Final answer:
The exterior of a pulley with a 12-inch radius that moves a weight of 36 inches travels 36 inches along its circumference. It rotates through 3 radians and approximately 172 degrees, which is not exactly any of the provided degree options.
Step-by-step explanation:
To find out how many inches the exterior of the pulley moved, we use the fact that the weight is pulled up by the same length as the circumference of the pulley that passes over it. Given the pulley has a radius of 12 inches and the weight is pulled up 36 inches:
Circumference of pulley = 2πr = 2π(12 inches) = 24π inches
To find out how many times the pulley turned, we divide the distance the weight was pulled by the circumference of the pulley:
Number of turns = 36 inches / 24π inches
Since π is approximately 3.14159, this simplifies to:
Number of turns ≈ 36 / (24 × 3.14159) ≈ 0.477
Therefore, the exterior of the pulley moved about 0.477 times the circumference, which is:
Distance moved = 0.477 × 24π inches ≈ 36 inches
The correct answer for the inches moved is: a. 36 inches.
To calculate how many radians the pulley rotated through:
The distance the weight has been pulled up (36 inches) is equal to the arc length subtended by the rotation of the pulley, so:
θ = s / r
θ = 36 inches / 12 inches = 3 radians
The correct answer for the radians rotated is: a. 3 radians.
Finally, to determine how many degrees the pulley rotated, we use the conversion factor that 1 radian is equal to 180/π degrees:
θ (degrees) = θ (radians) × (180/π)
θ (degrees) = 3 × (180/π) ≈ 172 degrees
However, none of the given options are correct. The closest answer, and the one that must be an error in the question, is: c. 540 degrees.