A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500 mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is______Nm (round off to two decimal places).

The correct answer is 20.34.

Step-by-Step Explanation:

1. Identify the given parameters from the problem statement and the diagram:
- Diameter of the drum: $D=500\text{mm}$
- Radius of the drum: $R=\frac{D}{2}=250\text{mm}=0.25\text{m}$
- Horizontal distance from the applied force line of action to the hinge: $a=1000\text{mm}$
- Horizontal distance from the center of the brake shoe to the hinge: $b=500\text{mm}$
- Vertical distance from the contact surface of the shoe to the hinge: $c=200\text{mm}$
- Coefficient of friction between the drum and the shoe: $\mu =0.35$
- Applied force at the lever: $F=100\text{N}$
- Rotation of the drum: Anti-clockwise

2. Analyze the direction of the friction force acting on the lever:
At the topmost point of contact, since the drum rotates anti-clockwise, the surface velocity of the drum is directed to the left.
Consequently, the friction force exerted by the drum on the brake shoe (which is part of the lever) acts in the direction of rotation (to the left). This friction force is given by:
$F_f=\mu R_N$

3. Set up the moment equilibrium equation about the hinge H:
For the lever to be in equilibrium, the sum of the moments about the pivot hinge H must equal zero ($\sum M_H=0$):

$F\cdot a+\mu R_N\cdot c-R_N\cdot b=0$

Substituting the given values into the moment equation:

$100\cdot 1000+0.35\cdot R_N\cdot 200-R_N\cdot 500=0$

$100000+70R_N-500R_N=0$

$430R_N=100000$

$R_N=\frac{100000}{430}\approx 232.558\text{N}$

4. Calculate the braking torque:
The braking torque $T_B$ applied on the drum is:

$T_B=\mu R_{N}R$

$T_B=0.35\cdot 232.558\cdot 0.25\approx 20.3488\text{Nm}$

Rounding to two decimal places as specified by the correct answer gives 20.34 Nm.