Is the Velocity of Two Objects in a Head-On Collision Necessarily Zero?

[gcombina]

Two objects of equal mass traveling toward each other with equal speeds undergo a head on
collision. Which one of the following statements concerning their velocities after the collision is
necessarily true?

A) They will exchange velocities
B) Their velocities will be reduce
C) Their velocities will be unchanged
D) Their velocities will be zero
E) Their velocities may be zero

I know the answer is E but why? What I understand is that when 2 cars collapse head on, they go backwards

 

[Nathanael]

What I understand is that when 2 cars collapse head on, they go backwards

They both go backwards? Or one goes backwards and one keeps going forward?

 

[Nick O]

Suppose the first mass is a glob of glue, and the second mass is a baseball. Since they stick together on contact (a perfectly inelastic collision) no bouncing can occur, so instead of exchanging velocities (like billiard balls), they combine velocities*. Since they were going equal speeds in opposite directions, the sum of the velocities would be zero.

*The "equal masses" part is important here!

 

[ehild]

The keywords are "necessarily true" and "may be zero". The momentum is always conserved. As the initial momentum was zero (equal masses, equal and opposite velocities) the final momentum is also zero. That happens if the final velocities are also equal in magnitude and opposite. The magnitude of the final velocities may be zero.

ehild

 

[gcombina]

and why "may be" why not, "will be zero" (answer D)?? if the momentum before was zero then for sure will be zero after, so why "may be zero"?

 

[Nathanael]

I think it's because, as you said, they could move backwards (if it's somewhat elastic) and still have a total momentum of zero


That's the only thing I can think of

 

[ehild]

and why "may be" why not, "will be zero" (answer D)?? if the momentum before was zero then for sure will be zero after, so why "may be zero"?

Read the whole sentence including the subject. "D) Their velocities will be zero"
"E) Their velocities may be zero"

The subject is "The velocities" and not "the sum of the momenta".

The overall momentum is zero, and it stays zero if both objects travel with opposite velocities of equal magnitude. The magnitude might be even zero.


ehild