Table of Contents
What happens if we differentiate force?
If you have a conservative force, essentially, F= -dU/dx. So differentiate again gives you the second derivative of the potential. If you look at that around an equilibrium point (that is the first derivative = 0), then you are getting the effective spring constant, or the linearized spring constant.
What does it mean to differentiate with respect to?
Differentiating an expression with respect to x means thinking of the expression as a function of x, so that x is the only variable, and other things are either constants or functions of x themselves… and then differentiating of course.
What is the differentiation of force?
For example, the derivative of force with respect to area is, by definition, the pressure (or in some contexts, the stress): In Fluid Dynamics, it is common to use a body force, which is written as: – i.e. the derivative with respect to volume.
What is the derivative of work with respect to time?
power
In calculus terms, power is the derivative of work with respect to time. If work is done faster, power is higher. If work is done slower, power is smaller.
What is the second derivative of force?
Summary
derivative | terminology | meaning |
---|---|---|
2 | acceleration | rate of change of velocity |
3 | jerk | rate of change of acceleration |
4 | jounce (snap) | rate of change of jerk |
5 | crackle | rate of change of jounce |
What is the difference between respect and differentiation?
As nouns the difference between respect and differentiation is that respect is (uncountable) an attitude of consideration or high while differentiation is differentiation (all senses).
How do you calculate the derivative of a body force?
In Fluid Dynamics, it is common to use a body force, which is written as: f → = d F → d V – i.e. the derivative with respect to volume. So there are multiple derivatives of F which have “names” – however, I suspect you might be talking about the derivative with respect to time.
Is force directly proportional to the rate of change of velocity?
If mass of object is considered as as constant than force is directly proportional to rate of change of velocity. This holds true in each aspect and for all type of force, be like gravitational, friction, viscous etc. But, yes, fiction, viscous have their own properties too.
Is there a name for the derivative of force?
As far as I can tell, no, the derivative of force does not have a name. As Jack Fraser points out in the comments, “yank” has been proposed, but it doesn’t seem to have real usage. The derivative of acceleration is called jerk, and generally when an engineer needs to discuss a change in force, they’ll talk about jerk. That term has genuine usage.
What are the derivatives of position called?
There are special names for the derivatives of position (first derivative is called velocity, second derivative is called acceleration, etc.), up to the eighth derivative and down to the -5th derivative (fifth integral).