T: Lorentz Transformation for Length and Relativistic Mass

[kathykoo9]

Using the Lorentz transformation, at what speed relative to speed of light c must you travel so that your length along the direction of motion is seen to decrease by a factor of 2? For this speed, hwo much would your mass be increased?

Please show steps, I'm confused with this question!

 

[ansgar]

first of all my dear friend, this is the wrong forum...

second, show us what you have tried so far - otherwise it is pointless and there is always a suspicion that this is homework.

 

[Andrew Mason]

Using the Lorentz transformation, at what speed relative to speed of light c must you travel so that your length along the direction of motion is seen to decrease by a factor of 2? For this speed, hwo much would your mass be increased?

Please show steps, I'm confused with this question!

Can you write out the Lorentz transformation for distance co-ordinates in two frames whose relative speed is v?

You are moving at speed v relative to an Earth observer, say.

Let one end of your length be at x=0 at time t=0 and let the other end be at x = L at time t=0 in your frame. Use the Lorentz transformation to translate those co-ordinates to the Earth observer's frame.

It is not considered correct to say that the mass increases. It certainly does not increase in your frame. Relativistic (apparent) mass may increase for an Earth observer and this is probably what you are being asked to find. Do you know the relationship between rest mass and relativistic (apparent) mass?

AM