A belt connects two pulley, one of radius 5 inches and the other 18 inches. Through how many revolutions will the smaller pulley make if the larger pulley makes 6 rev?
the length of belt that passes over the pulleys is the same
18 * 2π * 6 = 5 * 2π * r
To determine the number of revolutions the smaller pulley will make, we can use the principle of belt and pulley ratio. The ratio of the number of revolutions made by the two pulleys is equal to the ratio of their radii.
In this case, the radius of the smaller pulley is 5 inches, and the radius of the larger pulley is 18 inches. Therefore, the ratio of their radii is:
Ratio = Radius of larger pulley / Radius of smaller pulley
Ratio = 18 inches / 5 inches
Ratio = 3.6
Since we know that the larger pulley makes 6 revolutions, we can multiply this by the ratio to find the number of revolutions made by the smaller pulley:
Number of revolutions of smaller pulley = Number of revolutions of larger pulley * Ratio
Number of revolutions of smaller pulley = 6 rev * 3.6
Number of revolutions of smaller pulley = 21.6 rev
Therefore, the smaller pulley will make approximately 21.6 revolutions.
To determine the number of revolutions the smaller pulley will make, you need to compare the ratio of the radii of the two pulleys.
The ratio of the radii is given by:
Ratio = Radius of Larger Pulley / Radius of Smaller Pulley
In this case, the radius of the larger pulley is 18 inches, and the radius of the smaller pulley is 5 inches.
Ratio = 18 / 5
To find the number of revolutions the smaller pulley will make, you need to multiply the number of revolutions made by the larger pulley by the ratio of the radii.
Number of Revolutions of Smaller Pulley = Number of Revolutions of Larger Pulley * Ratio
In this case, the number of revolutions made by the larger pulley is 6.
Number of Revolutions of Smaller Pulley = 6 * (18 / 5)
Now, you can calculate the number of revolutions the smaller pulley will make by evaluating the expression:
Number of Revolutions of Smaller Pulley = 6 * (18 / 5) = 6 * 3.6 = 21.6
Therefore, the smaller pulley will make approximately 21.6 revolutions.