Question

What is the linear velocity in MILES PER HOUR of the tip of a lawnmower blade spinning at 2700 revolutions per minute in a lawnmower that cuts a path that is 26 inches wide

Answer 1

26 x π = circumference
81.6814 = circumference

2700/81.6814 = 33.6855 inches per minute

Convert to miles per hour by multiplying by (12 x 5280 x 60)

33.6855 x 12 x 5280 x 60 = Miles per hour

Answer 2

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,

$f=\frac{2700}{60}=45$

The frequency is 45 revolution per hour.

The angular velocity is $\omega=2\pi f$

$\omega=2\times 3.14\times 45$

$\omega=282.6$ rad/hr.

The width of the path is the diameter of the circle centered at the midpoint of the blade,

Diameter = 26 inches

Radius = $\frac{26}{2}=13$ inches

Converting inches into miles,

$1 \text{ inch} = 1.5783e^{-5}\text{ mile}$

$13 \text{ inch} =13\times 1.5783e^{-5}\text{ mile}$

$13 \text{ inch} =0.000205177\text{ mile}$

Velocity is given by,

$V=\omega R$

$V=282.6\times 0.000205177$

$V=0.0579830202$

Therefore, The velocity is 0.06 miles per hour.