Final answer:
To find the linear speed of the blade tip, the circumference of the rotor's path is multiplied by its rotational speed in rev/sec, resulting in a speed of 226.2 m/s. To determine the radial acceleration, the square of this speed is divided by the blade length, then divided by the acceleration due to gravity, yielding an acceleration 143.73 times that of gravity.
Step-by-step explanation:
Part A: Calculating the Linear Speed of the Blade Tip
To calculate the linear speed of the blade tip, we can use the formula for the circumference of a circle (C = 2πr) where r is the length of the helicopter blade. Since the blade is 3.60 m long, we can say:
C = 2π(3.60 m) = 22.62 m (circle's circumference).
The rotor makes 600 revolutions per minute, so we need to convert this to seconds:
600 rev/min × 1 min/60 sec = 10 rev/sec.
The linear speed v is the circumference multiplied by the number of revolutions per second:
v = C × rev/sec = 22.62 m × 10 rev/sec = 226.2 m/s.
Part B: Calculating the Radial Acceleration of the Blade Tip
The formula for centripetal (or radial) acceleration is a = v²/r. We already know v (226.2 m/s) and r (3.60 m), so we substitute these values into the formula to get the acceleration in m/s².
Now, to express this as a multiple of the acceleration of gravity g (9.8 m/s²), we divide the centripetal acceleration by g:
a/g = (226.2 m/s)² / (3.60 m) / 9.8 m/s²
By calculating that, we find the ratio of the radial acceleration to g is approximately 1408.53 m/s² / 9.8 m/s² = 143.73. Thus, the radial acceleration is 143.73 times the acceleration due to gravity.