(Solved): 4. A belt and pulley drive system is shown below. Pulleys 1 and 2 are the same size and are attach ...

4. A belt and pulley drive system is shown below. Pulleys 1 and 2 are the same size and are attached to each other by a belt. Pulley 2 and pulley 3 are mounted on the same shaft, with pulley 3 driving pulley 4 by means of a belt. Pulley 5 is mounted onto the same shaft as pulley 4 . Pulley 5 drives pulley 6 by means of a belt. Pulley 1 and 2 are the same size, and each have a diameter of \( 180 \mathrm{~mm} \). Pulley 4 has a diameter of \( 420 \mathrm{~mm} \). Pulley 5 has a diameter \( 180 \mathrm{~mm} \) and pulley 6 has a diameter of \( 60 \mathrm{~mm} \). Pulley 1 is driven by an electric motor at a speed of \( 2200 \mathrm{rpm} \). The desired output speed of pulley 6 is \( 80 \mathrm{rad} / \mathrm{s} \). Calculate the size (diameter) in \( \mathrm{mm} \) that pulley 3 needs to be in order to achieve this.