Exploring the Relationship Between Force and Acceleration in Classical Mechanics

[GreenLRan]

In class today, my professor said that you will never find a force that is a function of acceleration.

Why is this?


M$$\ddot{x}$$(t) = F(x,y,z,$$\dot{x},\dot{y},\dot{z}$$,t)
M$$\ddot{y}$$(t) = F(x,y,z,$$\dot{x},\dot{y},\dot{z}$$,t)
M$$\ddot{z}$$(t) = F(x,y,z,$$\dot{x},\dot{y},\dot{z}$$,t)

This is in a classical mechanics / dynamics course

 

[rock.freak667]

Usually forces vary with time, because acceleration would vary with time. I think he meant that you would not find a function such that F=2a²+a+3 as that would not work dimensionally.

 

[rcgldr]

What about a reaction force? For example a string attached to a ball and accelerating the ball, the force the ball exerts on the string is a function of the acceleration of the ball.

 

[rock.freak667]

What about a reaction force? For example a string attached to a ball and accelerating the ball, the force the ball exerts on the string is a function of the acceleration of the ball.

Well that is what I am saying, I think your professor meant that you would not usually measure force with acceleration or well plot force against acceleration.

 

[PJC01]

, so we are considering Newton's laws of motion. In this context, the relationship between force and acceleration is described by Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration (F=ma). This means that the force acting on an object is directly proportional to its acceleration. In other words, as the acceleration of an object increases, the force acting on it also increases.

However, the statement that "you will never find a force that is a function of acceleration" is not entirely accurate. In certain situations, such as when dealing with non-inertial reference frames or when considering relativistic effects, the relationship between force and acceleration may become more complex and may involve additional variables such as velocity or time. In these cases, the force acting on an object may be described as a function of its acceleration, but it is not a simple, direct relationship like in Newton's second law.

In classical mechanics, the concept of a force being a function of acceleration is not necessary or commonly used because Newton's second law is sufficient to describe the relationship between the two. However, in other branches of physics, such as quantum mechanics or general relativity, the relationship between force and acceleration may be more complex and may involve functions of acceleration. So while it may not be common in classical mechanics, it is not entirely true that a force can never be a function of acceleration.