Conservation of momentum and Mechanical energy

• ShizukaSm
In summary: Sure. If you include everything, then the total momentum will be conserved.How come? The table won't move, it's velocity will remain as 0.
ShizukaSm
Regarding momentum, and the "Law of conservation of linear momentum", my book states that it's more general than mechanical energy, since mechanical energy is only conserved for conservative forces, while linear momentum is conserved independent of the forces, as long as the sum of external forces is zero.

This really confuses me. Let's look at two situations:

Situation 1) Collision. When a collision between two balls occur, a vibration in the air is produced (the sound wave) which wastes a part of the energy, and thus mechanical energy isn't conserved. On the other hand, there are no external forces, so momentum is conserved.

Is this reasoning correct?

Situation 2) A ball is rolling on a table. There is friction. Ok, so, let's pick up our system as ball + table, in this case our momentum would be (Ball Momentum = x and Table momentum = 0), the friction force would be internal to the system, and yet we would lose momentum.
Now, for the mechanical energy part, friction would produce a certain heat, which would waste energy, and thus mechanical energy would also be reduced.

Is my second reasoning correct? And also, why isn't momentum conserved?

In the second case, momentum is conserved. Friction transfers the ball's momentum to the table, it does not just disappear.

How come? The table won't move, it's velocity will remain as 0.

ShizukaSm said:
The table won't move, it's velocity will remain as 0.
The table is attached to the earth. External forces come into play.

Doc Al said:
The table is attached to the earth. External forces come into play.

Fair enough, this will maybe seen stupid, but I really want to understand that, so let's pick up the system (earth + ball), in this case Earth's forces on the table would be internal to the system.

ShizukaSm said:
Fair enough, this will maybe seen stupid, but I really want to understand that, so let's pick up the system (earth + ball), in this case Earth's forces on the table would be internal to the system.
Sure. If you include everything, then the total momentum will be conserved.

ShizukaSm said:
How come? The table won't move, it's velocity will remain as 0.

Why would the table not move? It is much like the ball itself, it is just bigger, but still it is on some surface and there is friction in between. It will get some momentum, but because it so much heavier than the ball, its velocity will be very small, and its momentum will be transferred to the surface it is on very quickly.

1. What is conservation of momentum?

Conservation of momentum is a fundamental law 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. This means that the total momentum before an event is equal to the total momentum after the event.

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

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This is directly related to conservation of momentum because the total momentum of a system is the result of all the forces acting on it. Therefore, for every force acting on an object, there is an equal and opposite force acting on another object, resulting in a constant total momentum.

3. What is mechanical energy?

Mechanical energy is the sum of kinetic energy and potential energy in a system. Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or configuration. The conservation of mechanical energy states that the total mechanical energy of a closed system remains constant, as long as only conservative forces are acting on the system.

4. How is mechanical energy conserved in a system?

In a closed system, mechanical energy is conserved because it can only be transferred between different forms (such as kinetic and potential energy) but cannot be created or destroyed. This means that if there are no non-conservative forces (such as friction or air resistance) acting on a system, the total mechanical energy will remain constant over time.

5. Does conservation of momentum and mechanical energy apply to all systems?

Yes, both conservation of momentum and mechanical energy apply to all closed systems, regardless of size or complexity. These laws are fundamental principles in physics that have been extensively tested and have been found to hold true in all known systems, from subatomic particles to the entire universe.

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