Classical Physics Homework: Relativistic Velocity Addition

In summary, the relativistic sum of two speeds with a value of 0.01c each is 1.9998% of the speed of light, calculated using the relativistic velocity addition formula.
  • #1
seto6
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Homework Statement



Now, consider the relativistic velocity addition formula:

speed= (v+u)/(1+vu/c2.
If v = u = 0.01c = 1 % of c, what is the relativistic sum of the two speeds?
Express your answer as a percentage of the speed of light to five significant figures.

Homework Equations


the equation is given in the problem

The Attempt at a Solution



this is what i did speed= (1%+1%)/(1+(%*1%)/(100%2)

and got 1.98020% don't know where I am going wrong help!
 
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  • #2
There is nothing wrong. Maybe you round the number quite too much. I got 1.9998%c, very close to 2% (=u+v) as expected.
 
  • #3
i see. thanks man
 

FAQ: Classical Physics Homework: Relativistic Velocity Addition

What is relativistic velocity addition in classical physics?

Relativistic velocity addition is a formula used to calculate the combined velocity of two objects in motion relative to each other. It takes into account the principles of special relativity, which state that the laws of physics remain the same for all observers in uniform motion.

How is relativistic velocity addition different from the classical formula for velocity addition?

The classical formula for velocity addition, which is based on Newtonian mechanics, assumes that the laws of physics are the same for all observers regardless of their motion. However, the relativistic formula takes into account the effects of time dilation and length contraction at high velocities, resulting in a different calculation for combined velocity.

What is the equation for relativistic velocity addition?

The equation for relativistic velocity addition is v = (u + v) / (1 + (uv/c2)), where v is the combined velocity, u is the velocity of the first object, v is the velocity of the second object, and c is the speed of light in a vacuum.

How does relativistic velocity addition affect the concept of time and distance at high velocities?

Relativistic velocity addition takes into account the fact that time and distance are not absolute, but are relative to the observer's frame of reference. As an object approaches the speed of light, time will appear to slow down and distances will appear to shrink for an outside observer, resulting in a different calculation for combined velocity.

In what scenarios is relativistic velocity addition most applicable?

Relativistic velocity addition is most applicable in scenarios where objects are moving at speeds close to the speed of light, such as in particle accelerators or in space travel. It is also relevant in modern technologies, such as GPS systems, which must account for the effects of relativity in order to be accurate.

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