The mass of water passing through the turbine each second is 6.0 × 103 kg. The speedof the water is 2.0 m / s. 40% of the kinetic energy of the water is converted to electricalenergy.Calculate the electrical power generated
Question
The mass of water passing through the turbine each second is 6.0 × 103 kg. The speedof the water is 2.0 m / s. 40% of the kinetic energy of the water is converted to electricalenergy.Calculate the electrical power generated
Solution
To calculate the electrical power generated, we first need to find the kinetic energy of the water. The formula for kinetic energy is:
KE = 1/2 * m * v^2
where m is the mass and v is the velocity.
Step 1: Calculate the kinetic energy of the water KE = 1/2 * 6.0 × 10^3 kg * (2.0 m/s)^2 KE = 1/2 * 6.0 × 10^3 kg * 4.0 m^2/s^2 KE = 12,000 J (Joules)
Step 2: Calculate the amount of kinetic energy converted to electrical energy We know that 40% of the kinetic energy is converted to electrical energy. So, we calculate 40% of 12,000 J. Electrical energy = 0.40 * 12,000 J = 4800 J
Step 3: Calculate the electrical power generated Power is the rate of energy per unit time. In this case, the time is 1 second. So, the power is the same as the energy. Power = 4800 J/s = 4800 W (Watts)
So, the electrical power generated is 4800 Watts.
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