Conservation of Linear Momentum problem help

In summary, the conversation discusses a problem involving a block and a wedge on a horizontal table, with all surfaces being frictionless. The goal is to find the velocity of the wedge when the block touches the table. The attempt at a solution involved using the conservation of momentum in the x and y directions, but there were concerns about the y direction not being conserved. However, it is confirmed that conservation of momentum is not necessary and will automatically be accounted for in the equations from Newton's laws.
  • #1
wsender
4
0

Homework Statement


Having a little trouble with this problem. I've tried a few different manipulations using COM & COE and wasn't able to get it to fit the form.

"A block of mass m rests on a wedge of mass M which, in turn, rest on a horizontal table as shown in the figure. All surfaces are frictionless. If the system starts at rest with point P of the block a distance h above the table, find the velocity of the wedge the instant point P touches the table."



Homework Equations



KE+PE+W=KE+PE

P1=P2

See attached image file for solution and diagram.


The Attempt at a Solution



Tried using COM to solve this but ran into issues in the y direction regarding preservation.
 

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  • #3
wsender said:
Tried using COM to solve this but ran into issues in the y direction regarding preservation.
If your y direction is vertical, momentum is not conserved in the y direction. (The floor exerts a force.) But the horizontal component of momentum is conserved.
 
  • #4
Doc,

I worked that out as well and my Professor said that you can't use COM for any parts of the equation if either the X or Y component isn't conserved, is it true?
 
  • #5
wsender said:
Doc,

I worked that out as well and my Professor said that you can't use COM for any parts of the equation if either the X or Y component isn't conserved, is it true?
No, that's not true. (Perhaps you misheard him.) Momentum is a vector and it can be conserved in one direction but not another, which is the case here. There are no external horizontal forces on the system, so the horizontal component of momentum will be conserved.
 
  • #6
Doc Al said:
No, that's not true. (Perhaps you misheard him.) Momentum is a vector and it can be conserved in one direction but not another, which is the case here. There are no external horizontal forces on the system, so the horizontal component of momentum will be conserved.

No I definitely didn't mishear him. I brought up this exact point in class and he dispelled is validity. Thank you for confirming my suspicions.
 
  • #7
You don't have to assume conservation of momentum, it will automatically fall out of the equations from Newton's laws. Give it a shot.
 

Related to Conservation of Linear Momentum problem help

1. What is the Conservation of Linear Momentum?

The Conservation of Linear Momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time, regardless of any internal or external forces acting on the system. This means that the total momentum before a collision or interaction is equal to the total momentum after the collision or interaction.

2. How is the Conservation of Linear Momentum used to solve problems?

In order to solve problems involving the Conservation of Linear Momentum, one must first identify the system of interest and any external forces acting on the system. Then, using the principle of conservation of momentum, one can set up equations to solve for unknown quantities such as velocities or masses.

3. Can the Conservation of Linear Momentum be violated?

No, the Conservation of Linear Momentum is a fundamental law of physics and has been extensively proven to hold true in all physical systems. Any apparent violation of this principle is due to incomplete understanding or measurement errors.

4. What are some real-life applications of the Conservation of Linear Momentum?

The Conservation of Linear Momentum has numerous real-life applications, such as in car crashes, where the total momentum before and after the collision must be equal; in rocket launches, where the momentum of the fuel and exhaust gases must be balanced; and in sports, where the momentum of a moving object can be used to determine its speed and direction.

5. Are there any limitations to the Conservation of Linear Momentum?

The Conservation of Linear Momentum holds true for all closed systems, meaning that there are no external forces acting on the system. However, in real-life situations, there may be external forces that cannot be accounted for, such as air resistance, which may slightly affect the total momentum of the system.

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