A V-belt transmits10 kW at8 m/s. Small-pulley wrap170°, groove angle38°, friction coefficient0.28 and maximum stress4 MPa. Ignore centrifugal force. Find minimum belt area in mm² (one decimal).
Tension difference=P/v=10000/8=1250 N. V-belt ratio is T₁/T₂=exp[μθ/sin(19°)], where θ=170π/180. This is about12.83. Therefore T₁=1250r/(r−1)≈1355.8 N. Area=T₁/σallow≈1355.8/4=339.0 mm², within source rounding.
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