Question

The magnitude of force required to overcome friction and drive a nail through a piece of the wood can be approximated as a function of the length of nail (in millimeters) embedded in the wood based on the formula F(t) = 0.25l^4 - 8l^3 +80l^2. what is the minimum force required to overcome all frictional effects?

Answer 1

Here force is given by F = 0.25l^4 - 8l^3 +80l^2

We know that force will be minimum when derivative dF/dl = 0

4*0.25*l^3 - 3*8l^2 + 2*80l = 0

minima l= 0,

minimum value of F = 0 answer