A 2 -kg ball of putty moving to the right has a head-on...

A 2 -kg ball of putty moving to the right has a head-on inelastic collision with a $1-\mathrm{kg}$ putty ball moving to the left. If the combined blob doesn't move just after the collision, what can you conclude about the relative speeds of the balls before the collision?

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Key Concepts

Relative Speed Determination

This concept involves using the masses of the colliding bodies and the momentum cancellation condition to deduce the ratio between their speeds. Specifically, if one object's momentum cancels the other's, the speed of one must be proportionally adjusted relative to the mass difference.

Momentum Cancellation

When the combined mass of colliding objects remains at rest after the collision, it implies that the individual momenta of the objects were equal in magnitude but opposite in direction. This condition allows us to determine the necessary relationship between their speeds.

Inelastic Collision

An inelastic collision is one in which the colliding objects stick together after impact. While kinetic energy is not conserved in such collisions due to energy transformations into other forms (like heat or deformation), momentum conservation still applies.

Conservation of Momentum

This principle states that in an isolated system with no external forces, the total momentum before an event (such as a collision) is equal to the total momentum after the event. It is central in analyzing collisions because, regardless of energy losses, momentum remains unchanged.

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