Newton Mechanics vs Special Relativity Problem

[Kaleb]

Homework Statement

According to Newtonian mechanics the momentum of the bus in the preceding problem is p= mv. According to relativity, p = gamma*mv. How does the actual momentum of the bus moving at .99c compare with the momentum it would have if classical mechanics were valid?

*Note*
The previous problem only states a bus and has nothing to do with the question

Homework Equations

Classical
p = mv

Special
p=gamma*mv

The Attempt at a Solution

For classical I came up with 99%cX with x = mass
For special I came up with 70.2%cX with x = mass

 

[Doc Al]

What did you get for gamma?

 

[Moetasim]

Your attempted solution is not correct. The correct comparison would be:

Classical: p = 0.99m
Special: p = 7.02m

This means that according to special relativity, the momentum of the bus moving at 0.99c would be 7.02 times greater than the momentum predicted by classical mechanics. This is due to the fact that special relativity takes into account the effects of high speeds and time dilation, while classical mechanics does not. At speeds close to the speed of light, the difference in momentum becomes significant and cannot be ignored. This is one of the key differences between Newtonian mechanics and special relativity.