Editing Newton Beads (section)

== Why This Works ==

===Short Explanation===
The Newton Beads are a good way to show how ''Force'' and ''Energy'' are connected. When we set the buckets up, the beads in the high bucket have some ''Potential Energy'', or the potential for work. When they start to fall, the falling beads have ''Kinetic Energy'', or are doing physical work. This happens largely due to the ''Force of Gravity'', the force that pulls us down towards the Earth. But, we show that we can affect how fast the beads are falling by adjusting two things: the distance they travel, and the resistance they experience. If we adjust the height, we are adjusting how much Potential Energy is available. The higher we put the first bucket, the more Potential Energy is available, and the faster the beads can fall. If we grab the beads at the top of the falling string, we are applying ''Friction'', or a resisting force to the motion. If we only close our hand weakly around the beads, they can continue to fall, but at a lower speed. If we grab them tightly, they stop!

===Full Explanation===
This demonstration is primarily showing how a balances of forces affects the overall flow rate of the system. For this particular system, the forces of tension, gravity, and friction are all active, and each plays a different role in how the system flows.
* ''Tension'' is a measure of the force exerted across the length of the string of beads. The tension in the string of beads is not consistent throughout the entire chain, but rather can be measured at three different points: Just above the table, in the curve over the lip of the upper bucket, and at the floor inside the lower bucket.
* The ''Gravitational Force'' is the force of gravity all objects on the earth experience. The force of gravity over the system can be measured at the same points as for tension above.
* ''Friction'' is a resisting force. In this system, there is friction to be calculated at each of the points mentioned for tension above.
When the beads start falling from the upper bucket, we can calculate the tension, force of gravity and friction for each of the mentioned situations to find the direction the force is applied:
{| class="wikitable" style="color:black; background-color:#ddd; text-align: left; margin-right: auto"
|+ Direction of Forces
| '''+''' = up
'''-''' = down 
| Tension
'''T''' = ('''m'''/'''l''') * '''v'''<sup>2</sup>
| Force of Gravity
'''F'''<sub>g</sub> = '''m''' * g 
| Friction
'''F'''<sub>f</sub> = '''F'''<sub>g</sub> * '''µ''' 
|-
|Above the Table || + || - || +
|-
|Curve Over the Lip || + || - || +/-
|-
|Above the Floor || + || - || -
|}

The tension in the system is always positive, while the force of gravity is always negative. This is because the tension in the string is generated by the force of gravity acting on the string. For each unit length of the string, it has a set amount of mass (The '''m'''/'''l''' in the Tension equation refers to this). This mass is affected by the acceleration of gravity, which gives us the force of gravity. The acceleration of gravity on the string generates a velocity, which gives us the tension. These two forces counteract each other, as the tension in the string is constantly pushing up and against the force of gravity. But why does the tension push up? Simply put, it is because of all the non-moving beads! the tension of the string is pushing on the pile of still beads in the buckets. This means that the string in the bucket on the table is pushing off the beads below it, against the force of gravity!

The direction of the friction notably changes throughout the string's movement, due to ''where'' the friction is being generated. For the bucket on the table, the friction being applied is from the curve above. This curve minimizes the force of gravity applied downward into this bucket, and allows the tension to overcome and lift the beads up! However, once over the bend the friction in the curve is now working alongside the force of gravity. This causes the tension to lose the uphill battle, resulting in the beads being pulled down into the bucket on the floor!

Although this demonstration is often used to describe the balance between kinetic and potential energy, that isn't entirely true when looking at the system. There is a definite energy transfer happening; The bucket on the table has potential energy, and as the beads fall out of it they do have kinetic energy. However, this does not give a full answer to the system, especially if you do this demonstration with a strand of metal beads and see the curve form above the lip. In this case, the tension in the strand is causing it to stand up and against the force of gravity, even as it continues to be pulled down!