A wind column with a mass of 4 kg has an initial velocity of 40 m/s before interacting with a wind turbine. After the interaction, the wind has a velocity of 20 m/s. How much energy was transferred from the wind to the turbine?
Question
A wind column with a mass of 4 kg has an initial velocity of 40 m/s before interacting with a wind turbine. After the interaction, the wind has a velocity of 20 m/s. How much energy was transferred from the wind to the turbine?
Solution
To solve this problem, we need to use the principle of conservation of energy. The energy before the interaction should be equal to the energy after the interaction plus the energy transferred to the turbine.
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First, we calculate the initial kinetic energy of the wind column before the interaction. The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass and v is the velocity.
KE_initial = 1/2 * 4 kg * (40 m/s)^2 = 3200 Joules
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Next, we calculate the final kinetic energy of the wind column after the interaction.
KE_final = 1/2 * 4 kg * (20 m/s)^2 = 800 Joules
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The energy transferred to the turbine is the difference between the initial and final kinetic energy.
Energy_transferred = KE_initial - KE_final = 3200 Joules - 800 Joules = 2400 Joules
So, the wind turbine received 2400 Joules of energy from the wind column.
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