The inclined plane paradox (proved)

In summary, the inclined plane paradox involves a scenario where a block slides down an inclined plane, raising questions about the nature of acceleration and gravitational potential energy. The paradox is resolved by examining the forces acting on the block, showing that while the block accelerates down the incline, it does so in a way that conserves energy and adheres to Newton's laws of motion. The proof illustrates that the motion of the block can be accurately described using basic principles of physics, demonstrating that the paradox arises from a misunderstanding of the dynamics involved.
  • #1
migyonne
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Hello, I invite you to watch this video.
This is a simple experiment, which has never been carried out and which proves that momentum can undergo a 'repartition'...

[URL='https://youtu.be/JoM59at8cnY?si=lNA4tjiOihXwZ3U2]The Beauty of Momentum[/URL]

What do you think of this phenomenon ?
What conclusion can we draw from this?
Thanks a lot for your answers.
 
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  • #2
You bounce a ball bearing moving horizontally (a) off a vertical surface mounted on a cart; then (b) off a 45° sloped surface mounted on a cart. In case (a) the ball bounces directly back, so the cart gains more momentum than in case (b) where the ball is deflected upwards but continues in the same direction as the cart moves.

There's nothing there that's novel, nor remotely unusual, let alone paradoxical.
 
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  • #3
Ibix said:
There's nothing there that's novel, nor remotely unusual, let alone paradoxical.
what he said (very small).jpg
 
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  • #4
Thank you so much!
Do you have an experience reference or a formula, please?
It is very important for my studies
 
  • #5
migyonne said:
Thank you so much!
Do you have an experience reference or a formula, please?
It is very important for my studies
Well, it's basic Newtonian mechanics. How much have you studied momentum and elastic (that is, ideal) collisions?
 
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  • #6
This should be covered in any basic mechanics class. All that is needed is the basics of inelastic collisions including a coefficient of restitution. What you want to do is to open an introductory textbook.
 
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  • #7
It's a very messy experiment, unfortunately. In an ideal case you just need conservation of energy, momentum, and angular momentum. But because your equipment is very far from ideal (the cart is made of Duplo, if I am not mistaken) you need to worry about static and dynamic friction and other such losses. Also, your system is not closed, clearly transferring momentum to the Earth. A quantitative analysis would be challenging.

The ideal case is do-able I think, but I doubt it will come anywhere near matching what you see.
 
  • #8
Orodruin said:
This should be covered in any basic mechanics class. All that is needed is the basics of inelastic collisions including a coefficient of restitution. What you want to do is to open an introductory textbook.
I think he more needs to study elastic collisions, like the one in his example (link), but both would be a good idea.
 
  • #9
Thread level changed I-->B.
 
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  • #10
phinds said:
I think he more needs to study elastic collisions, like the one in his example (link), but both would be a good idea.
What makes you think the collisions are elastic? Just the fact that the cart jumps off the ground means it is not.
 
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  • #11
phinds said:
I think he more needs to study elastic collisions, like the one in his example (link), but both would be a good idea.
I'm with Orodruin on this one. The friction in this demo is crazy. If you can lay your hands on a Duplo cart I invite you to spin a wheel - precision engineering they are not.

Learning elastic collisions is probably something OP needs to do first, but this is very much an inelastic problem.
 
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  • #12
Ibix said:
If you can lay your hands on a Duplo cart I invite you to spin a wheel - precision engineering they are not.
As coincidence would have it, I am not unlikely to step on a Duplo cart when I make my way towards the bed shortly ... 😂

Edit: Not a Duplo cart, but a piece of a wooden puzzle … Generally I would say not rolling without resistance is a design feature of Duplo carts. It keeps parents’ backs unbroken.
 
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  • #13
Ibix said:
Learning elastic collisions is probably something OP needs to do first, but this is very much an inelastic problem.
It is, but I find the easiest path to understanding these problems is to analyze them in the absence of friction, then try to form an intuition for how friction changes that idealization.
(Of course that's just me, and I won't argue with anyone who prefers a different path)
 
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  • #14
What sleight of hand is needed to make this work?
migyonne said:
[URL='https://youtu.be/JoM59at8cnY?si=lNA4tjiOihXwZ3U2]The Beauty of Momentum[/URL]
 
  • #15
Hello,
Do you want to talk about the experience or the 'truncated' video link?
 
  • #16
sophiecentaur said:
What sleight of hand is needed to make this work?
Copy and paste the URL, deleting the question mark and everything after it.
 
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  • #17
It is missing a ’ after mentor edit. Originally it mixed up the URL and display text.
 

FAQ: The inclined plane paradox (proved)

What is the inclined plane paradox?

The inclined plane paradox refers to the counterintuitive result that the work done in moving an object up an inclined plane is the same as lifting it vertically to the same height, despite the different paths taken. This paradox highlights the principles of mechanical advantage and conservation of energy in physics.

How is the inclined plane paradox resolved?

The paradox is resolved by understanding that while the force required to move the object up the inclined plane is less than lifting it vertically, the distance over which the force is applied is greater. The product of force and distance, which is the work done, remains the same in both cases, consistent with the conservation of energy.

What role does friction play in the inclined plane paradox?

Friction adds an additional force that must be overcome when moving an object up an inclined plane. In real-world scenarios, the work done against friction must be included in the total work calculation. However, the fundamental principle that the work done against gravity remains the same still holds true in the absence of friction.

Can the inclined plane paradox be demonstrated experimentally?

Yes, the inclined plane paradox can be demonstrated experimentally using a setup with a smooth inclined plane, a pulley system, and weights. By measuring the force required to move an object up the plane and comparing it to the force required to lift the object vertically, one can show that the total work done is the same, confirming the theoretical prediction.

Why is the inclined plane important in understanding mechanical advantage?

The inclined plane is a classical example of a simple machine that illustrates the concept of mechanical advantage. By spreading the required lifting force over a longer distance, the inclined plane reduces the effort needed to raise an object, making it easier to move heavy loads. This principle is foundational in the study of mechanics and engineering.

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