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- Thread starter runevxii
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Andrew Mason

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You have to use the Lorentz transformation to determine when, in the snake's frame, the two cleavers cut.runevxii said:

[tex]t' = (t \pm vx/c^2)\gamma[/tex]

If t is the same for each cleaver (ie. in the rest frame) we can see that the t' is different for each of the two events because x differs by 1 m. So the time difference between the cuts in the snakes frame is:

[tex]\Delta t' = \gamma vx/c^2 = 1.25 * .6 * 1/c = .75/c[/tex]

In that time interval, the cleavers move x' = v\Delta t' = .75 * .6 = .45 m. Add this to the separation observed by the snake (.8 m) to give the distance between cuts (1.25 m) so the cleavers miss the snake at both ends.

AM

[Edit: I was using the reciprocal of gamma instead of gamma. Now corrected]

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I call one cleaver A and another B and set A as the origin in both inertial frames so that it's described by the 0 vector in both frames. Then B in the boy's frame is (t, x, y, z) = (0, 1, 0, 0). So if I do the Lorentz Transform with the 4x4 matrix lambda:

(B = beta, y = gamma)

[y -By 0 0]

[-By y 0 0]

[0 0 1 0]

[0 0 0 1]

then I end up with B in the snake's frame = (-By, y, 0, 0). By my calculations, t' = -By/c = -2.5 E -9 sec. I don't understand where the 0.48/c = 1.6 E-9 sec that you got came from.

I also see that I end up with x' = y = 1.25m, but it should be 0.8m I believe. Did I do something wrong and if so, what?

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Andrew Mason

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I was using the reciprocal of [itex]\gamma[/itex] so my numbers were not quite right (now corrected). The answer is 1.25 m. That is the distance between cleaver chops in the snake's frame. That distance is greater than the separation between the cleavers observed by the snake because in the snake's frame the cleavers are moving and the chops are NOT synchronous. Fortunately for the snake it is also greater than the snake's length.Jibobo said:

I call one cleaver A and another B and set A as the origin in both inertial frames so that it's described by the 0 vector in both frames. Then B in the boy's frame is (t, x, y, z) = (0, 1, 0, 0). So if I do the Lorentz Transform with the 4x4 matrix lambda:

(B = beta, y = gamma)

[y -By 0 0]

[-By y 0 0]

[0 0 1 0]

[0 0 0 1]

then I end up with B in the snake's frame = (-By, y, 0, 0). By my calculations, t' = -By/c = -2.5 E -9 sec. I don't understand where the 0.48/c = 1.6 E-9 sec that you got came from.

I also see that I end up with x' = y = 1.25m, but it should be 0.8m I believe. Did I do something wrong and if so, what?

AM

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