Exam Question: Relativity/Cathode Rays

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In summary, Marie explained that the textbook calculation may be incorrect because it does not take into account mass dilation. Albert's calculation were probably correct for this situation.
  • #1
Spastik_Relativity
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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 textbook. 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? I am 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!
 
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  • #2
Doesnt anybody have any input? i really do need soem help here.
the main question I am asking is whether the textbooks figures for q/m ratio take into account mass dilation or not
 
  • #3
Spastik_Relativity said:
Doesnt anybody have any input? i really do need soem help here.
the main question I am asking is whether the textbooks figures for q/m ratio take into account mass dilation or not

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.
 
  • #4
does that mean that the q/m ratio used in the textbooks is not the orignal one discovered by JJ Thompson?
 
  • #5
Spastik_Relativity said:
does that mean that the q/m ratio used in the textbooks is not the orignal one discovered by JJ Thompson?

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/honors.chem/lectures/lecture_2/node3.html [Broken]
 
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  • #6
those are great sites thanks for the help.
 

1. What is the theory of relativity?

The theory of relativity, proposed by Albert Einstein, is a scientific theory that explains the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and the speed of light is constant regardless of the observer's frame of reference.

2. How does the theory of relativity affect our understanding of the universe?

The theory of relativity has had a significant impact on our understanding of the universe. It has helped us understand how gravity works, the concept of spacetime, and has led to the development of technologies such as GPS. It has also challenged our traditional understanding of time and space and opened up new possibilities for scientific exploration.

3. What are cathode rays?

Cathode rays are streams of electrons that are produced when an electric current is passed through a gas at low pressure. They were first discovered by J.J. Thomson in the late 19th century and played a crucial role in the development of modern physics, including the understanding of atomic structure and the discovery of the electron.

4. How did the study of cathode rays contribute to the theory of relativity?

The study of cathode rays provided evidence for the theory of relativity by demonstrating that mass and energy are interchangeable. This concept, known as mass-energy equivalence, is a fundamental principle of relativity and was later confirmed through experiments such as the famous E=mc² equation proposed by Einstein.

5. How has the theory of relativity been tested and confirmed?

The theory of relativity has been extensively tested and confirmed through various experiments and observations, including the bending of starlight by gravity, the precision of atomic clocks, and the behavior of particles at high speeds. Additionally, the theory has been used to make accurate predictions about phenomena such as gravitational waves, which were recently detected for the first time.

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