Question

1.A space force service member finds himself floating 100 m from the ship in a training exercise where the drill instructor threw him out of the ship at 1 m/s. He is equipped with a shotgun that is built to work in space. The slug has a mass of 30 grams. He knows from the D.I.s’ safety brief that conservation of momentum and Newton’s third law of motion states if he shoots in the opposite direction he wants to go, he will move in the opposite direction. If his mass including spacesuit is 150 Kg and he has a 3.5 kg shotgun (Including ammo), what is the minimum speed of the slug to get him back to the ship? [12 gauge Mossberg 500 muzzle velocity is around 470 m/s] Is this velocity the space force member needs reasonable?

2. One solution to “artificial gravity” is to have space force service members on the inside of a rotating drum spinning on its axis at a constant rate. In micro gravity the human body does not do well for long periods of time. Muscle atrophy, bone loss, cataract... If the diameter of the space station is 800 m, how many revolutions per minute are needed for the “artificial gravity” acceleration to be 9.80 m/s2? (b) If the space station is a waiting area for space force members going to Mars, it might be desirable to simulate the acceleration due to gravity on the Martian surface is 3.70 m/s2. How many revolutions per minute are needed in this case?

Answer 1

Question 1

To get back to the ship, the minimum velocity he needs will be greater than zero, but in the opposite direction.

From this condition, we can say that the minimum velocity the slug needs to have is that which cancels out the momentum of the entire mass in the direction away from the spaceship. Anything greater than this will push the astronaut to the spaceship.

The initial entire mass is

The initial momentum is

Since the minimum final velocity has to be zero, we can equate the initial momentum to the required momentum of the bullet in the opposite direction.

This is far, far greater than that of a Mossberg shotgun, and hence, not reasonable

Question 2

To generate the g-force, we need the centripetal force to act as that. Hence, the pseudo-gravitational acceleration will be due to the centripetal acceleration.

Part a

Since a single revolution is two pi radians,

Part b

Here, the acceleration required is the gravitational acceleration of Mars.

Again, we find the revolutions per minute.