As discussed above, when the balls collide, momentum must be conserved. So we know that:. This leaves us with two unknowns, the final mass and the final velocity, so we need another equation. Since we know that this is an elastic collision, energy must be conserved so we can also use:. Putting this back into the momentum equation we see that if the mass must be the same, then the velocity must also be the same:.
This is always what happens with the cradle. Whenever a set number of balls is dropped on one side, the same number of balls go up on the other side to approximately the same height which was shown to be directly related to velocity.
This is a great demo to start with. Most people have seen it and it is very simple and easy to understand visually. The physics behind the demo section goes into much more detail than is necessary; the point of this demo is to explain simply, that momentum must be conserved. The best method is to explain, ask a question, then check with the demo. For younger students there is no need to go into the math. Each tab contains a different method for presenting this demo as written by a former outreach student.
This demonstration shows what [conservation of momentum] is. First off, does anyone know what momentum is encourage any response, right or wrong, and try to use them to lead to the next part? That means the heavier something is or the faster it is moving, the more momentum it has. So which would have more momentum, a semi-truck going 50 miles an hour or a motorcycle going the same speed? The useful thing about momentum is that it must be conserved.
This continuous clicking of balls is also proof of Newton's law of the conservation of energy, which states that energy can't be created or destroyed but that it can change forms. Newton's Cradle demonstrates this last part of the law quite well, as it converts the potential energy of one ball into kinetic energy that is transferred down the line of balls and ultimately results in the upward swinging of the last ball.
Follow LiveScience livescience. Live Science. Elizabeth Palermo. Changing the density of a material will change the way energy is transferred through it. Consider the transmission of vibration through air and through steel; because steel is much denser than air, the vibration will carry farther through steel than it will through air, given that the same amount of energy is applied in the beginning. So, if a Newton's cradle ball is, for example, more dense on one side than the other, the energy it transfers out the less-dense side might be different from the energy it received on the more-dense side, with the difference lost to friction.
Other types of balls commonly used in Newton's cradles, particularly ones meant more for demonstration than display, are billiard balls and bowling balls , both of which are made of various types of very hard resins.
Amorphous metals are a new kind of highly elastic alloy. During manufacturing, molten metal is cooled very quickly so it solidifies with its molecules in random alignment, rather than in crystals like normal metals. This makes them stronger than crystalline metals, because there are no ready-made shear points.
Amorphous metals would work very well in Newton's cradles, but they're currently very expensive to manufacture. The law of conservation of energy states that energy -- the ability to do work -- can't be created or destroyed. Energy can, however, change forms, which the Newton's Cradle takes advantage of -- particularly the conversion of potential energy to kinetic energy and vice versa.
Potential energy is energy objects have stored either by virtue of gravity or of their elasticity. Kinetic energy is energy objects have by being in motion. Let's number the balls one through five. When all five are at rest, each has zero potential energy because they cannot move down any further and zero kinetic energy because they aren't moving.
When the first ball is lifted up and out, its kinetic energy remains zero, but its potential energy is greater, because gravity can make it fall. After the ball is released, its potential energy is converted into kinetic energy during its fall because of the work gravity does on it. When the ball has reached its lowest point, its potential energy is zero, and its kinetic energy is greater. Because energy can't be destroyed, the ball's greatest potential energy is equal to its greatest kinetic energy.
When Ball One hits Ball Two, it stops immediately, its kinetic and potential energy back to zero again. But the energy must go somewhere -- into Ball Two.
Ball One's energy is transferred into Ball Two as potential energy as it compresses under the force of the impact. As Ball Two returns to its original shape, it converts its potential energy into kinetic energy again, transferring that energy into Ball Three by compressing it. The ball essentially functions as a spring.
This transfer of energy continues on down the line until it reaches Ball Five, the last in the line. When it returns to its original shape, it doesn't have another ball in line to compress.
Instead, its kinetic energy pushes on Ball Four, and so Ball Five swings out. Because of the conservation of energy, Ball Five will have the same amount of kinetic energy as Ball One, and so will swing out with the same speed that Ball One had when it hit. One falling ball imparts enough energy to move one other ball the same distance it fell at the same velocity it fell. Similarly, two balls impart enough energy to move two balls, and so on. But why doesn't the ball just bounce back the way it came?
Why does the motion continue on in only one direction? That's where momentum comes into play. Momentum is the force of objects in motion; everything that moves has momentum equal to its mass multiplied by its velocity. Like energy , momentum is conserved. It's important to note that momentum is a vector quantity , meaning that the direction of the force is part of its definition; it's not enough to say an object has momentum, you have to say in which direction that momentum is acting.
When Ball One hits Ball Two, it's traveling in a specific direction -- let's say east to west. This means that its momentum is moving west as well.
Any change in direction of the motion would be a change in the momentum, which cannot happen without the influence of an outside force. That is why Ball One doesn't simply bounce off Ball Two -- the momentum carries the energy through all the balls in a westward direction.
But wait. The ball comes to a brief but definite stop at the top of its arc; if momentum requires motion, how is it conserved? It seems like the cradle is breaking an unbreakable law.
The reason it's not, though, is that the law of conservation only works in a closed system , which is one that is free from any external force -- and the Newton's cradle is not a closed system. As Ball Five swings out away from the rest of the balls, it also swings up. As it does so, it's affected by the force of gravity, which works to slow the ball down. A more accurate analogy of a closed system is pool balls : On impact, the first ball stops and the second continues in a straight line, as Newton's cradle balls would if they weren't tethered.
In practical terms, a closed system is impossible, because gravity and friction will always be factors. In this example, gravity is irrelevant, because it's acting perpendicular to the motion of the balls, and so does not affect their speed or direction of motion. The horizontal line of balls at rest functions as a closed system, free from any influence of any force other than gravity.
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