Topic: Machine Design
An old clutch is to transmit a torque of 100 N-m. The inner and outer diameter of the clutch plate is 100 mm and 200 mm respectively. The force required for engagement is (assume $mu = 1/3$ with uniform wear theory)
- A. 4 kN
- B. 10 kN
- C. 25 kN
- D. 50 kN
Answer: A. 4 kN
Explanation: For an old clutch, uniform wear theory is used. Torque $T = (1/2) * mu * F * (R_o + R_i)$. Given $T = 100$ N-m = $100,000$ N-mm. Inner radius $R_i = 50$ mm, Outer radius $R_o = 100$ mm. $100,000 = (1/2) * (1/3) * F * (100 + 50) = (1/6) * F * 150 = 25F$. Solving for $F$, $F = 100,000 / 25 = 4000$ N = 4 kN.