Physics Forums prize question

[Count Iblis]

An object of mass m collides with a spaceship of mass M that is freely floating in intergalactic space. The mass was moving with a speed of v relative to the spacecraft and after the collision it sticks to the spaceship.

Estimate the probability that the collision won't affect the spaceship's center of mass motion at all.

 

[Redbelly98]

I would say the answer is obviously zero. So obviously I'm missing/misinterpreting something.

 

[Entropia]

I would approach this question by first considering the conservation of momentum and the conservation of energy. Since the collision results in the object sticking to the spaceship, the total momentum of the system (object + spaceship) before and after the collision must be equal. This means that the center of mass motion of the spaceship will not be affected if the initial momentum of the object is equal in magnitude and opposite in direction to the initial momentum of the spaceship.

To estimate the probability of this scenario, we would need to know the mass and velocity of the object, as well as the mass and velocity of the spaceship. Without this information, it is difficult to provide a specific probability. However, we can say that the probability would be higher if the mass of the object is significantly smaller than the mass of the spaceship, and if the object is moving at a similar velocity as the spaceship. This would result in a more equal distribution of momentum between the two objects, making it more likely that the center of mass motion of the spaceship will not be affected.

Additionally, the probability would also depend on the angle of collision and the elasticity of the collision. If the collision is perfectly head-on and the objects are perfectly elastic (meaning no energy is lost during the collision), then the probability would be higher. However, if the collision is at an angle and some energy is lost, it would be less likely for the center of mass motion to remain unaffected.

In conclusion, the probability of the collision not affecting the spaceship's center of mass motion would depend on various factors and would need more specific information to accurately estimate. However, we can say that it is possible for the collision to not affect the center of mass motion if certain conditions are met.

 

[Entropia]

I would approach this question by first considering the principles of conservation of momentum and conservation of energy. In this scenario, the mass and velocity of the object colliding with the spaceship would affect the overall momentum and energy of the system. However, since the spaceship is freely floating in intergalactic space, there are no external forces acting on it that could affect its center of mass motion.

Therefore, the collision between the object and the spaceship would only result in a transfer of momentum and energy within the system. This means that the center of mass motion of the spaceship would not be affected at all. The probability of this happening would be very high, as long as the masses and velocities of the objects involved are relatively small compared to the mass and velocity of the spaceship.

However, it is important to note that this probability is not absolute and could be affected by factors such as the angle and speed of the collision, as well as any potential external forces that may be present in the intergalactic space. Additionally, the materials and structure of the spaceship could also play a role in how the collision affects its center of mass motion.

In conclusion, based on the principles of conservation of momentum and energy, it is highly likely that the collision between the object and the spaceship would not affect the spaceship's center of mass motion. However, there are potential factors that could influence this probability. Further analysis and calculations would be needed to provide a more precise estimate.