How Does Relativity Affect the Motion of a Falling Stick?

In summary, the conversation discusses a situation where a stick falls from a stationary reference frame at a vertical speed of 0.6c, while another reference frame moves horizontally at 0.8c relative to the first. The goal is to calculate which end of the stick reaches the ground first and the angle it forms upon contact, as well as the kinetic energy in terms of stationary mass. The speaker suggests using the Lorentz time transformation to determine the contact time for each end of the stick in the moving reference frame, and then using the Lorentz transformation to calculate the spacetime coordinates of the events in the moving frame. The question is whether or not this approach is correct and how to solve it if it is not.
  • #1
pablodel
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Missing homework template due to originally being posted in other forum.
Hello my name is Pablo, I'm new in the forum and couldn't find any similar post so i decided to ask. I have the following situation:
In reference frame S (asumed stationary) there is a stick (length Lo in frame S) which falls from Yo at a vertical speed of 0.6c relative to S. In S the stick is horizontally positioned.
There's also another reference frame, S' which moves at 0.8c (positive x) relative to S (note that x and x' are aligned and y is parallel to y'). So I've got an object moving only vertically in a stationary reference fram and another reference frame which moves horizontally relative to the other frame.
I need to calculate which end of the stick gets to y'=0 first and also the tangent of the angle it forms when it first touches the ground. Finally i have to calculate the kinietic energy in terms of the stationary mass.

I used the Laurentz time transformation to get the contact timie for each of the ends of the stick in S' assuming the time in S is t=Yo/0.6c.
For the next step i did the following: the Δx'=Lo/γ and (i do not trust myself in this one) ΔY'=u'*Δt' where u' is the Lorentz transformation of the vertical speed relative to S and Δt' is the difference between the times i calculated previously. Is this correct? if it is not ok how can i solve this?
Thanks a lot
 
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  • #2
How about you start with defining two events: The left side of the stick reaches ground level and the right side of the stick reaches ground level. What are the spacetime coordinates of those events in S? Then use the Lorentz transformation to calculate their spacetime coordinates in S'.
 

FAQ: How Does Relativity Affect the Motion of a Falling Stick?

What is the concept of 2D relativity problem solving?

2D relativity problem solving is a scientific method used to solve problems involving motion and time in a two-dimensional space. It involves understanding the relationship between an object's position, velocity, and acceleration in a 2D plane.

How does 2D relativity differ from 3D relativity?

2D relativity only considers motion in two dimensions, while 3D relativity takes into account motion in all three dimensions. This means that 2D relativity is simpler and easier to understand, but may not accurately represent real-world scenarios.

What are the key equations used in 2D relativity problem solving?

The most commonly used equations in 2D relativity are the equations for displacement, velocity, and acceleration in two dimensions. These are:
- Displacement: Δx = xf - xi
- Velocity: v = Δx/Δt
- Acceleration: a = Δv/Δt = (vf - vi)/Δt

How can 2D relativity be applied in real-world situations?

2D relativity can be used to solve a variety of problems, such as predicting the path of a projectile, analyzing the motion of objects in a plane, and understanding the forces acting on an object. It can also be applied in fields such as astrophysics, engineering, and aviation.

What are some common mistakes to avoid in 2D relativity problem solving?

Some common mistakes to avoid in 2D relativity problem solving include forgetting to consider the direction of motion, using incorrect units, and not taking into account all relevant forces acting on an object. It is important to carefully read and interpret the problem and double check all calculations to avoid these mistakes.

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