circle, radius $r$;$$F_{Total}=\frac {m V^2}{r}=\frac {0.6 V^2}{0.5}=1.2V^2$$and this force, at that moment, must be acting vertically upward.
What are the forces acting that make up this total? The force of gravity, $0.6 g$, acts downward, and the tension in the stick, $F_{Tension}$, acts upward; so $$F_{Total}=F_{Tension}+(-0.6g)$$ $$F_{Tension}=F_{Total}+0.6g$$ $$F_{Tension}=1.2V^2+0.6g$$