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*From*: John Mallinckrodt <ajmallinckro@CSUPomona.Edu>*Date*: Tue, 02 Apr 1996 08:31:12 -0800 (PST)

Jonathan,

Maybe I'm missing something too, but I agree with YOU. The book's answer

to part b is simply wrong. I don't follow Marlow's explanation for why

you supposedly CAN just apply the time dilation factor. You can't because

the time interval in the frame of the spaceship is measured by clocks that

are separated along the direction of motion and, therefore, out of sync.

John

----------------------------------------------------------------

A. John Mallinckrodt email: mallinckrodt@csupomona.edu

Professor of Physics voice: 909-869-4054

Cal Poly Pomona fax: 909-869-4396

Pomona, CA 91768 office: Building 8, Room 223

web: http://www.sci.csupomona.edu/~mallinckrodt/

On Mon, 1 Apr 1996, JONATHAN GILLIS wrote:

A spaceship has a length of 200m in its own reference

frame. It is traveling at 0.95c relative to Earth.

Suppose that the tail of the spaceship emits a flash

of light. (a)In the reference frame of the spaceship,

how long does the light take to reach the nose?

(b)In the reference frame of the Earth, how long does

this take? Calculate the time directly from the motions of

the spaceship and the flash of light, and explain

why you cannot obtain the answer by applying the

time-dilation factor to the result from Part (a).

(from Ohanian's Principles of Physics)

The answers listed in the book are (a)6.67E-7s and (b)2.13E-6s I have no

difficulty with (a) as being simple v=d/t using c and the

non-length-contracted 200m since the observers are at rest relative to

the ship. It is part (b) that I am having trouble with. As I understand

it, observers that see the ship fly by will see its length contracted.

(It is actually contracted to 62.4m) So, since the speed of light is the

same in all reference frames, I figured this observer would see the light

travel 62.4m at a speed of c. Using v=d/t this gave me 2.08E-7s.

WRONG! I though about it, and I figured that this was wrong because not

only does the light pulse have to travel the length of the ship, but also

the distance that the ship travels while it is headed towards the nose.

Setting this up (which I think I set it up right) and solving still gave

me a wrong answer (4.16E-6).

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