Let's Calculate the Rotational Kinetic Energy of a Small Rescue Helicopter!
Have you ever wondered how the rotational kinetic energy of a small rescue helicopter is calculated?
Let's dive into the details of the calculation based on the given data:
Calculating Rotational Kinetic Energy
To calculate the rotational kinetic energy of a small rescue helicopter, we need to consider the rotational motion of its blades and their properties.
Given data:
- Length of each blade: 4.00 m
- Mass of each blade: 50.0 kg
- Total loaded mass of the helicopter: 1000 kg
- Rotational speed of blades: 300 rev/min
Now, let's break down the calculation:
Calculating Rotational Kinetic Energy of the Blades
First, we need to calculate the moment of inertia of one blade (I₁):
I₁ = 1/3 * m * L² = 1/3 * 50 * 4² = 267 kg-m²
Next, we find the inertia of all four blades (I):
I = 4 * I₁ = 4 * 267 = 1067 kg-m²
Given the rotational speed of 300 rev/min (5 rad/s), we can calculate the angular velocity (ω):
ω = 2 * π * f = 31.4 rad/s
Finally, we can determine the rotational kinetic energy (KE) of the blades:
KE = 1/2 * I * ω² = 1/2 * 1067 * 31.4² = 526,000 J
Therefore, the rotational kinetic energy of the small rescue helicopter's blades is 526,000 Joules.
Understanding these calculations gives us insight into the energy involved in the rotation of helicopter blades during a rescue mission.