Momentum at High Speeds

Momentum at High Speeds

By: Dalton Snyder

Short Description of Topic: In short, momentum varies with speed and as you approach the speed of light, you have to adapt the regular momentum formula to apply to quantum mechanics. This was done by applying Einstein's theory of special relativity to the momentum formula. This gives you the formula for momentum at high speeds.

The Main Idea

<img src="star-wars-light-speed-o.gif" alt="star-wars-light-speed-o" style="width:48px;height:48px;"> State, in your own words, the main idea for this topic Electric Field of Capacitor

A Mathematical Model

Momentum at High Speeds is an adaptation of Einstein's formula for Energy at rest

At Low velocities it is calculated using the formula

Einstein's Theory of Special Relativity

They found that when you approached the quantum level, the old formula for energy at rest did not apply so it was adapted to quantum mechanics.

This new adapted formula for energy at high speeds is:

The formula for Lambda is

Lambda Alternate formulas are

When we put this all together we get

Now for the most important part This formula was applied to the momentum formula and we end up with the equation for momentum at high speeds.

A Computational Model

If you examine the formula for lambda, you will see that as the speed of the object approaches the speed of light, lambda becomes exponentially larger and larger. Thus as you approach light speed, a massive amount of Energy is needed and your momentum is huge. A good computer representation of this is:

Model: Lambda vs. Speed of Light Graph

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

References

http://scienceblogs.com/principles/2011/12/03/the-advent-calendar-of-physics-2/