Relativity graph?

Question

The Graph is related to Relativity theory. Choose the effect of either Length contraction, Mass expansion or Time dilation.

Mr. Kirwin showed you the formulas. Calculate what the apparent variable l, m or t would be if you moved at high speed. Graph v on the x axis, your chosen variable( l, m or t) on the y axis. You should graph the velocity, v, as a multiple of c (the speed of light). Graph 15 sets of data starting with 0.1c, 0.2c etc up through .9c, .99c, .999c ...... getting really close to 1.0c which would be the speed of light. 0.1c means a velocity, v, of 0.1 times 300,000,000 m/s (I can't do an exponent to show 3 times ten to the eighth power here). .999c means a velocity, v, of .999 times 300,000,000 m/s. Decide how fast you would have to go before the effects of relativity would be noticeable.

Please use excel, or other graph program and email it to me. This may require you to figure out how to use a graphing program, so start early and post help on Moodle.

Answer 1

Do you have excel?

If so, you'll want to create two columns.  The first contains your x axis -- type in numbers that start small, and approach 300000000 (for instance, 3e7 6e7 1.2e8 2.4e8 2.9e8 2.99e8 and so on).  This is "v"

In the next column, you want to create an equation that uses the lorentz contraction, etc.  i.e. if the first column has numbers in A1 through A10, then in B1 you would type

=sqrt(1-A1^2 / (3e8)^2)

and then copy and past this into the column.

It would also be useful to plot out what would happen if there was no relativity -- i.e. in Column C just past all 1's.

Then, you have to subjectively make a call -- what is noticeable?  Depends on how big the thing is you're looking at.  For instance, a 1% change of an object 1 cm long is only 0.1 mm... probably not noticeable.  But a 1% change in an object 1 meter long would be 1 cm -- about the size of your pinky, so might be noticeable (then again, i'm not sure you'd really even be able to see a 1 cm object travelling at a about 50 million miles per hours!)