# I How does pendulum go slack above the horizontal?

1. Nov 4, 2016

### FallenApple

So say a pendulum consisting of a non rigid string and mass bob is swung above the horizontal position. It's given an impulse at the bottom so that in the swing, there is nothing but tension and gravity acting. At above the horizontal, the gravity is pointing down while the tension can only point radially inwards. There is nothing causing the rope to have tension then at this point. Gravity is pulling down. So what is pulling radially outwards to oppose the rope? So why is there tension?

at below the horizontal, there is tension because the weight is directly pulling on the rope. this makes sense.

But not above the horizontal.

2. Nov 4, 2016

### dextercioby

Do you know about pair forces? What are they and how do they influence the motion of the massive bob?

3. Nov 4, 2016

### Staff: Mentor

Your post and title seem to contradict each other...But you haven't described the pendulum's motion so it isn't clear to me what your issue is.

When the pendulum is swinging below the horizontal, there are two components that provide tension, not one: You have the gravity, but missed the centripetal acceleration of the weight.

Above the horizontal, while still swinging up, the centripetal force is still there, pulling the weight in a circle. But when it slows down enough that the centripetal acceleration no longer exceeds the acceleration due to gravity, the string goes slack.

4. Nov 4, 2016

### FallenApple

Sure newtons third law. But that doesn't explain why its taut above the horizontal. If anything, pushing force on the rope from the bob should make it go slack very quickly.

5. Nov 4, 2016

### FallenApple

Yes the centripetal force is still there. That is why there must be tension. I understand that.

But doesn't explain why there is tension when there is nothing pulling the rope.It's as if the rope knows to pull by itself.

6. Nov 4, 2016

### Staff: Mentor

What do you mean there is nothing pulling on the rope? You're talking about a pendulum: it primarily consists of a large mass. That's what is pulling on the rope always!

7. Nov 4, 2016

### FallenApple

Oh wait, I think i got it. The bob is going up, pulling on the rope, and the rope pulls back.

8. Nov 4, 2016

### Staff: Mentor

You are reasoning as though it were in static equilibrium. It is not. It is accelerating.

9. Nov 4, 2016

### FallenApple

Yeah I just got it. The motion of the bob is opposing the rope, causing the rope to be taut. There doesn't need to be a force component in the opposite direction of the rope. Just motion itself

10. Nov 4, 2016

### dextercioby

Above the horizontal, there's a net component of gravity increasing the pressure applied by the bob on the string, thus deforming it. You can see that when the bob is straight up, with the full gravity force of the bob pressing on the string and deforming it.

11. Nov 4, 2016

### A.T.

Just like your chair knows to push up on you.

12. Nov 4, 2016

### FallenApple

So that implies that the bob is pushing on the rope. So should not the rope push back?

13. Nov 4, 2016

### dextercioby

The rope pushes (acts on) back on the bob, it's the tension force for you put in Newton's second law.

14. Nov 4, 2016

### FallenApple

But then that would be a repulsive force.

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15. Nov 4, 2016

### dextercioby

What do you mean by repulsive ? That term makes sense to me only in electrostatics (the force between two charges of equal sign is called repulsive).

16. Nov 4, 2016

### FallenApple

In the pic, the tension is pulling here. But if the bob pushes on the string to the right to deform the string then the string must push to the left on the bob. But that isn't what happened in the pic

17. Nov 4, 2016

### Staff: Mentor

The string tries to push back on the bob, it just isn't very good at it. So the bob falls.

18. Nov 4, 2016

### FallenApple

So the string is pushing and pulling at the same time. The pushing force is a reaction to the weight pressing down and the pulling force is a reaction to the bob trying move away

19. Nov 4, 2016

### Staff: Mentor

No, at all times there is one resultant force on the string. It is either pushing or pulling.

20. Nov 4, 2016

### FallenApple

So when the mass is in orbit, the weight is not pressing down on the string. These moments would have the string pulling.

But as it slows, the weight will matter since the bob would fall into the string, making it start to buckle, and the string will be pushing here not pulling. But this is where the string goes slack?

21. Nov 5, 2016

### A.T.

The string goes slack if the centripetal weight component is more than the centripetal force required for the current speed.

22. Nov 5, 2016

### PeroK

I think you have got it, but you seem to be making this more complicated than it need be. Perhaps think first about a bob moving in a horizontal circle at the end of a string.

1) There is tension in the string because at all times the bob wants to move off in a straight line, and the string prevents it.

2) If you add an external centripetal force to the bob, the tension in the string will reduce, because now the external force is providing some of the force needed to stop the bob moving off.

3) If the external force equals the original tension in the string, then the bob will continue in its circular path but there will be no tension in the string.

4) If, however, the external force exceeds the original tension, then the bob will move inwards from its original path and the string will, of course, go slack.

For a vertical circle, with gravity as the external force, the situation is similar, except the speed of the bob is constantly changing, so the centripetal force required is changing. And, of course, below the horizontal gravity acts centrifugally (this means "away from the centre") thus increasing the tension in the string. Above the horizontal, you have a gravitational force acting increasingly centripetally and a slowing of the bob, which together reduce the required tension in the string. If the bob has insufficient speed, then gravity pushes the bob inwards, out of its circluar path, and the string goes slack.

23. Nov 5, 2016

### CWatters

Imagine cutting the rope as it passes the horizontal position. The mass/bob would continue up vertically for awhile due to it's inertia. With the rope attached the bob still tries to do that and this is what keeps the rope taught.