# Impact of 2 rigid beam without energy loss has multiple slns

• trytodoit
In summary, the discussion revolved around the impact of two rigid beams assuming no energy loss. It was noted that there are three free variables and only two equations, resulting in an infinite number of combinations. It was also mentioned that the system may be underconstrained due to the contact line between the beams. The assumption of no horizontal force may not provide a helpful constraint.
trytodoit
Today, I discussed my friend about two rigid beams impact and assuming no energy loss in the impaction.

As in the above figure, the upper beam move down with a uniform velocity ##v_c##, and hit a beam with ##0## velocity. After that the above beam will rotate and move away, which can be described by left end velocity ##v_l## and right hand velocity ##v_r##; the lower beam will rotate around the pined point at a angular velocity ##\omega##. Therefore, we have three free variables, but only to equations, one is conservation of angular moment, the other is conservation of energy. Consequently, there are infinite combination of these three variables, which is not intuitive.

For one rigid ball hit the beam, if there is no energy loss in the impaction, there will be only one solution. Why for two beams case, there are infinite number of combinations? If there are infinite combinations, what is the property that determine which combination of the three variable for the impaction?

It is probably a reasonable assumption that no horizontal force acts on the pivot during the collision (there is no friction!). That gives a third constraint, but I guess that does not help as your degrees of freedom don't consider horizontal motion at all.

Hmm... in general it is not surprising that systems are underconstrained if you have a contact line instead of a single point. Your system will react completely different if the left side would be a tiny bit ahead compared to the right side a tiny bit ahead, for example.

mfb said:
It is probably a reasonable assumption that no horizontal force acts on the pivot during the collision (there is no friction!). That gives a third constraint, but I guess that does not help as your degrees of freedom don't consider horizontal motion at all.

Hmm... in general it is not surprising that systems are underconstrained if you have a contact line instead of a single point. Your system will react completely different if the left side would be a tiny bit ahead compared to the right side a tiny bit ahead, for example.
The no horizontal force seems auto satisfied, which cannot introduce a equation into the system.

## 1. What is the impact of having 2 rigid beams without any energy loss?

The impact of having 2 rigid beams without any energy loss is that the system will have multiple solutions. This means that there will be more than one possible solution to the problem, making it more complex to analyze and solve.

## 2. Can you explain the concept of "rigid beam" in this context?

In this context, a rigid beam refers to a structure that is able to maintain its shape and resist deformation under external forces. This means that the beam will not bend or flex, and any external forces applied to it will be transmitted through the beam without any energy loss.

## 3. How does the absence of energy loss affect the solutions in the system?

The absence of energy loss means that the energy in the system is conserved. This can lead to multiple solutions as the system has more degrees of freedom and can take on different configurations while still maintaining energy balance.

## 4. Are there any real-world applications for this concept?

Yes, there are many real-world applications for this concept. For example, in engineering and construction, rigid beams are used to support structures such as bridges and buildings. The absence of energy loss in these structures ensures their stability and durability.

## 5. How can the impact of 2 rigid beams without energy loss be mitigated?

The impact of 2 rigid beams without energy loss can be mitigated by carefully considering and analyzing all possible solutions and their potential effects. This may involve using computer simulations or physical models to test different configurations and determine the most optimal solution.

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