Question

Work question.

Answer 1

If \[W=\int\limits_{}^{}F dx\]
Then \[F=dW/dx\]
(Ignoring dot productness in the original integral)
\[F=grad(W)\]
?

Answer 2

It means thast gradient of work done - distance graph gives the applied force

Answer 3

that

Answer 4

So F=grad(W) is correct?

Answer 5

I believe NO ...saying F= grad (w) is not appropriate, wholly. The gradient represents the steepness and direction of that slope...like the one you're drawing between work and distance ....so what if i say dx= 0 that is displacement is zero ..but i applied force of 1000 N....(force applied on wall ! )...in that case if you'll use F= dW/dx...F will be infinite..which means the line between work and displacement is perpendicular to displacement axis..further it means the work done is infinite but the fact is work = 0 ..since displacement is zero..no matter how much force applied... W= F. d...so you you can't call F= grad (W)

Answer 6

But as dW=F.vdt, then F.v=grad(W)?