In this article, we will discuss how objects change momentum when a constant force acts on them. We will discuss how the magnitude of the force acting on an object, also called its strength, and the length of time the force acts on the object affect this change in momentum.
More specifically, we will discuss how the acceleration of an object due to a force depends on the strength of that force and the length of time it acts on the object. You may have heard this concept described as how velocity is constant if acceleration is constant—these are actually equivalent statements!
You might see this concept presented in several different ways, so don’t worry if it seems like you’ve heard it before. The main point is that you understand how this concept relates to changing momentum, which is the topic we will be discussing in this article.
The mass of the object
So far, all the concepts we’ve discussed have been based on one principle: when a constant force acts on an object, the object’s change in momentum is proportional to the force.
But what if the object is not a single mass? What if it is a composite structure, like a spacecraft with internal partitions, engines, and external components? Then things get complicated.
Let’s start with something simple: A coffee cup containing a fixed volume of water is accelerated by a fixed force. What happens to the water? It gets spilled out due to the acceleration of the cup. Simple!
But what if we add some sugar to the water before putting it in the cup? Now we have a different problem. The solution may be able to slowly acclimate to the changing conditions due to its viscosity. But eventually, it will all spill out.
The acceleration of the object
In the case of a constant force acting on an object, the object’s change in momentum depends solely on the object’s acceleration. How much the object’s velocity changes depends solely on how much its acceleration changes.
Just like in the first two cases we looked at, this fact can be demonstrated with physics equations. If we combine thevelocity equation with theacceleration equation, we get something called the velocity-acceleration equation. This just says that velocity change is acceleration times time.
If we then plug in a specific time, we get a clear definition of acceleration. This shows that change in velocity is dependent upon acceleration, which confirms our intuition from the first section!
This last part is pretty cool: We can derive our intuition from physics equations, and vice versa.
The time that the force acted on the object
When a constant force acts on an object, the object’s change in momentum depends upon the time that the force acted on the object. How do we understand this statement?
If a constant force acts on an object for a longer time, then the resulting change in momentum will be greater. If the constant force acts on an object for a shorter time, then the resulting change in momentum will be smaller.
For example, imagine that you are walking down a hill and you start to slow down. You recognize that you are slowing down because you feel your forward momentum decreasing. What caused this to happen?
It was probably because of some sort of friction happening at the foot surface level. This friction acted as a constraining force that slowed you down. The longer you walked at the same speed, the more friction there was and the slower you came to a stop.
The distance between the object and the force
In physics, the word “constant” means that the force acting on an object does not change. For example, if there are two objects and one object is twice as far away from the force acting on it, then it will take twice as long for that object to experience the same change in momentum.
This is because when a constant force acts on an object, the change in its momentum depends only on the magnitude of its own velocity, not how long it is exposed to the force.
Put another way: The rate at which an object’s momentum changes is equal to the magnitude of its own velocity times how long it is exposed to the force.
In general, this fact can be expressed as: Force = mass x acceleration.
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