Chapter 05, Problem 090 An interstellar ship has a mass of 8.43 × 106 kg and is

Question

Chapter 05, Problem 090 An interstellar ship has a mass of 8.43 × 106 kg and is initially at rest relative to a star system. (a) What constant acceleration is needed to bring the ship up to a speed of 0.084c (where c is the speed of light, 3.0 × 108 m/s) relative to the star system in 2 days? (b) What is that acceleration in g units (enter the answer in the form N g, where N is a number)? (c) What force is required for the acceleration? (d) If the engines are shut down when 0.084c is reached (the speed then remains constant), how long (in s) does the ship take (from that point on) to journey 9 light-months, the distance that light travels in 9 months? Assume a month has 30 days.

Explanation / Answer

According to the concept of the motion in two dimensional

Given that

mass m=8.43*10^6 kg

speed v=0.084*3*10^8=0.252*10^8 m/s

time t=2 days =2*86400=172800 sec

now we find the acceleration

acceleration a=v-u/t=0.252*10^8/172800=145.8 m/s^2

now we find the acceleration value in g

acceleration a=145.8/9.8=14.9g

now we find the force required for the acceleration

force F=8.43*10^6*145.8=1229.1*10^6 N

now we find the time taken to travel in 9 light-months

distance s=9*30*24*3600*299337984=6.983*10^15 m

now we find the time t

time t=6.983*10^15/0.084*3*10^8=27.7*10^7 sec

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