- #1
PFuser1232
- 479
- 20
When we say that conservative forces don't vary with time, we are talking about a specific position, right? Because if the position is allowed to vary with time, then the force varies with time.
In general, the (net) force on a body may be written (in one dimension) as ##F = m\ddot{x} = mv \frac{dv}{dx}##
In other words, we can express it as a function of position or velocity: ##F = f(t) = g(x)##
For ##F## to be conservative, should ##f'(t) = 0##? Or should ##f'(t) = 0## only if ##x = a## where ##a## is a constant?
By the way, I have deliberately chosen the one dimensional case since I have very little knowledge of vector calculus.
In general, the (net) force on a body may be written (in one dimension) as ##F = m\ddot{x} = mv \frac{dv}{dx}##
In other words, we can express it as a function of position or velocity: ##F = f(t) = g(x)##
For ##F## to be conservative, should ##f'(t) = 0##? Or should ##f'(t) = 0## only if ##x = a## where ##a## is a constant?
By the way, I have deliberately chosen the one dimensional case since I have very little knowledge of vector calculus.
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