# What part of momentum moves the boat in the inclined plane paradox experiment?

• I
• migyonne
migyonne
Hello and thank you for welcoming me to your forum!
To get started, I would like to give you a little help:
In the pattern experiment, when firing the cannon,
if part of the momentum reaches the bird,
and if another part of the momentum manages to stun the fish,
what part of the momentum would be likely to make the boat move?

It seems that there is no example on the internet... nor in physical science books...

Is this problem troubling you?

Why does the bird fly upside-down?

The boat moves left when you fire the cannon.
The boat stops when the ball hits the inclined plane.
The momentum is then divided in two, half down among the fishes, half up to the birds.

Juanda, russ_watters and PeroK
Thank you for your answer. So you deduce that no part of force moves the boat to the right?

Let's say that many people do not admit that a force can be distributed in 2 different vectors...
More precisely, there is only half of the force which presses in the horizontal vector. Do you agree with this deduction?

migyonne said:
Let's say that many people do not admit that a force can be distributed in 2 different vectors...
More precisely, there is only half of the force which presses in the horizontal vector. Do you agree with this deduction?
Force, impulse and momentum are vectors. Whether everyone accepts this is not a question of physics.

You can use conservation of linear and angular momentum to analyse the above problem. Note, however, that gravity and the water provide external forces to the system of boat + cannonball.

migyonne said:
So you deduce that no part of force moves the boat to the right?
Ideally, the force of firing the ball from the cannon will be exactly cancelled by the later deflection of the ball. Each time the cannon is fired, the boat will step to the left a small distance, while the ball is moving horizontally to the right.

Non-ideally, the powder used to fire the cannon will accelerate the boat to the left, but will be absorbed by the air over the boat, not deflected, causing the boat to continue very slowly to the left, while the air moves slowly to the right. If the duck is hit by the cannonball, while it is flying upside down, it will quack up.

phinds
In my idea, if the ball hits a straight plane, the boat does not move. here, one half makes it move to the left since the other half goes in a vertical vector (up and down)... the total momentum is however preserved... do you agree with that?

migyonne said:
In my idea, if the ball hits a straight plane, the boat does not move. here, one half makes it move to the left since the other half goes in a vertical vector (up and down)... the total momentum is however preserved... do you agree with that?
You need to be more precise. Note that momentum is conserved in each direction separately. In this case, both horizontal and vertical momentum are conserved.

PS it's not some overall magnitude of momentum that is conserved.

Indeed, I have to be more precise but also very careful.
In this image, do you think:

We replace the flat plane with an inclined plane as shown on BalanceB.

-If we do this experiment, will BalanceB display the same indication?
-If we place a test tube as indicated, will this test tube receive an impulse (red arrow)?
-Is there still part of the vertical momentum in this horizontal vector?
(Question 1 is the most important)

migyonne said:
Indeed, I have to be more precise but also very careful.
In this image, do you think:

We replace the flat plane with an inclined plane as shown on BalanceB.

-If we do this experiment, will BalanceB display the same indication?
-If we place a test tube as indicated, will this test tube receive an impulse (red arrow)?
-Is there still part of the vertical momentum in this horizontal vector?
(Question 1 is the most important)View attachment 336126
You are also confusing force with impulse, which is force over time. In the second case, there is less change in momentum in the vertical direction, so less impulse. This may lead to less maximum force.

However, the change in horizontal momentum means that there is a torque on the scales, so you would need to analyse the reaction force for this as well.

In any case, what shows on each scale will be a variable force.

Ibix
PS in either case vertical momentum is transmitted ultimately to the Earth. In the second case, horizontal momentum is also transmitted to the Earth. In both cases, its the Earth that ultimately provides an external force that changes the momentum of the object. Note in particular that a ball bouncing elestically off the ground does not show conservation of momentum. In this scenario (like your diagram on the left), the direction of the vertical momentum is changed and this represents a change in momentum.

I think your mistake is to see momentum as some sort of "scalar" quatity that there is only so much of. It's not like energy. Momentum is a vector. In a collision with an inclined plane there is an external horizontal impulse on the object that results in horizontal momentum. Likewise, there may be a vertical impulse that reduces the vertical momentum to zero.

@migyonne PF is not for discussion of personal projects.

## What is the inclined plane paradox experiment?

The inclined plane paradox experiment involves a boat on an inclined plane and explores the principles of momentum and forces acting on the boat. The paradox arises from the seemingly contradictory behavior of the boat when it moves up or down the incline, challenging our understanding of momentum and energy conservation.

## How does momentum play a role in the inclined plane paradox experiment?

Momentum, which is the product of mass and velocity, plays a crucial role in the experiment. The boat's momentum changes as it moves up or down the inclined plane, and this change is influenced by the forces acting on the boat, such as gravity and friction. The paradox often involves analyzing how these forces cause the boat to accelerate or decelerate, thereby affecting its momentum.

## What part of the boat's momentum is responsible for its movement on the inclined plane?

The component of the boat's momentum that is parallel to the inclined plane is responsible for its movement. This component is influenced by the gravitational force acting along the plane and any other forces, such as friction or an external push, that act in the same direction. The perpendicular component of the momentum does not contribute to the boat's movement along the plane.

## Why is there a paradox in the inclined plane experiment involving momentum?

The paradox arises because the intuitive expectations about the boat's behavior often conflict with the actual physical principles governing momentum and energy. For example, one might expect the boat to always move in a certain way when an external force is applied, but the distribution of forces and the resulting momentum changes can lead to unexpected outcomes, challenging our understanding of the system.

## How can the inclined plane paradox be resolved in terms of momentum conservation?

The paradox can be resolved by carefully analyzing the forces and the resulting momentum changes. By applying the principles of momentum conservation and Newton's laws of motion, we can account for all forces acting on the boat and predict its behavior accurately. Understanding the vector components of momentum and how they interact with the inclined plane is key to resolving the paradox.

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