The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 6.60 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 2.34 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 2.34 m from the center of the circle, we need to use the formula for centripetal acceleration:

a = (v^2) / r

where:
a is the centripetal acceleration,
v is the velocity of the object moving in a circular path, and
r is the radius of the circular path.

In this case, the length of the blade of the helicopter is given as 6.60 m, which means the radius of the circular path is half of the length of the blade, or 3.30 m (6.60 m / 2). Let's call this radius r1.

The ratio of the centripetal acceleration at the end of the blade (r1) to that which exists at a point located 2.34 m from the center of the circle (r2) can be calculated as follows:

a1 / a2 = (v1^2 / r1) / (v2^2 / r2)

Now, the velocity v1 at the end of the blade, located 3.30 m from the center of the circle, can be calculated using the relationship between linear speed (v) and angular speed (ω):

v1 = ω * r1

Similarly, the velocity v2 at the point located 2.34 m from the center of the circle can be calculated using the same relationship:

v2 = ω * r2

Since ω is the same for both points (as the angular speed of the blade remains constant), we can cancel it out from the equation:

a1 / a2 = (v1^2 / r1) / (v2^2 / r2)
= (r1^2 / r1) / (r2^2 / r2)
= r1 / r2

Substituting the values, we have:

a1 / a2 = 3.30 m / 2.34 m

Therefore, the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 2.34 m from the center of the circle is approximately 1.41 (3.30 m / 2.34 m).

To find the ratio of the centripetal acceleration at the end of the blade to that at a point located 2.34 m from the center of the circle, we need to use the formula for centripetal acceleration.

The formula for centripetal acceleration is:

a = (v^2) / r

where a is the centripetal acceleration, v is the linear velocity, and r is the radius of the circular path.

In this case, we can assume that the angular velocity of the helicopter blade is constant.

Given:

Length of the blade (L) = 6.60 m
Radius of the circle at the end of the blade (r1) = 6.60 m
Radius of the circle at a point located 2.34 m from the center (r2) = 2.34 m

To find the ratio, we need to calculate the centripetal acceleration at the end of the blade and at the point located 2.34 m from the center.

Step 1: Calculate the velocity at the end of the blade (v1).
Since the angular velocity is constant, we know that the linear velocity is given by the equation:

v1 = ω * r1

where ω is the angular velocity.

Step 2: Calculate the velocity at the point located 2.34 m from the center (v2).
Using the same equation as step 1, we can calculate v2:

v2 = ω * r2

Step 3: Calculate the centripetal accelerations.
Using the formula a = (v^2) / r, we can calculate the centripetal accelerations:

a1 = (v1^2) / r1
a2 = (v2^2) / r2

Step 4: Calculate the ratio.
To find the ratio, divide a1 by a2:

ratio = a1 / a2

Now let's calculate the values step-by-step.

Step 1: Calculate the velocity at the end of the blade (v1).
Since the length of the blade is given and we know the angular velocity, we can calculate v1:

v1 = ω * r1

Step 2: Calculate the velocity at the point located 2.34 m from the center (v2).
Using the same equation as step 1, we can calculate v2:

v2 = ω * r2

Step 3: Calculate the centripetal accelerations.
Using the formula a = (v^2) / r, we can calculate the centripetal accelerations:

a1 = (v1^2) / r1
a2 = (v2^2) / r2

Step 4: Calculate the ratio.
To find the ratio, divide a1 by a2:

ratio = a1 / a2

Let's calculate each step now.