The problems with one pendulum transferring its motion to another pendulum are the mass of the rod and flex. I am guessing that a great deal of the motion is used up to move the rod and to flex the rod.
Ok, The WM2d Sim also had the same outcome. In WM2d you can create a perfect Newtons Cradle, using perfect world settings. So WM2d conserves momentum between masses of equal weight,( just like real world,) but comes up short with no rod weight, no rod flex, and no heat loss. What I am saying, is that this type of simulated collision can be made to follow real world, and perfect world conditions, and accurately, and predict situations like this.
In my build, I considered the rod weight and built to compensate for this (see the extra marbles glued in place), Even considering the real world rod flex in my build, a significant amount more energy is required to be put into the system to achieve even close to the 2x height that is predicted by these maths, which I now believe to be (unfortunately) wrong.
I will be happy to be wrong if someone else produces a build that contradicts my findings.
Edit: original text removed, not sufficiently on topic.
Tarsier79
I will be happy to be wrong if someone else produces a build...
I don't think it is necessary to produce a build. I think I can comment based on pure observation of the second part of the simulation titled "Elasticity 1". For my conclusion to be correct, the assumption is the small mass is 1/2 the mass of the larger.
What is observable in the Elasticity 1 simulation:
The smaller mass appears to accelerate at near twice the rate of the larger mass when it is released.
The smaller mass reaches a height of more than 90% of the height of the larger mass before its release.
That smaller mass may have a final velocity two times what the larger mass had at the moment of collision.
In this sim, I would conclude a complete transfer of momentum to the smaller mass.
(I don't know why the large mass appears to rebound unless the elasticity of the white ball is somewhat low).
In the M_Xfer video:
It is not clear to me why you thought the smaller mass would gain twice the height when the collision occurred with a pendulum. After all, it's not a lever or pulley.
Historically; ballistic pendulums have been used to prove that momentum is conserved in the interaction of objects. Tarsier:Your two unequal pendulum experiment is a lever arraignment but is still a ballistic pendulum.
My experiments with superimposed wheels (12 inch wheel on a 18 inch wheel) prove that energy can indeed be made with levers, and that momentum is always conserved.
I think you are running into both the spring and flex problem.
Good to be back. Got out of hospital Saturday after a week's visit. Survived again! ;-)
Thought about an example that may make it clearer. Imagine you have some thrusters that produce 1/4 pound thrust for 1/4 second. If you put 4 of them behind a pound you get 8 feet per second which gets you 1 foot of rise in earth's gravity well. If you burn them one at a time behind a 1/4 pound mass you end up with 32 feet per second which gets you 16 feet kinetic energy.
Does that make it clearer?
Not knowing is not the problem. It is the knowing of what just isn't so.
It is our responsibilities, not ourselves,that we should take seriously.
It is not clear to me why you thought the smaller mass would gain twice the height when the collision occurred with a pendulum. After all, it's not a lever or pulley.
Using the conservation of momentum, a half weight should reach 4x the height with a complete transfer.
With the "Elasticity 1" sim, I stand corrected, the transfer isn't complete, as the heavier weight should come to a complete stop. Even though it doesn't, and taking into account the height gained on rebound, it still reaches just under 2x. I did have another sim that did show a complete transfer, but will have to dig it up.
ADD:
Peq, could you point me to the location of that particular experiment? I think I will have to make some time to go through some of your extensive energy thread.
The discussion of the experiment you ask for is posted on Oct. 12 and 13. Very simply it states that a 2 kilogram rim with a radius of 9 inches is as easily rotated as a 3 kilogram rim at 6 inches. So after the application of the same force for the same time you can get 2 kilograms moving 3m/sec or 3 kilograms moving 2m/sec. this is the same momentum but not the same energy; and it is the use of levers to make energy. A wheel is a lever.
Our discussion shows that I violated my own rules. I didn't analyze your simulation completely, but just jumped on a couple of points of discussion, sorry. My rules are to remind myself to think clearly and carefully and tell myself that as a non-engineer and non-physicist, design what you choose, but only if you understand the underlying physics. Then, later, you can use your design as input to those physics maths thingies to obtain the values. When I first used WM2D, there were many problems with unseen (to me) forces, and occasionally there still are (smile). One of the most important lessons I learned was, analyze all the forces on scratch paper before investing time and energy into a simulation.
I originally wrote:
It is not clear to me why... the smaller mass would gain twice the height when the collision occurred at the midpoint with a pendulum. After all, it's not a lever or pulley.
When posting, I removed the words "at the midpoint". I thought they were extraneous because in the the video, it was rather obvious. My mistake.
The real issue here is... this is not purely a momentum exchange sim. This is a force simulation, and I could analyze the momentum later. First, as written earlier, I should analyze all the forces on scratch paper. I have two masses to consider. I plan to suspend the masses with rope, and the collision impact will not be on the smaller mass. It will be halfway up the pendulum and that is a consideration. It won't receive the collision force directly, but will receive a force as a result of the collision and maybe jerk energy. I would think the rope would deflect, but it could be modeled differently.
If I next consider the force applied to the smaller mass, I determine that after the collision, the rotating smaller mass will accelerate to a particular velocity and begin to rise. Oops!... rotating... rise... gravity. Gravity will also accelerate the mass, but with a different vector. I'm not going to get the height I originally expected.
WM2D, generally used for earth based designs, defaults to "Vertical" earth gravity.
If it wasn't a requirement to use rope in this simulation, I would use solid rods for pendulum material. Using the rectangle tool, draw a long narrow pendulum rod. Using a mouse, about the best you can hope for is a 1" wide rod. To change the width to actually appear narrow like a rod, just draw it reasonably narrow and then easily adjust the width to 0.500 in. using the Coordinates box at the lower left of the workspace.
If the Coordinates box is not visible, then, from the top menu, View --> Workspace --> Navigation --> Coordinates (check the box).
I had a moment of humor as I finished reading your post. A thought popped into mind of that scruffy, ex-drunk pilot in Independence Day who took down the alien ship, immediately after saying: "I'm baaa ack". I had to flick my vision to rereading the first words of your post. Good that you are back, and thanks for starting such a valuable thread.
The real issue here is... this is not purely a momentum exchange sim. This is a force simulation,
Agreed, every sim is a force simulation. I believe the subject of this thread is about using leverage in conjunction with a momentum transfer to achieve a gain in PE. Hence the sim and experiment.
Peq Thanks for that reference to your experiment. There are a few points I am slightly unsure of, but may do some testing to confirm these points.
I think the difference is the point of application of the force. Obviously, with two different length pendulums, gravity is going to be acting upon the pendulums at radii and therefore affects them differently... Hence the difference in time it takes for these to fall through the same angle.
What would be interesting, is dropping the two differing weights on a flywheel at the different radii and from the calculated height gain to see if the wheel is accelerated to the same speed in both cases.
velocity increase of wheel should be directly proportional to momentum added to it ie momentum of wheel should increase by that added to it. Anything else is illogical. Likewize momentum subtracted is proportional to momentum not where.
Not knowing is not the problem. It is the knowing of what just isn't so.
It is our responsibilities, not ourselves,that we should take seriously.
Yes: and there will be a point on the radius of the wheel that represents the average rotational inertia of the wheel. Different balanced wheels vary in the distribution of mass so that average point will also vary from wheel to wheel. Once you determine where that point is you can make all your calculation as if the wheel were a point mass. If you double the velocity of that point mass then you have doubled the momentum of the wheel.
This average point will move when you drop a ball onto and into the wheel, and the wheel will become unbalanced. So you would have to start with an unbalanced wheel at rest that is balanced by the incoming ball. But it should work. And of course a ball with 3 units of mass at 2 units of distance along the radius should equal 2 units of mass at 3 units of distance.
This should be a good experiment, the total momentum of the ball should equal the total momentum of the ball and wheel after the two combine.
I am working on another throwing wheel, so have fun Tarsier.
