The total power have three parts: 1) the shear power, 2) the friction power and 3) the power required to curl the chip.
I think that you refere to shear power.
You need to work with the Merchant circle. Is necessary to decompose indirectly the cutting force vector (Fc=Ft), into the shear direction to obtain the force in the shear plane (Fs). Then you multiply this force component with the speed in the shear plane (Vs). In this moment you obtain the shear power (Ps).
Later I send to you an image to help understanding.