A rope goes over a circular pulley with a radius of 6.3 cm. If the pulley makes four revolutions without the rope slipping, what length of rope passes over the pulley?
To find the length of the rope that passes over the pulley, we need to calculate the circumference of the pulley and then multiply it by the number of revolutions.
The circumference of a circle can be calculated using the formula:
C = 2 * π * r
Where:
C = circumference of the circle
π = pi (approximately 3.14159)
r = radius of the circle
Given that the radius of the pulley is 6.3 cm, we can substitute this value into the formula:
C = 2 * π * 6.3
Calculating the circumference using the formula, we get:
C ≈ 2 * 3.14159 * 6.3
C ≈ 39.478 cm
Now, to find the length of the rope that passes over the pulley, we multiply the circumference by the number of revolutions. Since the pulley makes four revolutions, we have:
Length of rope = 39.478 cm * 4
Length of rope = 157.912 cm
Therefore, the length of the rope that passes over the pulley is approximately 157.912 cm.
To find the length of rope that passes over the pulley, we need to calculate the circumference of the pulley and multiply it by the number of revolutions.
1. First, let's find the circumference of the pulley. The formula for the circumference of a circle is C = 2πr, where C represents the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
In this case, the radius of the pulley is given as 6.3 cm. Therefore, the circumference is C = 2 * 3.14 * 6.3 cm.
2. Now that we have the circumference of the pulley, we can calculate the length of the rope that passes over the pulley by multiplying the circumference by the number of revolutions.
Given that the pulley makes four revolutions, the length of the rope passing over the pulley is 4 * (Circumference of the pulley).
3. Let's substitute the value of the circumference we found earlier into the equation:
Length of rope = 4 * (2 * 3.14 * 6.3 cm).
Calculating this expression will give us the length of the rope passing over the pulley.
Four pulley circumferences
= 4 * (2 pi R) = 8 pi R
Plug in the numbers.