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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 厂鈥� 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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