Ii cant seem to figure this out

[1waystrpark]

Homework Statement

IF a meter stick travels at the speed of light relative to an observer, how long does the meter stick appear to the observer? show you calculations.

Homework Equations

The Attempt at a Solution

 

[JaredJames]

Please show an attempt as per PF guidelines.

Jared

 

[1waystrpark]

if speed of light is 299 792 458 m / s would the meter stick also seem this long?

 

[JaredJames]

I think this is an important point from a past thread:

Trick question. You should not *get* a reasonable answer. Why?

I've deliberately removed the post reference as I can't give you the full answer, but if you give it a shot I can help.

Note: Credit goes to DaveC and Co from the other thread for this answer.

Are you required to give a numerical answer? I see that "IF" is in capitals in the OP and so I'd assume they want a bit more than a blunt statement.

Jared

 

[rwisz]

I would like to clarify that a meter stick cannot travel at the speed of light relative to an observer. This is because the speed of light is the ultimate speed limit in the universe and it is impossible for any object with mass to reach or exceed this speed. Therefore, the premise of this question is not physically possible.

However, if we consider the hypothetical scenario where a meter stick is traveling at a speed very close to the speed of light, we can use the principles of special relativity to calculate the apparent length of the meter stick as observed by the observer.

According to special relativity, the length of an object appears shorter when it is moving at high speeds relative to an observer. This phenomenon is known as length contraction and can be expressed using the Lorentz factor (γ).

The Lorentz factor (γ) is given by the equation:

γ = 1/√(1 - v^2/c^2)

Where v is the speed of the meter stick and c is the speed of light.

In this scenario, let's assume that the meter stick is traveling at a speed of 0.99c (99% of the speed of light) relative to the observer.

Substituting the values in the equation, we get:

γ = 1/√(1 - (0.99c)^2/c^2)

γ = 1/√(1 - 0.9801)

γ = 1/√0.0199

γ = 1/0.141

γ = 7.07

This means that the meter stick will appear 7.07 times shorter to the observer. Therefore, if the actual length of the meter stick is 1 meter, it will appear to be 1/7.07 = 0.141 meters to the observer.

In conclusion, it is not physically possible for a meter stick to travel at the speed of light relative to an observer. However, if we consider a scenario where it is traveling at a speed very close to the speed of light, the apparent length of the meter stick can be calculated using the principles of special relativity.