Calculate the kinetic energy stored in a helicopter rotor consisting of four blades each 8m long and with a mass of 50kg if the tips of the blade are moving at 200m/s.
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To calculate the kinetic energy stored in a helicopter rotor, we need to use the formula for kinetic energy. Kinetic energy (KE) is given by the equation:
KE = 1/2 * m * v^2
where KE is the kinetic energy, m is the mass, and v is the velocity.
In this case, we have a rotor consisting of four blades, each 8m long and with a mass of 50kg. So, the total mass of the four blades is 4 * 50kg = 200kg.
First, let's calculate the velocity at the tip of the blade. We know that the tips of the blade are moving at 200m/s.
Now, let's plug in the values in the formula to calculate the kinetic energy:
KE = 1/2 * m * v^2
= 1/2 * 200kg * (200m/s)^2
Now, let's simplify the equation:
KE = 1/2 * 200 * (200)^2
= 1/2 * 200 * 40000
= 1/2 * 8000000
= 4000000 joules (J)
Therefore, the kinetic energy stored in the helicopter rotor is 4000000 joules (J).