6) suppose a student throws a pencil at the wall, and upon hitting the wall, the pencil
breaks in half. what happens to the original momentum of the pencil?

ORIGINAL MOMENTUM OF THE PENCIL GETS DISTRIBUTED TO THE BROKEN HALFS EQUALLY .

Explanation:

GENERALLY :

For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2. The above statement tells us that the total momentum of a collection of objects (a system) is conserved - that is, the total amount of momentum is a constant or unchanging value. Since the forces between the two objects are equal in magnitude and opposite in direction, and since the times for which these forces act are equal in magnitude, it follows that the impulses experienced by the two objects are also equal in magnitude and opposite in direction.

IN THIS CASE :

(neglecting the impulse and force of gravity)

The net external force on the system is ZEROThe collision and the breakage that happens is PURELY due to the internal force which are equal and opposite.When we consider the wall and the pencil together as a system , the net external force on the system is zero. We also assume that the wall is very heavy and thus it remains at rest even after the collision. Thus , according to the law of conservation of momentum,  the pencil must have the same momentum imparted to it initially.Therefore , the ORIGINAL MOMENTUM OF THE PENCIL GETS DISTRIBUTED TO THE BROKEN HALFS EQUALLY .