Question

The pulley on a motor shaft has a radius of 30 mm and rotates at 200 rev/s. Determine the number of revolutions per second of a shaft with a pulley of radius 240 mm which is connected to the motor shaft by a belt drive and no slipping occurs? ​

Answer 1

The shaft with a pulley of radius 240 mm connected to the motor shaft by a belt drive will rotate at a speed of 25 revolutions per second.

Step-by-step explanation:

The student's question pertains to a mechanical advantage system involving pulleys connected by a belt without slipping. Since no slipping occurs, angular velocity is inversely proportional to the radii of the pulleys, as per the principle of conservation of angular momentum. With the given motor pulley radius of 30 mm and its rotational speed of 200 rev/s, we can calculate the rotational speed of the shaft with the pulley of radius 240 mm.

Using the formula for gear ratios which is:

Speed of motor pulley (rev/s) × Radius of motor pulley (mm) = Speed of shaft pulley (rev/s) × Radius of shaft pulley (mm)

we find:

200 rev/s × 30 mm = Speed of shaft pulley (rev/s) × 240 mm

By solving for the speed of the shaft pulley, we get:

Speed of shaft pulley = (200 rev/s × 30 mm) / 240 mm =

25 rev/s

Therefore, the number of revolutions per second of the shaft with the pulley of radius 240 mm, connected to the motor shaft, is 25 rev/s.

Answer 2

25 rpm

Step-by-step explanation:

30 mm circumference = 2 pi r

total linear distance = 2 pi * 30 *200 mm

other pulley circumf = 2pi 240

total linear distance = 2 pi 240 * rev

the two distances are equal (no slippage)

2 pi 30 200 = 2 pi 240 * rev

rev = 30 * 200 / 240 = 25 rpm