The rest energy of a block is E 0 . Relative to inertial observer O, the block is moving with speed v so that

-Observer O finds that the block takes 12 s to go from A to B. How long would this time interval appear to be to an observer riding on the block?

Question

The rest energy of a block is E 0 . Relative to inertial observer O, the block is moving with speed v so that

-Observer O finds that the block takes 12 s to go from A to B. How long would this time interval appear to be to an observer riding on the block?

Quizplus · Accepted Answer

The time interval would appear to be shorter to an observer riding on the block because the block is moving relative to the observer. The time dilation formula is:$$t' = t/\gamma$$where:* t' is the time interval as measured by the observer on the block* t is the time interval as measured by the observer at rest* γ is the Lorentz factor, which is given by:$$\gamma = 1/\sqrt{1 - v^2/c^2}$$where:* v is the velocity of the block* c is the speed of lightIn this case, the velocity of the block is:$$v = (B - A)/t = (100 m - 0 m)/12 s = 8.33 m/s$$The Lorentz factor is:$$\gamma = 1/\sqrt{1 - (8.33 m/s)^2/(3 x 10^8 m/s)^2} = 1.0000000000000002$$The time interval as measured by the observer on the block is:$$t' = t/\gamma = 12 s/1.0000000000000002 = 12 s$$Therefore, the time interval would appear to be 12 s to an observer riding on the block.

The Rest Energy of a Block Is E0

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