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? (Do not put commas to your answer.)
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? (Do not put commas to your answer.)
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.
The kinetic energy of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity.
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Calculate the initial kinetic energy of the wind column before the interaction:
KE_initial = 1/2 * m * v_initial^2 KE_initial = 1/2 * 4 kg * (40 m/s)^2 KE_initial = 1/2 * 4 kg * 1600 m^2/s^2 KE_initial = 3200 Joules
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Calculate the final kinetic energy of the wind column after the interaction:
KE_final = 1/2 * m * v_final^2 KE_final = 1/2 * 4 kg * (20 m/s)^2 KE_final = 1/2 * 4 kg * 400 m^2/s^2 KE_final = 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 Energy_transferred = 3200 Joules - 800 Joules Energy_transferred = 2400 Joules
So, 2400 Joules of energy was transferred from the wind to the turbine.
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