How many bullets does an astronaut need to fire to return to the space shuttle?

In summary, an astronaut is drifting away from the space shuttle at a velocity of 1.1m/s. To return to the ship, he fires his gun's 30g bullets at a velocity of 250 m/s. The mass of the astronaut and his spacesuit is 123kg, and the gun has a mass of 12kg. To begin drifting back to the ship, the astronaut will need to fire approximately 20 bullets. However, to be completely accurate, the initial mass of the bullets and the recoil of the pistol should be taken into account, but in this case, the effect is negligible.
  • #1
lethal-octo
2
0

Homework Statement


An astronaut is drifting away from the space shuttle at a velocity of 1.1m/s. He fires his gun's 30g bullets to return to his ship. The mass of the astronaut and his spacesuit is 123kg, his gun has a mass of 12kg and the bullets leave the gun at a velocity at 250 m/s.
What is the approximate minimum number of bullets that he will need to fire to begin drifting back to the ship?

Homework Equations


mv=mv?

3. The attempt at a solution
mv=mv*(number of bullets)
(135)(1.1)=(0.03)(250)*n
148.5=7.5n
n=19.8
Therefore the astronaut will need to fire 20 bullets to start drifting backwards. Is this right?
 
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  • #2
lethal-octo said:
mv=mv*(number of bullets)
148.5=7.5n

Are these velocities measured relative to the space shuttle?
 
  • #3
Mister T said:
Are these velocities measured relative to the space shuttle?
I'm not really sure as this is a question from a practice exam, so I just plugged the variables in.
 
  • #4
lethal-octo said:
Therefore the astronaut will need to fire 20 bullets to start drifting backwards. Is this right?
Yes. To be completely accurate you would need to take into account that the initial mass includes the bullets, and this reduces with each shot fired. But you are not told the total initial mass of bullets, and the effect would be tiny anyway.
 
  • #5
Another point that is missed in idealized textbook problems is that the recoil of the pistol is equal and opposite not only to the momentum of the bullet, but to the momentum of the bullet plus the momentum of the expanding gases that propelled the bullet (at least the component in the same direction). This complicates accurate computation of pistol recoil considerably and renders simple formulas based on bullet mass and velocity a significant underestimate.

The attached photo shows stills from a high speed video taken in our lab to try and better quantify the contribution of the gases. The frames in view do a pretty good job showing the forward motion of the gases. Later frames (not shown) allow quantifying the subsequent rearward motion of the pistol. Bullet velocity was measured with an optical chronograph.
Sequence.png
 
  • #6
haruspex said:
Yes. To be completely accurate you would need to take into account that the initial mass includes the bullets, and this reduces with each shot fired. But you are not told the total initial mass of bullets, and the effect would be tiny anyway.
Presumably, the mass of the gun (12 kg) includes the mass of the bullets with which it is loaded.
 
  • #7
SteamKing said:
Presumably, the mass of the gun (12 kg) includes the mass of the bullets with which it is loaded.
Perhaps, but that is not at all clear.
 
  • #8
If the speed of the astronaut were a significant fraction of the muzzle speed, you'd have to take into account that the velocity of the bullets with respect to the gun is not the same as the velocity of the bullets with respect to the shuttle. In this case it's insignificant.
 

What is momentum and how is it related to astronauts and guns?

Momentum is a measure of an object's motion, determined by its mass and velocity. In the context of astronauts and guns, it refers to the transfer of momentum when a gun is fired and the astronaut experiences a recoil force.

How does firing a gun in space affect an astronaut's momentum?

Firing a gun in space will cause the astronaut to experience a recoil force in the opposite direction of the fired bullet, resulting in a change in the astronaut's momentum. This is due to the conservation of momentum principle.

Does the mass of the astronaut or gun affect the momentum in space?

Yes, the mass of the astronaut and the gun both play a role in determining the amount of momentum transferred when the gun is fired. The larger the mass, the greater the momentum.

Can an astronaut use a gun to change their own momentum in space?

Yes, an astronaut can use a gun to change their own momentum in space by firing the gun in the opposite direction of their desired movement. This is commonly seen in science fiction movies, but in reality, the effect would be very small due to the relatively low mass and velocity of the astronaut compared to the gun.

Are there any other factors that affect momentum in space besides mass and velocity?

Yes, in addition to mass and velocity, the direction of the object's movement also plays a role in determining its momentum. In space, there is no air resistance or friction, so an object's momentum will remain constant if there are no external forces acting on it.

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