Length Contraction: What Does it Mean for Mass?

[ally1h]

Homework Statement

A spear moves past you at a very high speed. As it passes, you measure its length at one half its normal length. From this measurement, what can you conclude about the moving spear's mass?

Homework Equations

The Attempt at a Solution

To have the spear appear that it is 1/2 its length means it is moving at a substantial fraction of the speed of light. And as the spear's velocity approaches the speed of light the relativistic mass appears greater and greater...

But is there some quantitative value I should know? Such as... the mass of the spear is twice its normal mass? Or some equation that relates the relativistic mass to length?

 

[LowlyPion]

I think in special relativity that you generally have the relationship that

Δx' = Δx/γ

Where γ is the Lorentz factor

γ = 1/(1-(v/c)²)^1/2

This can then relate to the mass as

m' = γm

Here is a jumping off page in Wikipedia that might be helpful:
http://en.wikipedia.org/wiki/Special_relativity#Time_dilation_and_length_contraction

 

[thomate1]

I can provide a response to this question by explaining the concept of length contraction and its implications for mass.

Length contraction is a phenomenon that occurs in special relativity, where the length of an object appears to decrease when it is moving at a high velocity. This is due to the fact that space and time are relative and are affected by an object's velocity. The faster an object moves, the more its length appears to contract in the direction of its motion.

In the scenario described, where the spear appears to be half its normal length, it is likely moving at a significant fraction of the speed of light. This means that the length contraction is more pronounced, and the spear's actual length is longer than what is measured by the observer. However, this does not mean that the mass of the spear has changed.

In special relativity, mass is also a relative concept and is affected by an object's velocity. This is known as relativistic mass, and it increases as an object's velocity approaches the speed of light. However, this increase in mass is not directly related to length contraction. Instead, it is a result of the energy an object possesses due to its high velocity.

So, in conclusion, the measurement of the spear's length does not provide any information about its mass. To determine the mass of the moving spear, other factors such as its velocity and energy would need to be taken into account.