A pulley with a diameter of 24 inches is driven by a belt which is moving 1045 ft/min. How many revolutions per minute are made by the pulley?
Well, that pulley must be having quite the spin party! Let's calculate the number of revolutions per minute. First, we need to find the circumference of the pulley, which can be calculated using the formula C = πd, where d is the diameter of the pulley. So, C = 3.14 * 24 = 75.36 inches.
Next, let's convert the belt speed from feet per minute to inches per minute, since we're dealing with inches. There are 12 inches in a foot, so 1045 ft/min * 12 in/ft = 12,540 in/min.
Now, we can find the number of revolutions per minute by dividing the belt speed by the circumference of the pulley: 12,540 in/min ÷ 75.36 in/rev = 166 revolutions per minute.
So, that pulley is spinning at quite the impressive rate of 166 revolutions per minute. I hope it's not getting too dizzy up there!
To find the number of revolutions per minute made by the pulley, we need to calculate the linear speed of the belt in inches per minute, and then divide it by the circumference of the pulley.
Step 1: Convert the belt speed from feet per minute to inches per minute.
1 foot = 12 inches
So, 1 ft/min = 12 in/min
1045 ft/min * 12 in/min = 12,540 in/min
Step 2: Calculate the circumference of the pulley.
The circumference of a pulley is given by the formula:
Circumference = π * diameter
Given diameter = 24 inches
Circumference = 3.14 * 24 inches = 75.36 inches
Step 3: Calculate the number of revolutions per minute.
Number of revolutions per minute = Linear speed / Circumference
Number of revolutions per minute = 12,540 in/min / 75.36 inches
Number of revolutions per minute ≈ 166.378
Therefore, the pulley makes approximately 166.378 revolutions per minute.
To find the number of revolutions per minute made by the pulley, we need to know the relationship between the linear speed of the belt and the rotational speed of the pulley.
The circumference of a circle (such as the pulley) is equal to the diameter multiplied by π (pi), which is approximately 3.14159.
Circumference of the pulley = 24 inches × π ≈ 75.398 inches.
Linear speed of the belt = 1045 ft/min.
Now, we need to convert the linear speed of the belt from feet per minute to inches per minute to match the units of the pulley's circumference. Since there are 12 inches in a foot:
Linear speed of the belt = 1045 ft/min × 12 inches/foot = 12540 inches/min.
To find the number of revolutions per minute made by the pulley, we can divide the linear speed of the belt by the circumference of the pulley:
Number of revolutions per minute = 12540 inches/min ÷ 75.398 inches = 166.327 revolutions per minute (approximately).
Therefore, the pulley makes approximately 166.327 revolutions per minute.
Circumference = pi*D = 3.14*2ft. = 6.28ft
Vp = Vb = 1045 ft./min
1045ft./min * 1rev./6.28ft = 166.4 rev/min.