# For those who think they understand Newton's Second Law

Discussion in 'Physics' started by studiot, May 20, 2009.

1. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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Many think they understand Newton's Second Law which mathematically put
asserts that

Force = mass x acceleration

This is not an expression of cause and effect. It is an expression of the equivalence of Force and Inertia (as measured by mass).

It does not imply that force causes acceleration nor that acceleration causes force.

Consider the following:

A heavy ball is suspended by a string from a beam B. The ball is set swinging in a circle, as described by the dashed line in the plan view. Without friction the ball would go on swinging round for ever.

The elevation describes the forces acting on the ball. There are three.

The weight of the ball is balanced vertically by the vertical component Tcosθ of the tension T in the string. The ball is in vertical equilibrium.

Is the ball also in horizontal equilibrium, since it neither gets nearer to nor further from the centre line?

If so what force balances the horizontal component of the string Tsinθ, which is definitely a force acting upon the ball?

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Last edited: May 20, 2009
2. ### mik3 Senior Member

Feb 4, 2008
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Analyze the centrifugal force and you will get it.

Nov 9, 2007
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Go on then

Feb 4, 2008
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I am bored.

Jan 6, 2009
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6. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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And I thought you were mik3

7. ### b.shahvir Active Member

Jan 6, 2009
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C'mon Mik3, take it up as a challenge

8. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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It's not a challenge, it's serious stuff.

There is no such thing as centrifugal force in the known universe.
CF is a mathematical fiction, albeit a convenient one.

Three forces only act on the ball

Gravity applies a vertical force
Tension in the string applies a vertical force.

Tension in the string applies a horizontal force.

There are no other agents in play.
I hope no one would suggest that any body can apply a force to itself?

9. ### sixstringartist Member

Apr 8, 2008
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Momentum of the ball is a factor in the horizontal and vertical movement

Last edited: May 20, 2009
10. ### mik3 Senior Member

Feb 4, 2008
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The tension of the string is canceled by another force opposite to it otherwise the ball would move towards the axis of rotation. They call this force centrifugal, which is not actually a force, but a cause of the balls inertia.

The only force which acts to move the ball is its weight and if an initial external force.

If there is not an initial push the ball can't make the complete rotation.

11. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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As you said, NO.

Neither the string nor gravity is capable of exerting a force acting to the right in my diagram.

12. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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The horizontal component creates a constant acceleratrion toward the center of the circle, but since the MOTION is always normal to the acceleration there is no change in energy. The F in F=MA is a VECTOR, remember, and don't you forget it!

eric

13. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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Yes but once the intial push is removed the ball will keep swinging round in a frictionless system.

Well nearly there but a bit confusing don't you think? This force,which is not actually a force?

Try rewriting Newton's Law not a F=ma but F - ma = 0. This is known as D'Alemberts principle.

14. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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Sorry, Eric this is an erroneous statement/explanation.

The string tension, which is real, exerts a real force on the ball to the left and therefore towards the axis of rotation.

15. ### mik3 Senior Member

Feb 4, 2008
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Well, actually there is a force but it is not a force caused by the ball itself but from the circular motion of the ball.

It is hard to explain.

The ball tends to move straight on the tangent of the motion path due to its inertia, however, the string pulls it back and makes it to turn and thus the ball makes this circular path, because the string has a fixed length.

16. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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I know it's hard to explain.
That's the purpose of this thread.

To bring out that there is more to Newton's Law than the half-truth hammered into schoolboys.

However I assure you there is no force.

If your method of reasoning requires a force look again at your method.

To exert a force on another object you require an external agent - either another object, such as the string, or a field such as gravity.

There is no other external agent available in this case.

17. ### mik3 Senior Member

Feb 4, 2008
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I should say its hard to imagine it, than hard to explain.

18. ### steveb Senior Member

Jul 3, 2008
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I think Eric (KL7AJ) essentially has the right answer. He is correct that the string causes the ball to accelerate toward the center. The ball's inertia will try to resist any change in velocity and so there is a reaction force outward. This is referred to as a reactive centrifugal force, and it is very real. Stating that centrifugal force is not real is not correct. There is a centrifugal force in a rotating reference frame that can be called ficticious, but reaction centrifugal force is real force in an inertial (i.e. nonrotating) reference frame.

19. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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So, Steve, you are suggesting that it is possible to for a body to apply a real force to itself?

20. ### mik3 Senior Member

Feb 4, 2008
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The ball is not applying a force to itself. It the movement of the ball which causes this centrifugal force due to its inertia. The ball applies a force to the string which is caused by its moment and the string applies reacts to this force by pulling the ball towards the axis of rotation.