Physics

Problem

The maximum horizontal force

F

that a student can exert on the end of a

0.40\,\text{m}

handle depends on the angle

\theta

between his forearm and the handle according to the empirical relation

F(\theta)=F_0\cos\theta

, where

F_0=250\,\text{N}

is a constant. The direction of the force is along the forearm and makes the same angle

\theta

with the handle. (i) Obtain an expression for the torque

\tau(\theta)

acting on the handle about the pivot in terms of

F_0

r

and

\theta

. (ii) Using calculus, determine the value of

\theta

that maximises

\tau(\theta)

. (iii) Calculate this maximum torque.