Respuesta :
The relationship between the length of the circle and its radius allows to find the result for the revolutions turned when the distance decreases 8.60m is:
Angle = 17.8 rev
The length of a circle is given by the expression.
L = 2π r
Where L is the length of the circle and r is the radius of the circle.
They indicate the radius of the drum is r = 7.71 cm = 7.71 10⁻² m, let's find the length of the circle.
Lo = 2 π 7.71 10⁻²
Lo = 0.4844 m
Let's find the angle that the drum has rotated, using a direct proportional rule. If rotate an angle of 2π radians when you descend 0.4844 m, what angle you rotate when you descend 8.60 m.
#_ angles = [tex]8.6 m \ \frac{2\pi \ rev} { 0.4844 m}[/tex]
#_angle = 111.55 radians
Let's reduce to revolutions.
# _angles = 111.55 radians ( [tex]\frac{1 rev }{2\pi rad}[/tex] )
#_angulo = 17.8 rev
In conclusion, using the relationship between the length of the circle and its radius, we can find the result for the revolutions turned when the distance decreases is:
Angle = 17.8 rev
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