WPE O22

Solution Q22

Solution: Power Delivered by Motor

Conveyor System

Calculation

We established in Question 21 that for the minimum driving force, the velocity is $v = \sqrt{gh}$.

The total force at this velocity is:

$$ F = \mu v + \frac{\mu g h}{v} $$

Substituting $v = \sqrt{gh}$:

$$ F = \mu \sqrt{gh} + \frac{\mu g h}{\sqrt{gh}} = \mu \sqrt{gh} + \mu \sqrt{gh} = 2\mu \sqrt{gh} $$

The power delivered by the motor is given by $P = F \cdot v$:

$$ P = (2\mu \sqrt{gh}) \cdot (\sqrt{gh}) $$ $$ P = 2 \mu g h $$

Correct Option: (d) $2\mu g h$