As a NASA mission specialist you are on a spacewalk doing a repair job on one of

Question

As a NASA mission specialist you are on a spacewalk doing a repair job on one of the solar panels of the International Space Station. You happen to look up and see a piece of space junk heading right for you. You quickly push off from the panel and just barely miss getting hit by the orbiting debris. Unfortunately, the hunk of space junk hits the solar panel, both destroying it and severing your safety cable that had attached you to the station. You now find yourself about 20 m from the station and floating away at a rate of about 0.1 m/s. To make things worse, you only have a 35 minute (2100 s) oxygen supply left... if you don't act fast you'll be lost in space! You have a massive 10 kg wrench in your hand... is it possible to get back to the station before your oxygen runs out? (Assume you can throw the wrench at a speed of 1.2 m/s and that with your bulky space suit, your total mass is about 100 kg). (a) Which conservation law will allow you to solve this problem? (b) Derive an equation for your velocity after you have launched the wrench. Please draw appropriate sketches. Evaluate the equation to find your speed (answer: 0.01 m/s). (c) Calculate the time it will take you to reach the space station. Will there be enough oxygen?

Explanation / Answer

a) there is no gravity in space.

and wrench is thrown due to internal force beteen specialist and wrench.

and work done due internal force on the system is zero.

hence momentum of specialist and wrench will be conserved.

b) Using momentum conservation,

intial velocity of specialist = 0.1 m/s

initial velocity of wrench = 0.1 m/s

final velocity of specialist = - v (it will be in opposite direction)

final velocity of wrench = 1.2 m/s   

initial momentum of system =final momentum of system

0.1 x 100 + 0.1 x 10 = 100 x -v + 10 x 1.2
11 - 12 = -100v

v = 0.01 m/s

c) distance = 20 m

speed = 0.01 m/s

time = distance / time = 20 / 0.01 = 2000 s

time (in min) = 2000/60 = 33.33 min

Yes, there will be enough oxygen.

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