| Solved Problem 3.5: Recoil of an astronaut who throws a wrench |
A 100 kg astronaut is motionless in space holding a 2 kg wrench. To get moving the astronaut throws the wrench at a speed of 5 m/s. How fast does the astronaut move backward?
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Astronaut's final velocity va
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Masses mw = 2 kg and ma = 100 kg; initial velocities v0 = 0; and final velocity vw = 5 m/s.
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Momentum: p = mv.
Momentum conservation: momentum before = momentum after.
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The astronaut moves backward (the negative direction) at a speed of 0.1 m/s.
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The momentum of an object can change. Imagine two roller skaters who are stationary, i.e., they each have zero momentum. If they push their arms against each other, they will move away apart. One skater acquires a momentum to the left, while the other acquires an equal but opposite momentum—towards the right! While each skater's individual momentum changed, the sum of their momenta did not change!
Many people think that rockets work by the propellant pushing against the air. If this were true, then how would rockets still work in outer space? There's nothing in the vacuum to push against! Rocket propulsion actually works through momentum conservation. The propellant is shot out of the thruster nozzles with a high momentum. In order to conserve momentum, the rocket must gain an equal momentum—but in the opposite direction.
