an electric hoist is used to life a piece of equipment y = 2.6 feet. the diameter on the hoist is x = 12 inches. find the number of degrees through which the drum must rotate (round to the nearest integer).
*I do apologize, there is a figure in my question, but I cannot paste it here
a complete turn of the hoist is π ft
a complete turn is 360°
So, the hoist turns through
(2.6/π) * 360°
To find the number of degrees through which the drum must rotate, we can use the formula for circumference and convert it to degrees.
1. First, let's calculate the circumference of the drum:
C = π * d, where d is the diameter of the hoist.
C = π * 12 inches
2. Next, convert the circumference to feet:
1 foot = 12 inches
C in feet = (π * 12 inches) / 12 inches per foot
3. Now, we need to find how many times the drum should rotate to lift the equipment 2.6 feet:
Number of rotations = Y / C in feet
Number of rotations = 2.6 feet / (C in feet)
4. Lastly, convert the number of rotations to degrees:
360 degrees = 1 full rotation
Number of degrees = Number of rotations * 360 degrees
Round the result to the nearest integer to obtain the final answer.
To find the number of degrees the drum must rotate, we need to use the given information about the height y and the diameter x.
First, let's convert the diameter x from inches to feet. Since there are 12 inches in a foot, we have:
x = 12 inches = 12/12 feet = 1 foot
Now, we can calculate the circumference of the drum using the formula:
C = πd
where C is the circumference and d is the diameter.
Plugging in the value for the diameter, we get:
C = π * 1 foot = π feet
Next, we can determine the length of cable that needs to be unwound from the drum to lower the equipment by y = 2.6 feet. This length is equal to the circumference of the drum.
Therefore, the length of cable unwound from the drum is:
Length = C = π feet
Now, to find the number of degrees the drum must rotate, we need to determine how much cable is needed to represent 1 full revolution or 360 degrees around the drum.
Since the length of cable for one full revolution is equal to the circumference, we can set up the following proportion:
Length for 360 degrees / Length = Degrees / 1
Plugging in the values, we have:
π / Length = Degrees / 1
Rearranging the equation to solve for Degrees, we get:
Degrees = (π / Length) * 1
Now, substituting the value for Length, we have:
Degrees = (π / π) * 1 = 1 * 1 = 1 degree
Therefore, the drum must rotate approximately 1 degree (rounded to the nearest integer) to lift the equipment y = 2.6 feet.