# Basic special relativity addition of velocities problem

• Aziza
In summary, the proton is moving at a speed of 0.54c relative to the laboratory frame. This was found using the formula u' = (u-v)/(1-(uv/c2)) where u is the velocity of the electron (0.9c) and v is the velocity of the proton with respect to the electron (0.7c). This is different from the given answer of 0.98c, which would only be correct if the proton were moving in the opposite direction with respect to the electron.
Aziza
"An electron moves to the right with a speed of 0.90c relative
to the laboratory frame. A proton moves to the right
with a speed of 0.70c relative to the electron. Find the
speed of the proton relative to the laboratory frame."

u' = (u-v)/(1-(uv/c2)) where u will be velocity of electron with respect to lab frame, v is velocity of proton with respect to lab frame and u' is their relative velocity. ie, u=0.9c, u'=0.7c

Solving for v yields 0.54c. But my solutions book says 0.98c? I am pretty sure they are wrong...it would be 0.98c if the proton were moving to the left with respect to electron...am i right?

Aziza said:
u' = (u-v)/(1-(uv/c2)) where u will be velocity of electron with respect to lab frame, Correct.
v is velocity of proton with respect to lab frame
No, v is the velocity of the proton with respect to the electron
and u' is their relative velocity.

No, u' is the velocity of the proton with respect to the lab, which is what you were asked to find.

The proton is moving faster than the electron and in the lab frame the electron is seen as moving 0.90c so you know that the proton is moving faster than that in the lab frame.

I think you need to reevaluate your formula or what you are defining the variables as.

Janus said:
No, v is the velocity of the proton with respect to the electron

No, u' is the velocity of the proton with respect to the lab, which is what you were asked to find.

According to my book this formula was derived u' being the relative velocity and v being the velocity with respect to lab..

nvm i got it!
v would be the electron speed rel to lab and u' the proton speed rel to electron

## 1. What is the concept of "addition of velocities" in special relativity?

The concept of addition of velocities in special relativity refers to the process of calculating the combined velocity of two objects moving relative to each other. In classical mechanics, velocities can simply be added together, but in special relativity, the addition of velocities involves a more complex formula that takes into account the effects of time dilation and length contraction.

## 2. How does special relativity affect the addition of velocities?

Special relativity affects the addition of velocities by introducing the concept of relative velocities. This means that the velocity of an object depends on the observer's frame of reference. In addition, special relativity also takes into account the effects of time dilation and length contraction, which can impact the calculation of the combined velocity of two objects.

## 3. What is the formula for calculating addition of velocities in special relativity?

The formula for calculating addition of velocities in special relativity is v = (u + v)/(1 + uv/c^2), 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.

## 4. Can the combined velocity of two objects in special relativity exceed the speed of light?

No, according to special relativity, the speed of light in a vacuum is the maximum speed that any object can attain. Therefore, the combined velocity of two objects in special relativity cannot exceed the speed of light.

## 5. How is the concept of addition of velocities in special relativity applied in real-world situations?

The concept of addition of velocities in special relativity is applied in various real-world situations, such as in space travel, particle accelerators, and GPS systems. In these scenarios, the effects of special relativity, such as time dilation and length contraction, must be taken into account in order to accurately calculate velocities and make precise measurements.

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