Answer:
The velocity is 0.06 miles per hour.
Step-by-step explanation:
Given : A lawnmower blade spinning at 2700 revolutions per minute in a lawnmower that cuts a path that is 26 inches wide.
To find : What is the linear velocity in miles per hour of the tip of a lawnmower blade?
Solution :
A lawnmower blade spinning at 2700 revolutions per minute.
i.e. the frequency of blade is f=2700 rpm
Converting minute into hour,
[tex]f=\frac{2700}{60}=45[/tex]
The frequency is 45 revolution per hour.
The angular velocity is [tex]\omega=2\pi f[/tex]
[tex]\omega=2\times 3.14\times 45[/tex]
[tex]\omega=282.6[/tex] rad/hr.
The width of the path is the diameter of the circle centered at the midpoint of the blade,
Diameter = 26 inches
Radius = [tex]\frac{26}{2}=13[/tex] inches
Converting inches into miles,
[tex]1 \text{ inch} = 1.5783e^{-5}\text{ mile}[/tex]
[tex]13 \text{ inch} =13\times 1.5783e^{-5}\text{ mile}[/tex]
[tex]13 \text{ inch} =0.000205177\text{ mile}[/tex]
Velocity is given by,
[tex]V=\omega R[/tex]
[tex]V=282.6\times 0.000205177[/tex]
[tex]V=0.0579830202[/tex]
Therefore, The velocity is 0.06 miles per hour.
