What is the percentage increase in tool life when the cutting

Direction: In a machining experiment, tool life was found to vary with the cutting speed in the following manner:

VTⁿ = C

∴ Tⁿ =	C
	V

or T =		C		^1/n	=		C		²
		V					V

or T ∝	1
	V²

∴	T₀	=	V²
	T		V₀²

∴	T₀	=	(V₀/2)²
	T		V₀²

or	T₀	– 1 = 4 – 1
	T

Hence percent increase = 300%
Alternately:
When cutting speed is halved

60 × (8.1)^0.5 =	60	= (T₂)^0.5
	2

or	T₂	= (2)²
	81

or T₂ =4 × 81

% change in tool life =	T₂ − T₁
	T₁

=	(4 × 81) − 81	× 100
	81

= 3 ×	81	× 100 = 300%
	81