The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 7.0 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 2.7 m from the center of the circle.

To find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 2.7 m from the center of the circle, we need to use the formula for centripetal acceleration.

Centripetal acceleration is given by the equation: ac = v² / r

where ac is the centripetal acceleration, v is the linear velocity, and r is the radius of the circle.

First, let's calculate the linear velocity at the end of the blade. The linear velocity is the tangential speed at any given point on the rotating object and is given by the equation: v = ωr

where ω is the angular velocity and r is the radius.

Here, we are not given the angular velocity, but we can find it using the fact that the entire blade of the helicopter completes one revolution in a certain time period. Since one revolution is equivalent to 2π radians, we can use the equation: ω = 2π / T

where T is the time period for one revolution.

To find T, we need to know the rotational speed of the helicopter. If we assume that the helicopter is rotating at a constant rate of 300 revolutions per minute, we can convert it to radians per second by multiplying by 2π/60, as 1 minute is equal to 60 seconds.

ω = (300 rev/min) * (2π rad/rev) * (1 min/60 s) = 10π rad/s

Now that we have the angular velocity, we can calculate the linear velocity at the end of the blade:

v = ωr = (10π rad/s) * (7.0 m) = 70π m/s

Next, let's calculate the centripetal acceleration at the end of the blade:

ac(end) = v² / r(end) = (70π m/s)² / 7.0 m = 700π² m²/s²

Now, let's calculate the centripetal acceleration at the point located 2.7 m from the center of the circle:

ac(2.7) = v² / r(2.7) = (70π m/s)² / 2.7 m = 6230π² / 9 m²/s²

Finally, we can find the ratio of the centripetal acceleration at the end of the blade to that at a point located 2.7 m from the center:

ac(end) / ac(2.7) = (700π² m²/s²) / (6230π² / 9 m²/s²)

Simplifying the expression, we get:

ac(end) / ac(2.7) = 9 / 623

Therefore, the ratio of the centripetal acceleration at the end of the blade to that at a point located 2.7 m from the center is approximately 0.014 in decimal form or 1/70 in fraction form.