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Chapter 37: Q77P (page 1151)

A spaceship at rest in a certain reference frame S is given a speed increment of 0.50c. Relative to its new rest frame, it is then given a further 0.50c increment. This process is continued until its speed with respect to its original frame S exceeds 0.999c. How many increments does this process require?

Short Answer

Expert verified

A minimum of 7 increments would require to exceed 0.999c.

Step by step solution

01

Relativistic velocity addition

Suppose an object is moving with the velocity u'with respect to S’ frame, which is moving with the velocity vwith respect to frame Sthen the velocity of the object uwith respect to S frame is

u=u'+v1+u'vc2

02

Determine the number of increments required.

In the first increment, the spaceship moves with u1=0.5cwith respect to the S frame. In this new rest frame, a further 2nd increment of v = 0.5c is given. The velocity relative to the S frame is

u2=u1+v1+u1vc2=0.5c+0.5c1+0.25c2c2=1c1.25=0.8c

This process is repeated; in the new obtained rest frame, the 3rd increment of 0.5c is given. Then the velocity relative to the S frame will be

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