A pulley revolving at 200 revolutions per minute has a diameter of 15 inches. It is belted to a second pulley which revolves at 150 revolutions per minute. Find the diameter, in inches, of the second pulley.
not just answer, please
total number of inches/min of belt must match, so
200*pi*15 = 150*pi*d
d = 200/150 * 15 = 20
Why did the pulley get dizzy? Because it was revol-ution!
To find the diameter of the second pulley, we can use the formula for the belt speed relationship between two pulleys. The belt speed is determined by the revolutions per minute (RPM) of the pulley and the diameter of the pulley. The formula is:
Belt speed (feet per minute) = π × Diameter (inches) × RPM
We'll start by calculating the belt speed for both pulleys:
For the first pulley:
Diameter = 15 inches
RPM = 200 revolutions per minute
Belt speed of the first pulley = π × 15 inches × 200 RPM
For the second pulley:
Let's assume the diameter of the second pulley is D inches.
RPM = 150 revolutions per minute
Belt speed of the second pulley = π × D inches × 150 RPM
Since both pulleys are belted together, their belt speeds should be equal. So we can set up an equation by equating the belt speeds of the two pulleys:
π × 15 × 200 = π × D × 150
Simplifying the equation:
3000π = 150πD
We can cancel out π on both sides of the equation:
3000 = 150D
Now, solve for D:
D = 3000 / 150
D = 20
Therefore, the diameter of the second pulley is 20 inches.
To find the diameter of the second pulley, we can use the concept of pulley ratios.
The pulley ratio is the ratio of the number of revolutions of the first pulley to the number of revolutions of the second pulley. In this case, the pulley ratio can be calculated as:
Pulley ratio = (Revolutions of first pulley) / (Revolutions of second pulley)
Given that the first pulley revolves at 200 revolutions per minute and the second pulley revolves at 150 revolutions per minute, we can substitute these values into the formula:
Pulley ratio = 200 / 150 = 4 / 3
The pulley ratio is 4/3, which means that for every 4 revolutions of the first pulley, the second pulley completes 3 revolutions.
Now, we know that the diameter of the first pulley is 15 inches. We can use this information to find the diameter of the second pulley.
The pulley ratio is also equal to the ratio of the diameters of the two pulleys. In mathematical terms:
Pulley ratio = (Diameter of first pulley) / (Diameter of second pulley)
Substituting the known values, we get:
4/3 = 15 inches / (Diameter of second pulley)
To find the diameter of the second pulley, we rearrange the equation:
Diameter of second pulley = (15 inches * 3) / 4
Diameter of second pulley = 45 inches / 4
Diameter of second pulley ≈ 11.25 inches
Therefore, the diameter of the second pulley is approximately 11.25 inches.