A flat belt on a pulley of radius 20 cm transmits 6.283 kW at 600 rpm, with friction coefficient 0.3. Torque and tightening force F are shown. Find minimum F preventing slip (two decimal kN).
Angular speed is $2\pi(600/60)=20\pi$ rad/s, so torque is about 100 N·m. Thus $T_1-T_2=\tau/r\approx500$ N. At limiting slip with π-radian wrap, $T_1/T_2=e^{0.3\pi}$. The applied tightening force balances both belt pulls: $F=T_1+T_2=500(e^{0.3\pi}+1)/(e^{0.3\pi}-1)\approx1139$ N. Rounded: **1.14 kN**.
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