# Why Velocity Same at Min Separation? | Conservation of Momentum

• EgpYo
In summary, according to conservation of momentum, the velocity at minimum separation is the same for both pucks, but this does not necessarily mean that their velocities are 0. The minimum separation can still occur while the pucks are moving.
EgpYo

## Homework Statement

Why is the velocity the same at minimum separation?
For example, two positively charged pucks are traveling towards each other. Find the minimum separation.

They oppose each other so they should slow down and reach minimum separation when their velocities are 0. It does not make sense to solve for when their velocities are the same. Because I get an answer of 1.0m/s, but how can they be at minimum separation if they are still moving?

## Homework Equations

Conservation of momentum

## The Attempt at a Solution

Use conservation of momentum to solve for the velocity. This is what the book says, but why? Shouldnt the minimum distance be when both of their velocities are 0?

Much depends upon the frame of reference used to judge what the velocities are, what the initial speeds of the pucks are (are they different?), the masses of the pucks (are they different?). While minimum separation will take place when the relative velocity of the pucks is zero, the two may still have some nonzero velocity in the lab frame of reference.

## 1. Why is velocity the same at minimum separation?

According to the law of conservation of momentum, the total momentum of a closed system remains constant. This means that the total momentum of the two objects at any point in their motion will always be the same. Therefore, at minimum separation, the velocities of the objects must also be the same in order to maintain the total momentum of the system.

## 2. How does the conservation of momentum apply to minimum separation?

The conservation of momentum states that in a closed system, the total momentum before an event is equal to the total momentum after the event. In the case of minimum separation, the total momentum of the system must remain constant, so the velocities of the objects must be the same in order to maintain this balance.

## 3. Is the velocity the same for all objects at minimum separation?

No, the velocity at minimum separation will depend on the masses of the objects involved. The heavier object will have a lower velocity, while the lighter object will have a higher velocity in order to maintain the same total momentum.

## 4. Why is the conservation of momentum important in understanding minimum separation?

The conservation of momentum is important because it helps us understand the relationship between the velocities of objects in a closed system. In the case of minimum separation, it explains why the velocities of the objects must be the same in order to maintain the total momentum of the system.

## 5. Does the conservation of momentum only apply to minimum separation?

No, the conservation of momentum applies to all interactions between objects in a closed system. It is a fundamental law of physics that helps us understand the behavior of objects in motion and their interactions with each other.

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