# Special relativity assignment - pole moving in two dimensions

• luisf
In summary, the problem involves a pole moving at different speeds in different directions in frame S, and then examining how it passes through a hole in the frame S' which is moving with velocity v relative to S. The pole is apparent length of 6 ft in S, but due to length contraction in S', it becomes wider by a factor of 3. The question is how the pole will fit through the now 3 ft wide hole. The solution may involve skewing of the pole in S' due to length contraction in both x- and y-directions.
luisf
Hi!
I'm a bit stuck with this special relativity assignment, here's is the problem:
In a frame S a pole moves in the $x$-direction at speed $v$ such that $\gamma(v)=3$ and in the negative $y$-direction at speed $w$, while remaining parallel to the $x$-axis and being of apparent length 6 ft. The centre of the pole passes the centre of a 9-ft hole in a plate that coincides with the plane $y=0$. Explain, from the point of view of the usual second frame S' moving with velocity $v$ relative to S, how the pole gets trough the now 3-ft hole.

So the problem here is that not only does the hole shrink in S', as stated in the problem description, the pole should also be wider by a factor of 3 in this frame. So we have an 18 ft wide pole that has to move through a 3 ft wide hole. Since it will obviously fit through the hole in S, there must be an explanation for how it would fit in S' and usually there's some quirk of some physical law that will just take care of things. I can't really think of any law that would aid me in this situation however, the only explanation I can think of is that the pole is perhaps skewed in S' because of length contraction in both $x$- and $y$-direction. I'm not at all sure how that would work though, hopefully I could get some guidance from you guys.

Thanks.

See if the ends of the pole will pass through the opening.

## 1. What is special relativity in physics?

Special relativity is a theory in physics that explains the relationship between space and time. It was developed by Albert Einstein in the early 20th century and is based on two main principles: the laws of physics are the same for all observers in uniform motion, and the speed of light is constant for all observers regardless of their relative motion.

## 2. How does special relativity apply to a pole moving in two dimensions?

In the context of special relativity, a pole moving in two dimensions would be considered as an observer in motion. This means that the laws of physics, including the principles of special relativity, would apply to the pole in the same way as they would to any other observer. This includes the effects of time dilation and length contraction.

## 3. What is the concept of time dilation in special relativity?

Time dilation is a phenomenon predicted by special relativity where time appears to pass at different rates for different observers depending on their relative motion. This means that time can appear to slow down or speed up depending on how fast an observer is moving and the frame of reference they are in. This effect is most noticeable at speeds close to the speed of light.

## 4. How does length contraction work in special relativity?

Length contraction is another consequence of special relativity where an object in motion appears to contract in the direction of its motion. This means that the length of an object will appear shorter to an observer in motion relative to the object than it would to an observer at rest. This effect is also most noticeable at speeds close to the speed of light.

## 5. What are some real-world applications of special relativity?

Special relativity has had a significant impact on our understanding of the universe and has led to many practical applications. Some examples include the development of atomic clocks, GPS technology, and particle accelerators. The principles of special relativity are also crucial in fields such as astrophysics, nuclear physics, and cosmology.

Replies
4
Views
419
• Special and General Relativity
Replies
16
Views
1K
Replies
19
Views
1K
Replies
9
Views
1K
Replies
9
Views
1K
• Special and General Relativity
Replies
2
Views
859
• Special and General Relativity
Replies
21
Views
974
Replies
2
Views
1K
• General Discussion
Replies
5
Views
910
• Special and General Relativity
Replies
20
Views
792