Optimizing Power Transmission with Differentiation: Solving for Maximum Velocity

[pat666]

Homework Statement

(a) A belt of mass m per unit length is wound partly around a pulley. The power P(v) transmitted is given by P=Tv-mv³ where T is the tension and v is velocity of the belt. Use differentiation to show that the maximum transmission occurs when v=sqrt(T/3m).

Homework Equations

The Attempt at a Solution

I differentiated to get P'=T-3mv²
then max occurs when P'=0
so 0=T-3mv², run into trouble here:
v_max=+-sqrt(-T/3m)
how do I get rid of that minus T?

thanks

 

[Quinzio]

You're able to differentiate, then you have problems using baisc algebra... I'm puzzled.

$$0=T-3mv^2$$

Move 3mv^2 on the other side, change sign !

$$3mv^2=T$$

$$v^2=\frac{T}{3m}$$

$$v=\sqrt\frac{T}{3m}$$

 

[pat666]

s**t, now I look stupid!
Thanks - guess I had a bit of a brain explosion.