A moving rod is observed to have a length of 2.00 m and to be oriented at an angle of 30.0° with respect to the direction of motion as shown in Figure P39.20. The rod has a speed of 0.995c. (a) What is the proper length of the rod? (b) What is the orientation angle in the proper frame?

Question

wolfe8 · Answer

Here: http://en.wikipedia.org/wiki/Length_contraction The formula is in there.

roadjester · Answer

@wolfe8 I tried applying the same equation earlier. I'm not getting what I'm supposed to.
The proper length of the rod is 17.3 meters but I keep getting 20.02504

wolfe8 · Answer

Can you attach the figure for us to refer to?

roadjester · Answer

attachment

wolfe8 · Answer

I would assume we have to resolve it to have the horizontal length. 2 cos 30 and then use the formula.

roadjester · Answer

@wolfe8 I actually don't understand why I need to use the cos30.

wolfe8 · Answer

Because I think the formula works for the length that is parallel to the direction of motion. The stick is moving to the right on the horizontal line, so we can only apply the formula for the horizontal length, I think.

roadjester · Answer

@wolfe8 what about part b? the orientation angle in the proper reference frame?

wolfe8 · Answer

As you can already tell I'm not 100% sure here. I'm just trying. But I think angles are not influenced by relativity since angles do not change no matter how far or close the intersection is from you. You might want to look up in your notes or the internet about this. Or you can just wait for someone who can actually answer this. @LastDayWork maybe?

roadjester · Answer

This may just be me, but it seems that more people tend to be in the math group. just an observation

wolfe8 · Answer

True. Because most people ask math questions.

lastdaywork · Answer

@roadjester 
-A rod's length remains unchanged when it is moved perpendicular to its length.
-The length of a rod moving parallel to itself is shorter than its rest length by the factor γ

"... (a) What is the proper length of the rod?..."
Resolve either length vector or velocity vector as @wolfe8 told before.

"...(b) What is the orientation angle in the proper frame?..."
In the (apparent) triangle of the figure, one side-length will alter while the other remains same. Use trigonometry to find the new angle.

vincent-lyon.fr · Answer

The apparent length of the rod is 1.732 m in the x-direction and 1 m in the y-direction.

Proper length will be given by :
1 m is y-direction
applied formula in the x-direction. -> 17.34 m

Proper length is 17.37 m