Relativistic particles travelling at near light speed, past a detector

[bruce123]

Homework Statement

Part a - A set of particles are traveling at a constant speed close to the speed of light, past a detector. From the detector's point of view, it takes a set period of time (t seconds) for the entire set of particles to pass by a set point on the detector. Write an expression to link the time t, with the constant speed v and the length of the set of particles, l.

Part b - Looking at the problem from the particle's point of view, write an expression to link the length l with the length of the set of particles from the particle's point of view, l'. Then, write a final expression to link t and v to l'.

Homework Equations

L=L0 $\sqrt{1-v2/c2}$

The Attempt at a Solution

Part a - I'm thinking that because it's all in one frame, you could simply use a modified form of the distance = speed x time. In other words, L = v x t.

Part b - As L=L0 $\sqrt{1-v2/c2}$, this can be altered so L'=L $\sqrt{1-v2/c2}$. Therefore we can alter the original L = v x t to form L' = L $\sqrt{1-v2/c2}$ = v x t.


I'm not too confident with this area of physics and am struggling with most of these equations! Any help would be much appreciated! :)

 

[anathema]

Your approach for part a is correct. The link between time t, speed v, and length l is given by the equation: l = v x t. This is because the particles are traveling at a constant speed and the distance they travel is equal to the product of their speed and time.

For part b, we need to consider the length l' from the particle's point of view. This length is contracted due to the effects of special relativity. The equation for length contraction is given by L'= L \sqrt{1-v2/c2}, where L is the length of the set of particles from the detector's point of view and v is their speed.

Therefore, we can write the final expression as: l' = L \sqrt{1-v2/c2} = v x t, where l' is the length of the set of particles from the particle's point of view, L is the length of the set of particles from the detector's point of view, v is the speed of the particles, and t is the time taken for the particles to pass by a set point on the detector.

I hope this helps clarify the concept for you. If you have any further questions, please don't hesitate to ask. Keep up the good work in your studies!