Question

A drum brake is shown in figure. The drum is rotating first in anticlockwise and then in clockwise direction. The coefficient of friction between drum and shoe is 0.2. The dimensions shown in the figure are in mm. The ratio of braking torque in first and second case is ________ (Correct upto three decimal place)

• A. 0.852

Answer 1

The correct option is A 0.852
Case - 1: Drum rotating in ACW


Taking moment about O,

$1000\times 0.4-N\times 0.25-f_1\times 0.10=0$

or $400-0.25N-\mu N\times 0.10=0$

$(0.25+0.1\mu )N=400$

$N=\frac{400}{0.25+0.2\times 0.1}=1481.48N$

$f=\mu N=0.2\times 1481.48=296.296N$

Torque, $T_{b1}=f_1\times R=296.296R$

Case-2: Drum rotaing clockwise:


Taking moment about O,

$1000\times 0.4-N\times 0.25+f_2\times 0.1=0$

$(0.25N-\mu N\times 0.1)=400$

$N=\frac{400}{(0.25-0.2\times 0.1)}=1739.13N$

$f_2=\mu N=0.2\times 1739.13=347.826N$

$Torque$, $T_{b2}=f_2\times R=347.826R$

Ratio = $\frac{T_{b1}}{T_{b2}}=\frac{f_{1}R}{f_{2}R}=\frac{296.296}{347.826}=0.852$