# Problem Set Involving Inertia and Balloons

• Matt Poirier
In summary, the screenwriter is seeking advice on the scientific accuracy of various scenes in a science-fiction movie about a space-faring family. In one scene, the parents on the spaceship would move towards the right wall as the ship makes an abrupt left turn due to their inertia. In another scene, the child firing a projectile weapon would be thrown backward by the weapon's impact. The total momentum of the child and projectile before being fired is zero, but after being fired, it is large and directed backward. In a scene where the spaceship lands on a water-covered planet, the weight of the spaceship is equal to the weight of the fluid it displaces. In a scene where the spaceship accelerates forward, both balloons inside would move towards the
Matt Poirier

## Homework Statement

1. You are consulting for a screenwriter who is working on a science-fiction movie about the trials and tribulations of an space-faring family. She wants the script to be reasonably realistic from a scientific perspective, so she is seeking your advice on a variety of scenes in the movie. In one scene, the family's spaceship must make an abrupt left turn to avoid hitting an asteroid. The parents are standing motionless on the command bridge as the ship makes its left turn. According to real physics, what would happen to the parents?
Select one:
a. They would float straight upward to the ceiling of the command bridge.
b. They would continue to stand motionless on the command bridge.
c. They would move toward the left wall of the command bridge.
d. They would move toward the right wall of the command bridge.

2.In another scene, one of the children stands motionless before firing a projectile weapon at a massive alien creature. The child remains stationary, but the creature is thrown backward (away from the child) by the weapon’s impact. According to real physics, what would happen to the child as the child fires the weapon?
Select one:
a. The child would be thrown forward (toward the alien creature).
b. The child would remain stationary.
c. The child would be thrown forward (toward the alien creature).
d. The child would be thrown backward (away from the alien creature).

3.
In the situation described in the previous question, compare the total momentum of the child and projectile before the projectile is fired with their total momentum just after the projectile is fired.
Select one:
a. Their total momentum is zero before the projectile is fired, but is large and directed backward (away from the alien creature) after the projectile is fired.
b. Their total momentum before and after the projectile is fired are not related to one another and cannot be compared.
c. Their total momentum is zero before the projectile is fired and remains zero just after the projectile is fired.
d. Their total momentum is zero before the projectile is fired, but is large and directed forward (toward the alien creature) after the projectile is fired.
4.
In another scene, the spaceship visits an Earth-like planet that no longer has any dry land and is now covered entirely by water. The spaceship lands on the water, slows to a stop, and floats motionless on the surface of the water. The family can look down on the water's surface through a window. While it is floating motionless, compare the total weight of the spaceship to the weight of the fluid that spaceship displaces (the fluid that would otherwise occupy the space now occupied by the spaceship).
Select one:
a. The total weight of the water that the ship is displacing is equal to the total weight of the ship.
b. The total weight of the water that the ship is displacing is greater than the total weight of the ship.
c. The total weight of the water and air that the ship is displacing is equal to the total weight of the ship.
5.
At the end of the balloon scene, the spaceship turns on its rocket engine and accelerates forward rapidly. Now what happens to the two balloons? [Hint: while the ship is accelerating forward, it will tend to leave everything in the ship behind because of inertia. Those things need forces to push them forward so that they accelerate with the ship. Any object that experiences too much or too little force will not quite move with the ship.]
Select one:
a. Both balloons will move toward the rear of the ship (opposite the direction of the acceleration).
b. The balloons will approximately hover in place.
c. The helium-filled balloon will move toward the front of the ship (in the direction of the acceleration), while the air-filled balloon will move toward the rear of the ship (opposite the direction of the acceleration).
d. Both balloons will move toward the front of the ship (in the direction of the acceleration).
6.
Further on in the movie, the spaceship lands on a planet very similar to Earth, except that atmospheric pressure near the ground is twice its Earth value. Gravity is the same as on Earth, so everyone weighs the same as on Earth. The children play with a super-long drinking straw to see how high then can suck the water up the straw. How does the maximum height to which the water will rise inside the straw compare to its value on Earth?
Select one:
a. With twice the atmospheric pressure pushing up on the column of water, that column can be twice as tall on this planet as on Earth.
c. When you drink water through a straw, you aren't attracting the water toward your mouth. Instead, you are allowing atmospheric pressure to push the water up toward the relatively vacuum inside the drinking straw and The water can rise to the same height on this planet as it can on Earth, because gravity is the same on both planets.
d. The water can rise to any height inside a drinking straw on both planets.
7.
In yet another scene, the children are play with balloons while the spaceship is traveling at constant velocity in deep space, far from any planet and therefore without any gravity. One balloon contains ordinary air and another balloon contains helium. The helium-filled balloon is supposed to float up to the ceiling while the air-filled balloon is supposed to sink to the floor. According to real physics, what will happen to the two balloons when the children release them?
Select one:
a. Both balloons will sink to the floor.
b. Both balloons will float to the ceiling.
c. The helium-filled balloon will float to the ceiling and the air-filled balloon will sink to the floor.
d. Both balloons will approximately hover in place.

## The Attempt at a Solution

#1: D, Because they have mass in space, inertia is still a factor, and they then fly over to the right side wall, since inertia wants to make them moving in the same direction.
#2 D, The child would be thrown backward, since momentum is a conserved quantity, the impulse the projectile exerts on the alien must be the same it exerts on the child when leaving the gun in the other direction.
#3 C, Since momentum is a conserved quantity, it should be 0 before and after.
#4 C, I think it should be the same as the ship, but I am not sure... this just sounds right from intuition.
#5 A, The balloons will move to the back of the ship because of inertia, nothing is pushing them forward to accelerate with the ship.
#6 C, I believe it would rise as the same height on earth...But again I am not sure of the principles behind this. In a vacuum, there is no pressure, so only gravity matters, which is the same on both planets
#7. D, They hover in place because there's no gravity to push them down and no buoyant force to push them up, since gravity isn't there to provide a pressure gradient.

Sorry for the long post, thank you for your help!

1-3 correct.
4. Review Archimedes's principle.
5. When the spaceship accelerates forward, there would be artificial gravity with the "floor" being the rer of the ship. So the balloons will fall to the "ground"?
6. Think again.
7. Correct. There is no up or down in this case.

## 1. What is inertia and how does it relate to balloons?

Inertia is the tendency of an object to resist changes in its state of motion. In the case of balloons, the air inside the balloon has inertia and will continue to move in a certain direction until acted upon by an external force.

## 2. How does the size of a balloon affect its inertia?

The size of a balloon does not directly affect its inertia. Instead, it is the amount of air inside the balloon that determines its inertia. A larger balloon with more air will have more inertia compared to a smaller balloon with less air.

## 3. Can you demonstrate the concept of inertia using balloons?

Yes, you can demonstrate inertia using balloons by filling them with different amounts of air and releasing them at the same height. The balloon with more air will take longer to reach the ground due to its higher inertia.

## 4. How does inertia play a role in the movement of helium balloons?

Inertia plays a role in the movement of helium balloons because the helium gas inside the balloon has a lower density compared to air, causing the balloon to rise. The inertia of the helium gas causes it to continue moving upwards until it reaches a point of equilibrium with the surrounding air.

## 5. Is there a relationship between the shape of a balloon and its inertia?

The shape of a balloon does not directly affect its inertia. However, the shape can indirectly affect the amount of air that can be contained in the balloon, which in turn affects its inertia. A larger, rounder balloon can hold more air and therefore have more inertia compared to a smaller, flatter balloon.

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