energy-conservationforcesfree-body-diagramnewtonian-mechanicsstring
Consider a ball tied to a string and it is imparted a velocity we have studied that condition for looping the loop is that tension at the uppermost point must be zero, but why is this condition imposed please explain?
If tension becomes zero at some point below the uppermost point won't the ball complete the loop because it still has some velocity?
The loop has a curvature. As a result, when you take a small element of the loop, the tension force applied to it from both the sides is at an angle, which results in a force component to the inside.
Since your question asks for a rationale behind the tension force, I'll leave it here. You can now try yourself to find the tension by equating the outward force with the inward force. Or, if you are given the total outward force, you can integrate the tension force over the loop and then equate the total outward and inward forces.
To find the minimum velocity at the bottom-most point, we find the minimum velocity at the uppermost point. This minimum velocity is the one such that the centripetal force is equal to the force of gravity. Any lower and gravity will pull the object down and out of the loop, any higher and a faster velocity would be required to generate it (thus, not a minimum). Because this is the case, we set the tension to be zero because gravity can account for the entire centripetal force. Using this minimum velocity at the topmost point, we can use conservation of energy to find the minimum velocity at the bottom-most point.
Best Answer
If the tension is equal zero at some point below the uppermost level, the tension at higher points would need to be negative for the circular motion to continue. Of course, the tension cannot be negative, instead, the rope would become loose and the object would fall.