How to Calculate Rotational and Translational Kinetic Energy of a Helicopter?
a) What is the formula to find the rotational kinetic energy in the blades of a helicopter?
b) How do you calculate the translational kinetic energy of a helicopter when it flies at a certain speed?
c) What is the maximum height a helicopter could fly if all of its rotational kinetic energy is used to lift it?
a) Answer
The formula for rotational kinetic energy is KE_rot = (1/2)Iω², where I is the moment of inertia.
b) Answer
The formula for translational kinetic energy is KE_trans = (1/2)mv², where m is the mass of the helicopter and v is its velocity.
c) Answer
To calculate the maximum height, set the rotational kinetic energy equal to the potential energy due to gravity, KE_rot = mgh, and solve for h.
A small rescue helicopter has 4 blades, each 4m long and 50kg in mass, and it carries a load of 1000kg.
a) To find the rotational kinetic energy in the blades when rotating at 300 rpm, we can use the formula KE_rot = (1/2)Iω², where I = 4mr²/3 for 4 blades. Calculate the values and solve for KE_rot.
b) For the translational kinetic energy of the helicopter when flying at 20 m/s, apply the formula KE_trans = (1/2)mv² using the given velocity and mass of the helicopter.
c) To determine the maximum height the helicopter could fly if all its rotational kinetic energy is utilized for lifting, set KE_rot equal to the potential energy due to gravity, solve for h, and find the height it could reach.