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. What that means is that if two things crash into one another we can use their combined momentum before the crash to predict what will happen after the collision.
When I drop one of these balls with a mass of say one ball, it will have a set speed at the bottom. When it collides with the other balls let the ball go it will push exactly one ball up at the same speed on the other side. Now that we know that, what will happen if I drop two balls together? What about 3? For fun I like to go through all the balls up to and including just swinging all of them as technically it still works and the kids usually laugh at that.
Not only does this show us that momentum and energy must be conserved, but also that we can use our understanding of physics to predict what will happen! This, however, is better shown with the Happy and Sad Ball demonstration. Conservation of energy can be brought up, as well as conversion from potential to kinetic energy when lifting and letting the balls go. A good demonstration to follow up with would be the Large and Small Ball Collision demonstration.
Back to Top. Newton's Cradle. During the first swing maximum momentum for ball 1 and 2 during its descent were 6. Table 4 shows that balls 4 and 5 reach maximum momentums of 6. Balls 1 and 2 reach maximum momentum values of 5. Trial three consisted of starting the pendulum by pulling ball one, two and three away from the resting pack and releasing it. Please download pdf document for further details Bottom of page :.
Trial four consisted of starting the pendulum by pulling four balls away from the static and releasing them. Total momentum was calculated by adding together the individual velocities of each ball to gain the total active velocity this total was then multiplied by the mass to calculate total momentum. Total momentum was also used to individual ball momentums within the system can vary widely so by calculating the total momentum and velocity the likelihood of error is reduced.
Table 5 illustrates the total momentum values through swing 1, trial 1 the yellow highlighted row in each table represents contact point with the static balls.
Peak momentum for ball 1 occurs 4 frames before contact with the static balls with a value of 5. Ball 5 reaches its peak momentum of 5. Table 6 illustrates the total momentum values through swing 1, trial 2. Peak momentum for the active balls occurs 5 frames before contact with the static balls with a value of Balls 4 and 5 reach their peak momentum of Vertical displacement of the ball is calculated by measuring the maximum height of the balls COM to a line that runs through the balls static COM.
Point of maximum height and velocity were calculated by exporting the data, from Quintic Linear Analysis. The Gravitational constant was taken as 9. Appendix A shows the kinetic and potential energy of the five balls throughout the first pendulum swing.
Graph 1 illustrates the tabular data from Appendix A. The Graph shows that at the start of the swing, ball one has a potential energy value of 0. As the ball begins to descend down its arc, potential energy decreases as it is being converted in to kinetic energy. This is known as an inverse relationship, as one value increases the other decreases. 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. It's here, in the small time between the first ball's impact and the end ball's swinging out, that momentum is conserved.
When the ball reaches its peak, it's back to having only potential energy, and its kinetic energy and momentum are reduced to zero. Gravity then begins pulling the ball downward, starting the cycle again.
0コメント