Momentum and Energy and Galilean Relativity

• Red Rubbie
In summary, when two bodies with equal and opposite velocities collide, their total momentum is 0 and they can potentially coalesce or explode. When viewed from a frame of reference located on one of the bodies, the momentum of the system may appear to be 2v, but this is due to the frame of reference moving with velocity -v with respect to the stationary frame of reference. There is nothing inherently wrong with this scenario.
Red Rubbie

Homework Statement

Suppose you have two bodies (assume a unit mass) approaching one another at the same speed, i.e., the velocities, v, have the same magnitude but are in opposite directions. Presumably the center of mass is half way between them, and it is not moving. It appears that the momentum of the system is 0. When they collide they both stop, i.e., their individual momentum becomes 0, their total momentum is 0, and the collision results in something happening - they both coalesce into a (hotter) stationery mass, they explode, etc.

Now consider the same situation from a frame of reference located on one of the bodies. Relative to this frame of reference, the momentum of the system seems to be 2v, the velocity of the moving body relative to the stationery body forming the frame of reference. When the 'moving' body hits the 'stationery' body, then the center of mass ( hot coalesced bodies, a mess of particles, whatever) will move in the direction of the moving body with a velocity, v.

What's wrong with this?

Consider the same situation with energy replacing momentum.

The Attempt at a Solution

Abject failure.

Last edited:
Red Rubbie said:
Now consider the same situation from a frame of reference located on one of the bodies. Relative to this frame of reference, the momentum of the system seems to be 2v, the velocity of the moving body relative to the stationery body forming the frame of reference. When the 'moving' body hits the 'stationery' body, then the center of mass ( hot coalesced bodies, a mess of particles, whatever) will move in the direction of the moving body with a velocity, v.

What's wrong with this?

Nothing. The frame of reference moves with velocity -v with respect to the stationary frame of reference: that is, the bodies are in rest in it.

ehild

1. What is momentum and why is it important in physics?

Momentum is a physical quantity that is defined as the product of an object's mass and velocity. It measures the amount of motion an object possesses and is important in physics because it is conserved in a closed system, meaning that the total momentum before and after a collision or interaction remains the same.

2. How is energy related to momentum?

Energy and momentum are closely related in physics. In fact, momentum can be thought of as the quantity of motion, while energy is the ability to do work. The kinetic energy of an object is directly proportional to its momentum, as the faster an object is moving, the more energy it possesses.

3. What is Galilean relativity and how does it relate to momentum and energy?

Galilean relativity is a physical principle that states that the laws of physics are the same in all inertial reference frames. In other words, the laws of motion and conservation of momentum and energy will hold true regardless of an observer's frame of reference. This means that the momentum and energy of an object will remain the same regardless of the observer's point of view.

4. Can momentum and energy be transferred between objects?

Yes, momentum and energy can be transferred between objects through collisions or interactions. In a closed system, the total momentum and energy will remain the same, but individual objects may exchange momentum and energy with each other.

5. How does the conservation of momentum and energy apply in real-life situations?

The conservation of momentum and energy has many real-life applications, such as in car crashes, sports, and rocket propulsion. In these situations, the total momentum and energy of the system will remain constant, allowing us to make predictions and understand the behavior of objects in motion.

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