Question

A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The wheel has a radius of $200mm$ and the wrap angle of the band is ${270}^{\circ }$. The braking force applied to the lever is limited to $100N$, and the coefficient of friction between the band and the wheel is $0.5$. No other information is given.

The maximum tension that can be generated in the band during braking is

• A. $1200N$
• B. $2110N$
• C. $3224N$
• D. $4420N$

Answer 1

The correct option is B $2110N$


$\theta ={270}^{\circ }$
$\mu =0.5$

Taking moment about O,
$\Sigma M_0=0$

$\Rightarrow T_2\times 1-100\times 2=0$
$T_2=200N$
$\frac{T_1}{T_2}=e^{\mu \theta }=e^{0.5\times \frac{3\pi }{2}}$

$T_1=2110N$

Maximum tension produced in band is $2110N$