Is Force Ever a Function of Acceleration in Classical Mechanics?

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In classical mechanics, forces are typically not expressed as direct functions of acceleration due to dimensional inconsistencies. The discussion highlights that while acceleration may change over time, forces generally depend on position, velocity, and time rather than acceleration alone. A specific example mentioned involves a string attached to a ball, where the force exerted by the ball on the string can be related to its acceleration. However, the consensus is that force is not commonly measured or plotted against acceleration in standard practice. Overall, the professor's assertion emphasizes the conventional approach to analyzing forces in dynamics.
GreenLRan
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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
 
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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.
 
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.
 
rcgldr said:
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.
 

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