Conservation of Linear momentum and Kinetic energy

In summary, the conversation discusses a scenario in which two masses are attached to a horizontal string without friction and moved away from the equilibrium position by an undefined distance. After passing through the equilibrium position, one of the masses is removed and the conservation of linear momentum is applied. The final kinetic energy of the system is derived and it is noted that the conservation of linear momentum does not apply in this scenario as it is not a closed system. This leads to the conclusion that the extra energy comes from the removal of one of the masses from the system.
  • #1
eonden
5
0
Suppose that we are working with a horizontal string with two masses attached. There is no friction on the floor and we move those two attached masses away from the equilibrium position by an undefined distance.
Once the string with those two attached masses passes through the equilibrium possition, we remove one of the attached masses.
As there are no forces present in that moment (as we are in the equilibrium position), we should apply the conservation of the linear momentum such that:
(m1 + m2 ) * v_slow = m1 *v_fast (as we remove the m2 with no speed)
So, we move from an initial Kinetic energy = ((m1+m2)*v_slow^2)/2
To a final Kinetic energy = (m1*v_fast^2)/2 from which we can derive using the conservation of the linear momentum --> ((m1+m2)^2 * v_slow^2)/(2*m1) and as ((m1+m2)^2)/m1 > (m1+m2), we have essentialy given energy to the system.
Can someone explain me where does this "extra" energy come from?
Thanks
 
Physics news on Phys.org
  • #2
eonden said:
Suppose that we are working with a horizontal string with two masses attached. There is no friction on the floor and we move those two attached masses away from the equilibrium position by an undefined distance.
What do you mean by "equilibrium position"? Please define the scenario you have in mind more completely.
 
  • #3
Doc Al said:
What do you mean by "equilibrium position"? Please define the scenario you have in mind more completely.

https://ecourses.ou.edu/ebook/dynamics/ch10/sec101/media/d0121.gif

We start from an original position and move the masses away from the origin to the maximum amplitude of the Simple Harmonic Motion. Once we get to that position, we let it contract by the spring force.
Sorry for not including a simple diagram with the doubt.
 
  • #4
If I understand you correctly, you want to remove part of the moving mass from the system at some point?
If so, then you can't use conservation laws - these work only for close systems.

In other words, if you magically remove one of the masses, the other one will not change velocity.
 
  • #5
eonden said:
https://ecourses.ou.edu/ebook/dynamics/ch10/sec101/media/d0121.gif

We start from an original position and move the masses away from the origin to the maximum amplitude of the Simple Harmonic Motion. Once we get to that position, we let it contract by the spring force.
Sorry for not including a simple diagram with the doubt.
I see one mass attached to a wall by a spring. Your first post mentions two masses attached by a string. Are you changing the scenario?

You pull the mass from the equilibrium position and let it go. So what? (I don't see what this has to do with conservation of momentum.)

Please restate your question with reference to the diagram.
 
  • #6
Bandersnatch said:
If I understand you correctly, you want to remove part of the moving mass from the system at some point?
If so, then you can't use conservation laws - these work only for close systems.

In other words, if you magically remove one of the masses, the other one will not change velocity.

Thanks, completely forgot that when talking about closed systems no matter can be exchanged.
Sorry for the stupid question.
 

Related to Conservation of Linear momentum and Kinetic energy

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, as long as there are no external forces acting on the system.

2. How is the conservation of linear momentum related to Newton's third law of motion?

The conservation of linear momentum is closely related to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This means that when two objects interact, the total momentum of the system remains constant.

3. What is the equation for calculating linear momentum?

The equation for calculating linear momentum is p = mv, where p is the momentum of an object, m is its mass, and v is its velocity. This equation can also be written as F = Δp/Δt, where F is the net force acting on an object and Δp/Δt is the rate of change of momentum.

4. How does the conservation of kinetic energy differ from the conservation of linear momentum?

The conservation of kinetic energy states that the total kinetic energy of a closed system remains constant, while the conservation of linear momentum states that the total momentum of the system remains constant. This means that in some cases, energy can be lost or transformed into other forms, but momentum remains the same.

5. Can the conservation of linear momentum and kinetic energy be violated?

No, the conservation of linear momentum and kinetic energy are fundamental laws of physics and have been extensively tested and proven. In isolated systems, these principles hold true and cannot be violated. However, in real-world situations, external forces and other factors may affect the conservation of these quantities.

Similar threads

An intuitive understanding of momentum and kinetic energy
    • Mechanics
Replies
11
Views
1K
Energy transformed in a collision
    • Mechanics
Replies
5
Views
987
Spin created due to an Elastic Collision of two solid balls
    • Mechanics
Replies
4
Views
2K
Calculating Final Positions & Velocities for M1, M2 & Spring After DeltaT
    • Mechanics
Replies
6
Views
959
Inelastic Collision: Kinetic Energy vs Momentum
    • Mechanics
Replies
11
Views
2K
Conservation of linear momentum when wheels are included
    • Mechanics
Replies
11
Views
2K
B Conservation of momentum in a closed system
    • Mechanics
Replies
3
Views
996
Reduce Kinetic Energy Losses when Two Objects Collide
    • Mechanics
Replies
3
Views
1K
I Drag equation - relative flow velocity
    • Mechanics
Replies
11
Views
2K
Confusion about work done by friction as negative or positive
    • Mechanics
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top