# Conditions for conservation of momentum

• Krushnaraj Pandya
In summary, for the classic wedge and block system with friction between the block and wedge, but not between the wedge and table, and all other surfaces being smooth, the momentum in the horizontal direction will be conserved if the system is considered as a whole. However, if only the block or wedge is considered individually, there will be external forces (friction) acting on them, resulting in a change in momentum in the horizontal direction.
Krushnaraj Pandya
Gold Member

## Homework Statement

Consider a classic wedge and block system, (block on top of wedge(inclination theta)). there is friction between the block and wedge (not enough to prevent block from sliding). All other surfaces are smooth. For the motion that follows after releasing the block from rest, is momentum in the horizontal direction conserved?

## Homework Equations

There is no exact formula for momentum conservation but I guess p1=p2 in general

## The Attempt at a Solution

Momentum is conserved when net external force is zero. Since friction is an internal force here momentum conservation should be applicable along x-axis but it seems counter-intuitive so I'm just confirming

Last edited:
Krushnaraj Pandya said:

## Homework Statement

Can we apply momentum conservation in the horizontal direction if friction is present between the wedge and block and nowhere else, I suppose we can since friction here is an internal force (although we can't apply energy conservation since friction is dissipative) but it feels somewhat counter-intuitive so just making sure. Thank you very much

all relevant

## The Attempt at a Solution

Mentioned above
Can you provide a more complete statement of the problem in (1), include the relevant equations instead of using a wild card in (2) and explain your reasoning in (3) separately from (1)? The template is meant to be used so that we can understand what's on your mind and what difficulties you have. Thank you.

kuruman said:
Can you provide a more complete statement of the problem in (1), include the relevant equations instead of using a wild card in (2) and explain your reasoning in (3) separately from (1)? The template is meant to be used so that we can understand what's on your mind and what difficulties you have. Thank you.
Alright, sorry. I've changed it- thanks for pointing it out :D

We don't know what "the wedge and the block" are or what you're trying to analyze.

An internal force is one between components of a system, and that depends on where you draw the boundaries of your system. If I catch a ball and I consider the ball to be the system, then I am an external force. The ball's momentum changes. But if I am standing on ice I might want to include myself as part of the system, in which case the action of my catching the ball is considered an internal force, and the total momentum of the system (myself and ball) is unchanged.

RPinPA said:
We don't know what "the wedge and the block" are or what you're trying to analyze.

An internal force is one between components of a system, and that depends on where you draw the boundaries of your system. If I catch a ball and I consider the ball to be the system, then I am an external force. The ball's momentum changes. But if I am standing on ice I might want to include myself as part of the system, in which case the action of my catching the ball is considered an internal force, and the total momentum of the system (myself and ball) is unchanged.
Lets say I want to find the velocity of the wedge when the velocity of the block is given. Considering the block+wedge as the system, can I write initial momentum=final momentum. Its a simple question really :D
Here's an image-

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RPinPA said:
in which case the action of my catching the ball is considered an internal force, and the total momentum of the system (myself and ball) is unchanged.
So I guess yes. This is the same case since there is friction between your hand and the ball

Also I just found a solved example in my book which states the same thing so my question is solved. Thank you very much, the "ball catching" analogy was really helpful

Krushnaraj Pandya said:

## Homework Statement

Consider a classic wedge and block system, (block on top of wedge(inclination theta)). there is friction between the block and wedge (not enough to prevent block from sliding). All other surfaces are smooth. For the motion that follows after releasing the block from rest, is momentum in the horizontal direction conserved?

If your system is the block and wedge then yes. There are no external horizontal forces, no friction between wedge/block and table, so the table is irrelevant in the horizontal plane.

If your system was just the block then no. There is an external force (friction with the wedge) that has a horizontal component.

If your system was just the wedge then no. There is an external force (friction with the block) that has a horizontal component.

## What is conservation of momentum?

Conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time, regardless of any external forces acting on the system.

## What are the conditions required for conservation of momentum?

In order for momentum to be conserved, the system must be closed, meaning that there are no external forces acting on the system. Additionally, the system must be isolated, meaning that there is no exchange of momentum with any other external objects.

## Can momentum be created or destroyed?

No, momentum cannot be created or destroyed. It can only be transferred between objects within a closed and isolated system. This is known as the principle of conservation of momentum.

## How does conservation of momentum apply to collisions?

In a collision, the total momentum before the collision is equal to the total momentum after the collision. This means that the net momentum of the system remains constant, even though the objects involved may change their velocities.

## Does conservation of momentum have any real-life applications?

Yes, conservation of momentum has many real-life applications, such as in rocket propulsion, car safety, and sports. By understanding the principles of conservation of momentum, scientists and engineers are able to design and create more efficient and safer technologies.

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