On a V-belt drive with a 180-degree arc of contact on an 8" diameter driver pulley, what is the length of the belt in contact?

To determine the length of the belt in contact on a V-belt drive with a 180-degree arc on an 8" diameter driver pulley, it’s essential to first calculate the circumference of the pulley and then find the length of the arc corresponding to the 180-degree contact.

The formula for the circumference of a circle is π multiplied by the diameter. For an 8" diameter pulley, the circumference is:

C = π × 8" = 25.12"

Since the question specifies a 180-degree arc of contact, this means the belt only makes contact over half of the full circumference. To find the length of the belt in contact, we can divide the full circumference by 2:

Length of contact = 25.12" / 2 = 12.56"

This calculated length is correct as it directly aligns with the proportion of the full circumference involved in the belt's operation and reflects the physical characteristics of the V-belt drive correctly.