A rope is attached to a pulley with a weight attached to the end of the rope. What is the radius of the pulley if rotating the pulley 51.6 degrees lifts the weight 11.4 inches
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equate the arc length formula with the height lifted off the ground and solve for radius, be sure to convert degrees to radians
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What's s in the equation
There is no arc length. ???
read my first post
A full rotation would be 360 degrees. so 51.6 degrees would be a partial rotation.
51.6/360 would be the equivalent rotation. This partial rotation is equivalent to 11.4 inches of rotation. Other words a point on the circumference moved 11.4 inches.
So 51/360 of a rotation is equal to 11.4, what would a full (1)rotation be equal to?
From that we can conclude that .1433x=11.4 in. (51.6 degrees is 14% of 360degrees)
x=81.42in.,or the circumference of pulley is 81.42in. C=pi D.
D=C/pi=81.42/pi=25.9, radius would be D/2 or approx 12.9in