Determine for each of the following statements whether it isalways true or can b

Question

Determine for each of the following statements whether it isalways true or can be false.

Momentum of a system may be conserved even when mechanicalenergy is not.
Kinetic energy is conserved in an elasticcollision.
In an elastic collision the momentum isconserved.
In a perfectly inelastic collision, the kinetic energy isconserved.
Two objects of same mass and moving at the same speed have thesame momentum.
Determine for each of the following statements whether it isalways true or can be false.

Momentum of a system may be conserved even when mechanicalenergy is not.
Kinetic energy is conserved in an elasticcollision.
In an elastic collision the momentum isconserved.
In a perfectly inelastic collision, the kinetic energy isconserved.
Two objects of same mass and moving at the same speed have thesame momentum.

Explanation / Answer

True. Consider thecollision of two objects of equal mass traveling in opposite directions with the same speed. Assume that they collideinelastically. The mechanical energy of the system is not conserved (it is transformedinto other forms of energy), but the momentum of the system is the same afterthe collision as before the collision; that is, zero. Therefore, for anyinelastic collision, the momentum of a system may be conserved even when mechanical energyis not.

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