Question

If a system feels any external force, must it then by necessity not satisfy conservation of momentum? What if it feels two such external forces that happen to balance? What if it feels two such external forces that happen to balance in just (say) the x-direction but do not balance in (say) the y-direction?

For a system that’s initially at rest (zero initial total momentum and zero initial kinetic energy) but then ends up with multiple objects moving (non-zero final total momentum and non-zero final kinetic energy), what would you have to do to use conservation of mechanical energy in order to determine info about the objects’ velocities?

Answer 1

Ans

1) When the net external force on a system is not zero, then the momentum is not conserved.

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2) If the system feels two external forces that happen to balance then the net external force on the system, hence the momentum is conserved.

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3) Since the external forces do not balance in the y direction, so the net external force on the system is not zero.

So, the total momentum is not conserved.

The momentum is conserved in x direction though.

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4) Please note the total momentum is zero even after it breaks into multiple object as the system breaks due to intern.al forces on the objects inside the system. These forces can not change the total momentum which is zero initially. The objects will have non zero total kinetic energy but zero total momentum.

The energy of the system after its ends up with multiple objects is equal to the energy obtained when the system breaks into multiple objects.

So we need to subtract this energy(that breaks the system) from the total kinetic energy to apply conservation of mechanical energy.