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Chapter 36: Q. 68 (page 1062)

Many science fiction spaceships are powered by antimatter reactors. Suppose a 20mlong spaceship, with a mass of 15000kg

when empty, carries 2000kgof fuel: 1000kgeach of matter and antimatter. The matter and antimatter are slowly combined, and the energy of their total annihilation is used to propel the ship. After consuming all the fuel and reaching top speed, the spaceship flies past a space station that is stationary with respect to the planet from which the ship was launched. What is the length of the spaceship as measured by astronauts on the space station?

Short Answer

Expert verified

The length is17.69m.

Step by step solution

01

Given information

We have given,

length =20m

We have to find the contracted length of the space ship.

02

Step 2; Simplify

we have to find the velocity of the rocket that we will find by relativistic energy,

E=mc2E=2000kg脳(3脳108m/s)2 E=18脳1019J

Then energy is used to speed up the rocket is,

E=mroc21-v2c21-v2c2=0.88

Then the length contraction formula is

L'=L1-v2c2L'=(20m)(0.88)L'=17.69m

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