Wrong sign in my answer, why? SR + Addition of velocity....

In summary: But if ##\theta' = 0## (which is the same as ##\theta = 0##), we have:$$u' = \frac{u - v}{1 + uv}$$In summary, the conversation discusses the transformation of velocities in Special Relativity and addresses a discrepancy in the provided answer. The problem involves the use of the speed of light, cosine, and sine functions to solve for the velocity of particle u. The main question is whether the answer provided is correct or if there was an assumption made about the direction of velocity.
  • #1
642
160
Homework Statement
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Relevant Equations
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mn.png


Adopt the speed of light equals one.
Calls ##cos = c##, ##sin = s##

$$ux' = \frac{v-uc}{1-uvc}$$
$$uy' = \frac{us}{\gamma(1-uvc)}$$
$$tan \theta' = uy' / ux' = \frac{us}{\gamma(v-uc)}$$

So that's basically my solution. The problem is: The answer is ##\frac{us}{\gamma(v+uc)}##. Now, i can't understand why there is a plus sign instead my minus sign. Seems that, to got the answer provided, it was assumed that, for example, ##ux' = \frac{v+uc}{1+uvc}##. Certainly wrong, since if v = uc, ux' should be zero.

So my question is, maybe my answer is right, the problem is that i assumed v to the right and the author assumed v to the left? Or did i a mistake? WHere?
 
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  • #2
Please show your work, not just the final result. It is impossible to help you and tell you where you have gone wrong if you do not provide this.
 
  • #3
Orodruin said:
Please show your work, not just the final result. It is impossible to help you and tell you where you have gone wrong if you do not provide this.
Hello. The work is already showed, i am not sure what do you mean. I am just using the transformation of velocities in SR. Assuming that the velocity of particle u is $$\vec{u} = u cos (\theta) \hat{i} + u sin (\theta) \hat{j}$$ and $$\vec{v} = v \hat{i}$$
 
  • #4
I would say both are wrong. If ##\theta = 0## we have:$$u' = \frac{u - v}{1 - uv}$$
 

1. Why is the sign in my answer wrong?

The sign in your answer is likely wrong because you did not properly account for the direction of the velocity. In physics, direction is important and can affect the sign of a value. Make sure to carefully consider the direction when solving problems involving velocity.

2. How does SR (Special Relativity) affect the addition of velocity?

SR, or Special Relativity, affects the addition of velocity by introducing the concept of time dilation and length contraction. This means that as an object approaches the speed of light, time slows down and its length appears to decrease. This can affect the addition of velocities, as the relative speed between two objects may not be what is initially perceived.

3. What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they have slightly different meanings in physics. Velocity is a vector quantity that includes both the speed of an object and its direction of motion. Speed, on the other hand, is a scalar quantity that only represents the magnitude of an object's motion, without considering its direction.

4. How can I avoid making sign errors in my calculations?

To avoid making sign errors in calculations involving velocity, it is important to carefully consider the direction of motion and to use proper notation. This means using positive and negative signs to indicate the direction of motion, and consistently using the same direction throughout the calculation. It may also be helpful to draw diagrams or use visual aids to better understand the problem and the direction of motion.

5. Can I use the wrong sign in my answer and still get the correct result?

In some cases, using the wrong sign in your answer may still result in the correct numerical value, but it is important to understand the underlying concepts and principles in physics. Using the correct sign is crucial for accurately representing the direction of motion and understanding the physical phenomenon being studied. It is always best to double-check your work and ensure that the sign in your answer is correct.

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