Variation of mass in a system and acceleration

In summary, the decrease in velocity of a system can be caused by various factors, such as the addition of sand to a freight car. This decrease is not solely due to the varying mass of the system, but also the friction force produced by the sand. While it may seem that there are no external forces acting on the system, there is actually a force caused by the friction. Additionally, the concept of conservation of linear momentum can also explain the decrease in velocity mathematically. Two physical explanations have been provided, one involving the averaging effect and the other involving the friction as an external force.
  • #1
Soren4
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Is it really possible for a system to decrease its velocity with no forces acting on it, just because the mass in it is "varying"?

Consider for example a freight car and a hooper from which sand is released into the car. The freight car will decrease its initial velocity if there is no force supplied, but that's not because its mass is increasing, but because the sand that comes into the freight car produces friction with it (equivalently "tries" to be accelerated) and the friction force is the one that makes the velocity of the freight car decrease.

So actually there is a force, which cause the acceleration (deceleration). Is this correct? Or it is really just the increasing of mass that change the velocity of the freight car?
 
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  • #2
Soren4 said:
Is it really possible for a system to decrease its velocity with no forces acting on it, just because the mass in it is "varying"?

Consider for example a freight car and a hooper from which sand is released into the car. The freight car will decrease its initial velocity if there is no force supplied, but that's not because its mass is increasing, but because the sand that comes into the freight car produces friction with it (equivalently "tries" to be accelerated) and the friction force is the one that makes the velocity of the freight car decrease.

So actually there is a force, which cause the acceleration (deceleration). Is this correct? Or it is really just the increasing of mass that change the velocity of the freight car?
I know a physical explanation would be more affective, but mathematically, conservation of linear momentum would cause the velocity to decrease even if mass just appeared in the freight car.
 
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  • #3
Here are two physical explanations. Pick one that feels right.

Draw the boundary for the system containing the freight car between the sand that is still falling and the sand which has just hit the pile and has not yet finished sliding to rest. The freight car loses velocity because the average velocity of its contents is decreased by the addition of the new zero-velocity sand. The force of friction does not enter in because it is an internal force.

Draw the boundary for the system containing the freight car between the sand which is sliding to rest and the sand that has finished settling. The freight car loses velocity from friction. Under this description, the friction is an external force. The averaging effect does not enter in because the sand that moves from outside the system to inside is at zero velocity relative to the car.
 
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1. What is the relationship between mass and acceleration in a system?

The relationship between mass and acceleration in a system can be described by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, the more massive an object is, the more force is needed to accelerate it, and the less massive an object is, the less force is needed to accelerate it.

2. How does the variation of mass affect the acceleration of a system?

The variation of mass in a system directly affects the acceleration of the system. As the mass of the system increases, the acceleration decreases, and vice versa. This is because the mass of an object determines its inertia, or resistance to changes in motion. A system with a larger mass will have a greater inertia and require more force to accelerate, resulting in a lower acceleration.

3. Can the acceleration of a system change without a change in mass?

Yes, the acceleration of a system can change without a change in mass. This can occur if there is a change in the net force acting on the system. According to Newton's Second Law, an increase in net force will result in an increase in acceleration, and a decrease in net force will result in a decrease in acceleration. Therefore, if the mass of the system remains constant but the net force changes, the acceleration will also change.

4. How does the variation of mass affect the motion of a system?

The variation of mass in a system can affect the motion of the system in several ways. As mentioned earlier, a greater mass will result in a lower acceleration, which means the system will take longer to reach a certain speed or change in direction. In contrast, a lower mass will result in a higher acceleration, allowing the system to reach a certain speed or change in direction more quickly. Additionally, the mass of a system can also affect its momentum, which is the product of mass and velocity. A system with a larger mass will have a greater momentum, making it more difficult to stop or change its direction.

5. How does the mass of individual objects within a system affect the overall mass and acceleration of the system?

The mass of individual objects within a system can affect the overall mass and acceleration of the system. Adding or removing objects with different masses will change the total mass of the system, which will then affect the acceleration of the system. If the objects have varying masses but the same force is applied to the system, the object with a higher mass will have a lower acceleration compared to an object with a lower mass.

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