The Lee-Tseung Lead Out Theory

[Top Gun]

Second point:

The work done by the constant force F of 10 units
= 10*9.8*(M1-M2) = 10*9.8*0.164405 = 16.11171 joules

Wrong again. Now your force is tangential and not horizontal any more. So the force applied will split in to horizontal and vertical components. It will do work in both directions. You are applying tangential force but considering it as horizontal force.

With the pulley, the force can be considered constant.  The applied force F drops a distance of (M1-M2).  That represents the work done externally.

[Kul_ash]

Firt one for starter:

When you are pulling string from middle point, L is effectively altered and has become L/2 = 0.5 m. Because the final angel you are showing is not the angle between support and bob, but the angle between point of force application and support.

In Pendulum14.jpg, L is distance between the pivot and the knot. 

We are dealing with the parallelogram of forces in this experiment.

Please refer to your point no. 4 in previous post!
4)   The length of the pendulum string is L = 1 meter

You have not mentioned anywhere that L is the distance between pivot and knot.

Because the point is your vertical lift of bob is going to be lesser that what you have shown considering L = 1m.

Here is some bad sketch to explain this.

[Kul_ash]

More on the experiment related to Pendulum12.jpg


Let us do a more exact analysis on the vertical work or the potential energy gained by the weight of 60 units and the external work done by the constant force F as illustrated in Pendulum12.jpg.  I am using Pendulum14.jpg to help in the illustration.

Let us assume that
(1)   The initial length of string from the pulley to the initial position is M1 and can be adjusted to exactly 2 meters.
(2)   The horizontal distance between the initial position to the pulley is M2 + DX as shown.
(3)   If the string is non-stretchable, the constant force F would have dropped a distance = M1 ? M2.  This distance is slightly more than dX
(4)   The length of the pendulum string is L = 1 meter
(5)   Pythagoras theorem tells us that M1*M1 = dH* dH + (dX+M2)*(dX+M2)
(6)   The Mass of the bob = 60 Kg
(7)   The acceleration due to gravity = 9.8m/s/s
(8 )   The constant force F = 1/6 that of the weight = 1/6 Mg
(9)    The final angle is given by tan(a) = F/Mg = 1/6 = 10.46 degrees

Using the Excel Spreadsheet program, we can determine that
(1)   The vertical displacement of the bob = dH = L(1-cos9a))
= 0.013599 meters
(2)   The horizontal displacement of the bob = dX = Lsin(a)
= 0.164359 meters
(3)   (M2+dX) = sqrt((M1*M1) ? (dH*dH)) = 1.99954 meters
(4)   M2 = 1.835595 meters
(5)   M1-M2 = 0.164405 meters

Thus the potential energy (mgh) gained by the 60 unit bob
= 60*9.8*0.013599 = 7.99645 joules

The work done by the constant force F of 10 units
= 10*9.8*(M1-M2) = 10*9.8*0.164405 = 16.11171 joules

This more exact analysis still shows that the work done or energy supplied by the constant force F in pendulum12.jpg is different from the potential energy gained by the 60 kg weight.

This means that we cannot close our eyes and apply the Law of Conservation of Energy.  We must do a detailed force, displacement, work and energy analysis.

Pendulum12.jpg can be verified by experiment.

Can any one find any errors in the mathematics???

And the funniest part is this:

You have applied external work of 16 joules. As per pulley's functioning, equal and opposite work is transferred to pendulum system. No wonder your vertical work done is less than work supplied by external force. Because as pendulum has moved horizontally and vertically, addition of both works should be equal to 16 joules (Ignoring friction and air resistance) . Am i correct?  So where is the problem? You additional work supplied will always be more that work done on pendulum system and that is law of conservation of energy!  You just proved it works!
lol. i guess you are mixing these two works and thats why dividing and showing the factor of 2. You two units of horizontal energy leading one unit of vertical energy is based on this falacy. It means if you supply two times external work, you get 1 time internal work done in vertical direction. Where is the horizontal internal work done on pensulum system?

so 2 times horizontal work supplied = 1 time vertical work + 1 time horizontal work. That is the law of conservation of energy.

[Top Gun]

so 2 times horizontal work supplied = 1 time vertical work + 1 time horizontal work. That is the law of conservation of energy.

Please analyze the last term of your statement ?+ 1 time horizontal work? mathematically. 

[Koen1]

well it comes down to a simple
"input = output".
zero excess output.

And I still think you can't input a constant force in an oscillating system
if you want to keep it oscillating... Only pulsed input will be usefull.

you do seem to realise you need to input energy for the system to do anything...
Then why is it so difficult to understand that there needs to be excess energy
input for any excess energy output to occur?