On a piece of machinery, the centers of two pulleys are 3 feet apart, and
the radius of each pulley is 6 inches. How long a belt (in feet) is needed to
wrap around both pulleys?
2(pi/2*.5 + .5 + 3 + .5 + pi/2*.5) = 8+pi
CFC
To determine the length of the belt needed to wrap around both pulleys, you can use the formula for the circumference of a circle:
Circumference = 2 * π * radius
First, convert the radius of each pulley from inches to feet:
Radius = 6 inches = 6/12 = 0.5 feet
Next, calculate the circumference of each pulley:
Circumference = 2 * π * 0.5 feet
Now, add the two circumferences together to get the total length of the belt:
Total Length = 2 * (2 * π * 0.5 feet)
Simplifying the equation gives us:
Total Length = 2 * π * 0.5 feet + 2 * π * 0.5 feet
Total Length = 4 * π * 0.5 feet
Finally, calculate the value of the total length:
Total Length = 2π feet = 6.28 feet
Therefore, a belt of approximately 6.28 feet is needed to wrap around both pulleys.
To find the length of the belt needed to wrap around both pulleys, we can use the formula for the circumference of a circle. The circumference of a circle is given by the formula:
C = 2πr
where C is the circumference and r is the radius of the circle.
In this case, the radius of each pulley is given as 6 inches, which is equivalent to 0.5 feet (since 1 foot = 12 inches).
So, the circumference of each pulley is:
C = 2π(0.5) = π feet
Now, to find the belt length needed to wrap around both pulleys, we need to find the sum of the circumferences of both pulleys.
The centers of the pulleys are 3 feet apart, which means the belt needs to cover a distance equal to the sum of their circumferences plus the distance between them.
Therefore, the length of the belt needed can be calculated as:
Belt Length = 2C + Distance Between Pulleys
Belt Length = 2(π) + 3
Belt Length = 2π + 3 feet
So, the length of the belt needed to wrap around both pulleys is approximately 2π + 3 feet.