Length Contraction Homework: Find Length of Moving Rod

Click For Summary

Homework Help Overview

The problem involves a rod with a rest length moving at a significant fraction of the speed of light, requiring the application of length contraction principles from special relativity. The rod is oriented at an angle to the direction of motion, which complicates the measurement of its length from a stationary observer's perspective.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of length contraction specifically to the component of the rod's length that is parallel to the direction of motion. There is an exploration of how to calculate the contracted length using the Lorentz factor (gamma) and the implications of the rod's angle.

Discussion Status

Some participants have provided guidance on focusing on the x-component of the rod's length and have noted the need to consider both components (x and y) to find the total length as perceived by a stationary observer. There is ongoing exploration of the calculations involved.

Contextual Notes

Participants are navigating the complexities of relativistic effects and the geometry involved in measuring the length of the rod at an angle. There is mention of specific values for speed and angles, but the discussion remains open-ended regarding the final calculation.

Aeighme
Messages
25
Reaction score
0

Homework Statement



A rod of rest length L0 = 10.4 m moves with a speed v = 0.42c along the x axis. The rod makes an angle of q0 = 66.1° with respect to the x' axis (primed frame is moving with the rod). What is the length of the rod as measured by a stationary observer?

Homework Equations



L=L1*(1/gamma)


The Attempt at a Solution


I have tried this several times, but can't seem to get it right.
L0=L1=10.4
gamma=(1-.422)-.5
Just solved for L..but didn't work.
 
Physics news on Phys.org
Careful. Only the component parallel to the direction of motion contracts.
 
So only the x component...is contracted. so L*cos(66.1)=L(x)?
 
Aeighme said:
So only the x component...is contracted. so L*cos(66.1)=L(x)?
Right. (That's L0, of course.)
 
Doc Al said:
Right. (That's L0, of course.)

now I multiply that by 1/gamma or (1-Beta2).5
and beta = .42...

so L=3.8238
 
Aeighme said:
now I multiply that by 1/gamma or (1-Beta2).5
and beta = .42...

so L=3.8238
OK so far, but realize that this is just the x-component, Lx not the full L. What's the y-component? Then calculate the measured length of the rod.
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 166 ·
6
Replies
166
Views
15K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 44 ·
2
Replies
44
Views
2K
Replies
4
Views
1K
Replies
3
Views
4K
  • · Replies 78 ·
3
Replies
78
Views
7K
  • · Replies 33 ·
2
Replies
33
Views
3K
Replies
1
Views
3K