Linear momentum conservation vs mecanical energy conservation

In summary, when a ball A with mass ma and initial velocity v collides with a ball B with mass mb initially at rest, the resulting velocity v' for both balls is given by v' = mav/(ma + mb). This can be derived from linear momentum conservation. However, using mechanical energy conservation gives a different result, suggesting that there may be energy dissipation in the collision. This raises the question of whether the collision is elastic.
  • #1
jaumzaum
434
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A ball A (mass ma) with initial velocity v colides with a ball B (mb) initially stopped. A and B gets the same direction/velocity v', Calculate v'

By linear momentum conservation
ma.v = (ma + mb).v'
v' = mav(ma + mb)

But by mecanical energy conservation

ma.v²/2 = (ma + mb).v'²/2
v' = v (ma/(ma + mb))^(1/2), which is wrong

Why we can't use mecanical energy conservation, is there a energy dissipation?
 
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  • #2
jaumzaum said:
A ball A (mass ma) with initial velocity v colides with a ball B (mb) initially stopped. A and B gets the same direction/velocity v', Calculate v'
...
Why we can't use mecanical energy conservation, is there a energy dissipation?

Well, for A and B to get the same direction/velocity v' after the collision, don't they have to stick?

Does that sound like an elastic collision?
 

1. What is the difference between linear momentum conservation and mechanical energy conservation?

Linear momentum conservation is a principle that states that the total momentum of a system will remain constant, unless acted upon by an external force. Mechanical energy conservation, on the other hand, states that the total sum of kinetic and potential energy in a system will remain constant, unless acted upon by non-conservative forces like friction.

2. How are linear momentum and mechanical energy related?

Linear momentum and mechanical energy are both measures of an object's motion. However, they are not directly related to each other. Linear momentum is a measure of an object's mass and velocity, while mechanical energy is a measure of an object's position and motion.

3. Can linear momentum be conserved without mechanical energy conservation?

Yes, linear momentum can be conserved without mechanical energy conservation. This can occur in situations where external forces act on a system, causing changes in mechanical energy, but the total momentum remains constant.

4. Is it possible for mechanical energy to be conserved without linear momentum conservation?

Yes, it is possible for mechanical energy to be conserved without linear momentum conservation. This can occur in situations where there is no net external force acting on a system, so the total momentum remains constant, but there may be changes in the distribution of kinetic and potential energy within the system.

5. How do these conservation principles apply in real-world situations?

In real-world situations, both linear momentum and mechanical energy conservation are important principles in understanding and predicting the behavior of systems. They are commonly used in fields such as physics, engineering, and mechanics to analyze and design systems and structures. For example, in a car crash, the total linear momentum of the cars involved will be conserved, but there may be changes in the mechanical energy due to the forces involved.

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