Exam Question: Relativity/Cathode Rays

Spastik_Relativity

I just did a test yesterday and there was a question about cathode ray tubes, it went soemthing liek this.
Albert calutated the charge to mass ratio of the cathode rays to be 1.3*10^11 and his velocity to be 3*10^8. His answers didnt agree to that of the text book. Marie another student, explain to Albert why his calculation were probably correct for this situation. What did Marie say?

I wrote that perhaps it wasnt a perfect vacuum so particle collisions may have slowed to electrons. Also mass dilation would have slowed to electron.

Is this correct? Im not sure whether the textbook calcultion already take into account mass dilation. Also my friend suggested length contration/time dilation would have effected its velocity. I wasnt quite sure becuase its not in an inertial frame of reference becuase the elctrons were accelerated to that speed. Any input will be useful.

Thanks!

Spastik_Relativity

Doesnt anybody have any input? i really do need soem help here.
the main question im asking is whether the textbooks figures for q/m ratio take into account mass dilation or not

OlderDan

Assuming the numbers in the problem are in MKS units, then the ratio certainly suggest the relativistic mass is being used in the calculation. From the ratio you could find the velocity required to increase the mass sufficiently to achieve that ratio. Your velocity number, being rounded off to one decimal place lacks precision, so there is no way you can verify the velocity calculated from the ratio is the stated velocity. To within roundoff error, the velocies would agree.

Spastik_Relativity

does that mean that the q/m ratio used in the textbooks is not the orignal one discovered by JJ Thompson?

OlderDan

There was considerable variability in the values he reported. Here is the information he published.

http://web.lemoyne.edu/~giunta/thomson1897.html

Some of the velocities he reported were in the neighborhood of 10% of light speed, but not much higher, so relativistic mass effects are much smaller than the variation in his measurements. The value stated in this problem is considerably different from today's accepted value of 1.759 x 10^11 C/kg

http://www.nyu.edu/classes/tuckerman...e_2/node3.html

Spastik_Relativity

those are great sites thanks for the help.