# Where does the KE come from?

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#1
If two particles collide on a linear track and coalesce. Where the mass of each particle is 1kg, and before the collision one particle has a velocity of 2m/s and the other is stationary. After the collision the total momentum will be the same (2kgm/s).

Yet the total KE has increased from 1/2*1*2^2 = 2 to 1/2*2*1^2 = 1

Where did this extra KE come from?

EDIT:
And if there is a stationary particle of mass 10kg, that splits into two particles A and B travelling in opposite directions with mass 8kg and 2kg respectively. If we give particle B velocity of 4m/s, then to conserve momentum particle A must have a velocity of 1m/s? This all seems correct to me as momentum and mass are both conserved.

However when looking at their KE, particle A has a KE of 4J but particle B has a KE of 16J? Where am I going wrong here? Is there something I'm missing that means that one of either KE or momentum isn't conserved in interactions like these??
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2 years ago
#2
going from 2 J to 1 J is a decrease - you're allowed to have KE decreasing - the rest of the energy is dissipated to the environment or to internal energy of the trucks.
Energy is only conserved in collisions when the collision is 'perfectly elastic'... i.e. the trucks are free to move off at different velocities after the collision and it's typical for some energy to be lost in collisions where the trucks stick together - you'd normally have to insert some energy dissipative material between i.e. plasticine between them to make them stick.

momentum is always conserved though.

---
The reason that momentum is conserved in collision and explosions is because the impulse of particle A pushing on particle B is the same as the impulse of particle B pushing on A.
You can't have particle A pushing on particle B with a greater force than the force of particle B pushing on particle A.. or one particle pushing for a longer time.

What this means for exploding particles is that the more massive particle will have to have the smaller change in velocity.
F=ma gives a lower acceleration to the more massive particle and the duration of the force is equal for both particles... so it reaches a lower speed.

i.e. you can't just make up collisions or explosions with arbitrary numbers and wonder why they aren't obeying the rules... the rules tell you what the possible numbers are
1
#3
(Original post by Joinedup)
going from 2 J to 1 J is a decrease - you're allowed to have KE decreasing - the rest of the energy is dissipated to the environment or to internal energy of the trucks.
Energy is only conserved in collisions when the collision is 'perfectly elastic'... i.e. the trucks are free to move off at different velocities after the collision and it's typical for some energy to be lost in collisions where the trucks stick together - you'd normally have to insert some energy dissipative material between i.e. plasticine between them to make them stick.

momentum is always conserved though.

---
The reason that momentum is conserved in collision and explosions is because the impulse of particle A pushing on particle B is the same as the impulse of particle B pushing on A.
You can't have particle A pushing on particle B with a greater force than the force of particle B pushing on particle A.. or one particle pushing for a longer time.

What this means for exploding particles is that the more massive particle will have to have the smaller change in velocity.
F=ma gives a lower acceleration to the more massive particle and the duration of the force is equal for both particles... so it reaches a lower speed.

i.e. you can't just make up collisions or explosions with arbitrary numbers and wonder why they aren't obeying the rules... the rules tell you what the possible numbers are
So in the case of a decaying isotope, it's completely stationary and has no kinetic energy, it emits an alpha particle and the isotope now moves in the opposite direction to conserve momentum. However now that both the particles are moving they must both have kinetic energy, when before they had none? Where does this come from?
0
2 years ago
#4
(Original post by Retsek)
So in the case of a decaying isotope, it's completely stationary and has no kinetic energy, it emits an alpha particle and the isotope now moves in the opposite direction to conserve momentum. However now that both the particles are moving they must both have kinetic energy, when before they had none? Where does this come from?
Well 'nuclear energy' is the short answer - I guess you'll be covering nuclear processes later in A2
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2 years ago
#5
(Original post by Joinedup)
Energy is only conserved in collisions when the collision is 'perfectly elastic'... i.e. the trucks are free to move off at different velocities after the collision and it's typical for some energy to be lost in collisions where the trucks stick together - you'd normally have to insert some energy dissipative material between i.e. plasticine between them to make them stick. …

I disagree with the underlined statement. Energy is always conserved in regardless of the type collision. Sometimes, people would say the energy of a system is conserved unless no work is done. It is the kinetic energy of the system that is not conserved in the inelastic collision.

(Original post by Joinedup)
…. momentum is always conserved though.
Momentum of a system may not be conserved. One should be careful about saying “momentum is always conserved though”. It really depends on the system that you choose to analyse. The total linear momentum of the system cannot change provided no net external force acts on the chosen system.
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2 years ago
#6
(Original post by Retsek)
So in the case of a decaying isotope, it's completely stationary and has no kinetic energy, it emits an alpha particle and the isotope now moves in the opposite direction to conserve momentum. However now that both the particles are moving they must both have kinetic energy, when before they had none? Where does this come from?
The kinetic energy of the alpha particle and the daughter nucleus originate from the change in binding energy of the parent nucleus.
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