Who can reaction be greater than action?

Question

In the topic of conical pendulum, we resolve the tension into two components, one along mg and other acting towards the centre (providing the necessary centripetal force). But tension is the reaction to weight. My doubt is that in this case only one component of tension is equal to the weight of bob. whereas the other component is directed towards the centre. this means that tension is greater than weight. But tension is the reaction to weight. How can this be possible? Please explain

Answer 1

If you let the pendulum hang, without disturbing it, it will hang straight down. Then the tension in the string will be equal to the force of gravity on the weight. To get it to move to the side, you must apply a force that is perpendicular to the force of gravity, that is, you are applying additional force. So it is reasonable that the tension in the string will reflect both of these forces and be greater than if only one force was creating it.



So you can see that tension is not only proportional to weight; that the weight it supports is only one component of the net force that results in the strings tension.



But you can have still OTHER reasons why the tension could be higher. Imagine that the point the string is attached to is accelerating upwards. That would create another force that would, indeed, again increase the tension on the string.

Answer 2

Your problem is that Tension is Not the reaction to Weight. I think there would be less confusion if the 3rd law were stated this way;



"If Object A exerts a force on object B then object B will exert an equal but opposite force on A".



The weight of a pendulum bob is due to the Earth exerting a gravitational force on it. The reaction then, is the bob exerts an equal force on the Earth.



The string tied to the bob exerts a force on it. The reaction is the bob exerts an equal force on the string. We usually call both of these forces Tension.



Now, as you have found out, there is no fundamental reason why the Tension and Weight should be equal, because they are not action/reaction pairs. Under certain circumstances they will be equal (like when the pendulum hangs motionless), but this is to satisfy the 2nd law and conditions of equilibrium, and has nothing to do with action/reaction.

Answer 3

The problem is that you're trying to apply Newton's third law to a one-body system. The pendulum bob is the one body. Newton's third law tells us about what happens between two bodies when they interact. The second body in your problem is the unmentioned object that the string is attached to that serves as an anchor point. Teachers never mention this aspect of problems and never mention the forces acting on the anchor point. So when you assume that such a fixed anchor point exists and ignore all the forces acting on it, then yes you ruin the third law. Essentially, you are forgetting the force necessary too keep the pendulum's anchor point fixed in space. Include this force and you will see that indeed the total force produced by the string on the anchor point is equal and opposite to the force produced by the string on the pendulum bob.

Answer 4

In this case the vertical component of Tension is reaction to weight.