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A large pulley with a diameter of 1300 mm rotates at 230 r/min. determine the belt velocity if the belt is 10 mm thick.

October 7, 2026Physics

ScanSolve AI Answer

Answer

\text{15.79 m/s}

3 steps

Identify the given values and convert them to standard units.
Pulley diameter, $D_p = 1300 \text{ mm} = 1.3 \text{ m}$ .
Rotational speed, $N = 230 \text{ r/min}$ .
Belt thickness, $t = 10 \text{ mm} = 0.01 \text{ m}$ .
Calculate the effective diameter ( $D_{eff}$ ) for the belt's center line.
The belt velocity is measured at the center of the belt's thickness.
$D_{eff} = D_p + t$ $D_{eff} = 1.3 \text{ m} + 0.01 \text{ m}$ $D_{eff} = 1.31 \text{ m}$
Calculate the belt velocity ( $v$ ).
The formula for belt velocity is:
$v = \frac{\pi D_{eff} N}{60}$ $v = \frac{\pi \times 1.31 \text{ m} \times 230 \text{ r/min}}{60 \text{ s/min}}$ $v = \frac{\pi \times 1.31 \times 230}{60} \text{ m/s}$ $v \approx 15.79 \text{ m/s}$
The belt velocity is approximately $\text{15.79 m/s}$ .

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