Question

A belt-driven machine has a moment of inertia of 240 ft-lb-s2 . The belt tensions differ by 80 lb as the belt passes over the 18-in.-diameter driver pulley. Calculate the speed it reaches if it starts from rest and accelerates uniformly for 40 seconds.

Answer 1

To calculate the speed reached by a belt-driven machine that starts from rest and accelerates uniformly for 40 seconds, we need to find the angular acceleration using the moment of inertia and then calculate the speed using the formula Speed = (angular acceleration) × (time) × (radius).

Step-by-step explanation:

To calculate the speed reached by a belt-driven machine that starts from rest and accelerates uniformly for 40 seconds, we need to use the formula:

Speed = (angular acceleration) × (time) × (radius)

First, let's find the angular acceleration using the moment of inertia:

Angular acceleration = (difference in belt tensions) / (moment of inertia)

Plugging in the values:

Angular acceleration = 80 lb / 240 ft-lb-s2

Now, we can calculate the speed:

Speed = (angular acceleration) × (time) × (radius)

Remember to convert the radius from inches to feet before calculating the speed.