At CHMSC Mechanic Shop a pulley system is used to lift engines from cars. The pulley system consists of a cable that goes around a pulley with a radius 6 feet. How many degrees of rotation are required for an engine to be lifted 24π feet?
each rotation would pull it up by one circumference, which is
2πr ft or 12π ft
so what is 24π/(12π) ?
good heavens, why would you lift the engine this high??
To find the number of degrees of rotation required for the engine to be lifted, we need to determine the length of cable that corresponds to a lift of 24π feet.
The formula to find the length of cable when it goes around a pulley is given by:
Length of cable = 2π * radius
Let's substitute the given radius into the formula:
Length of cable = 2π * 6 feet
Length of cable = 12π feet
Now, we can set up a proportion to find the length of cable corresponding to a lift of 24π feet:
Length of cable / Lift distance = 12π feet / 24π feet
Since the units of π feet cancel out, we are left with:
Length of cable / Lift distance = 12 / 24
Simplifying the right side of the equation, we get:
Length of cable / Lift distance = 1/2
Now, let's convert this ratio to degrees of rotation. We know that a full circle corresponds to 360 degrees of rotation. So, for a ratio of 1/2, the degrees of rotation would be half of 360.
Degrees of rotation = (1/2) * 360
Degrees of rotation = 180 degrees
Therefore, 180 degrees of rotation are required for the engine to be lifted 24π feet using the pulley system.