A single-plate dry friction clutch in a tractor has friction linings on both sides ($n = 2$). The outer radius of the friction lining is $r_o = 150\text{ mm}$ and the inner radius is $r_i = 100\text{ mm}$. The total axial clamping spring force is $W = 3500\text{ N}$ and the coefficient of friction is $\mu = 0.30$. Assuming uniform wear theory ($r_m = \frac{r_o + r_i}{2}$), the torque transmitting capacity of the clutch in $\text{N}\cdot\text{m}$ is ________ (round off to 1 decimal place).
Answer Key:
262.5
Step-by-Step Solution & Explanation
```
Friction Clutch Torque Model (Uniform Wear):
Outer radius: r_o = 0.15 m
Inner radius: r_i = 0.10 m
Axial force: W = 3500 N
Friction surfaces: n = 2
mu = 0.30
```
**Step-by-step Calculation:**
1. Mean radius of friction surface under uniform wear theory:
$r_m = \frac{r_o + r_i}{2} = \frac{0.150 + 0.100}{2} = 0.125\text{ m}$
2. Friction torque transmitting capacity ($T$):
$T = n \times \mu \times W \times r_m$
$T = 2 \times 0.30 \times 3500\text{ N} \times 0.125\text{ m} = 2100 \times 0.125 = 262.5\text{ N}\cdot\text{m}$