A pulley is turning at 30 revolutions per second slows down uniformly to 20 revolutions per second in 2 seconds .
Calculate the number of revolutions it make to a complete stop
To calculate the number of revolutions the pulley makes to a complete stop, we need to determine the rate at which it slows down. We know that the pulley turns at 30 revolutions per second initially and slows down uniformly to 20 revolutions per second in 2 seconds.
We can use the formula for uniform acceleration, which relates the initial velocity (v0), final velocity (v), time (t), and acceleration (a):
v = v0 + at
In this case, the initial velocity (v0) is 30 revolutions per second, the final velocity (v) is 20 revolutions per second, and the time (t) is 2 seconds. We need to find the acceleration (a).
Rearranging the formula, we have:
a = (v - v0) / t
Substituting the given values, we get:
a = (20 - 30) / 2
a = -10 / 2
a = -5 revolutions per second squared
The negative sign indicates deceleration or slowing down.
Now, we can use another formula to find the time it takes for the pulley to come to a complete stop. The formula is:
v = v0 + at
Since we want to find the time (t) when the final velocity (v) is 0 revolutions per second (complete stop), we substitute v = 0 into the formula:
0 = 30 + (-5)t
-5t = -30
t = -30 / -5
t = 6 seconds
Therefore, it takes 6 seconds for the pulley to come to a complete stop. To find the number of revolutions it makes during this time, we multiply the initial velocity by the time:
Number of revolutions = v0 * t
Number of revolutions = 30 revolutions/second * 6 seconds
Number of revolutions = 180 revolutions
Therefore, the pulley makes 180 revolutions before coming to a complete stop.