9. Work & Energy

When you ride a bicycle at constant speed, nearly all the energy you expend goes into the work you do against the drag force of the air. Model a cyclist as having cross-section area 0.45 m² and, because the human body is not aerodynamically shaped, a drag coefficient of 0.90. Use 1.2 kg/m³ as the density of air at room temperature. Metabolic power is the rate at which your body 'burns' fuel to power your activities. For many activities, your body is roughly 25% efficient at converting the chemical energy of food into mechanical energy. What is the cyclist's metabolic power while cycling at 7.3 m/s?

How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m? How much power must the motor supply to do this in 50 s at constant speed?

What is the power produced by a light bulb with a voltage of $120V$ and a current of $0.045A$?

Water flows slowly over a dam at the rate of 320 kg/s and falls vertically 88 m before striking the turbine blades. Calculate the rate at which mechanical energy is transferred to the turbine blades, assuming 55% efficiency.

(II) Water is stored in an artificial lake created by a dam (Fig. 20–22). The water depth is 48 m at the dam, and a steady flow rate of 35 m³/s is maintained through hydroelectric turbines installed near the base of the dam. How much electrical power can be produced?

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How much work can a 3.0-hp motor do in 1.0h?

How much power must an elevator motor supply in order to lift a 1000 kg elevator at constant speed a height of 100m in 50 seconds?

If a circuit dissipates a reference power $P_0$ under certain conditions, what is the power dissipated by the circuit in terms of $P_0$ if the voltage across the circuit is doubled while the resistance remains constant?

A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying a 40 kg backpack filled with gear. How much power does he need to reach the top in 55 s?

The position of a 280-g object is given (in meters) by x = 4.0t³ - 8.0t² - 44t, where t is in seconds. What is the average net power input during the interval from t = 0s to t = 2.0 s, and in the interval from t = 2.0 s to 4.0 s?

Which of the following best describes what one $W$ is equal to?

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.

Which of the following is the correct SI unit for power?