9. Work & Energy

Power

9. Work & Energy

Power

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Power of Pushing a Box

Power of a Winch on an Incline

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08:32

Anderson Video - Power

Anderson Video - Hydroelectric Dam

Anderson Video - Your Electric Bill

Calculating Power in Physics: Example Problems

Average power output for a crane lifting a load.

Introduction to power: definition, examples, power vs. time graphs, constant velocity power formula.

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Multiple Choice

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?

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Textbook Question

A 20.0-kg rock is sliding on a rough, horizontal surface at 8.00 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.200. What average power is produced by friction as the rock stops?

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Textbook Question

(II) An outboard motor for a boat is rated at 35 hp. If it can move a particular boat at a steady speed of 35 km/h, what is the total force resisting the motion of the boat?

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Textbook Question

(II) A driver notices that her 950-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 km/h?

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Textbook Question

(II) During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a 33° angle. If a player has a mass of 88 kg, estimate his average power output on the way up. Ignore friction and air resistance.

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Textbook Question

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

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Textbook Question

A gardener pushes a 12 kg lawnmower whose handle is tilted up 37° above horizontal. The lawnmower's coefficient of rolling friction is 0.15. How much power does the gardener have to supply to push the lawnmower at a constant speed of 1.2 m/s? Assume his push is parallel to the handle.

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Textbook Question

(a) How much work must you do to push a 10 kg block of steel across a steel table at a steady speed of 1.0m/s for 3.0 s? (b) What is your power output while doing so?

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Textbook Question

A hydroelectric power plant uses spinning turbines to transform the kinetic energy of moving water into electric energy with 80% efficiency. That is, 80% of the kinetic energy becomes electric energy. A small hydroelectric plant at the base of a dam generates 50 MW of electric power when the falling water has a speed of 18 m/s . What is the water flow rate—kilograms of water per second—through the turbines?

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Textbook Question

Astronomers using a 2.0-m-diameter telescope observe a distant supernova—an exploding star. The telescope's detector records 9.1 x 10¯¹¹ J of light energy during the first 10 s. It's known that this type of supernova has a visible-light power output of 5.0 x 10³⁷ W for the first 10 s of the explosion. How distant is the supernova? Give your answer in light years, where one light year is the distance light travels in one year. The speed of light is 3.0 x 10⁸ m/s .

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Textbook Question

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. (c) The food calorie is equivalent to 4190 J. How many calories does the cyclist burn if he rides over level ground at 7.3 m/s for 1 h?

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Textbook Question

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

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Textbook Question

A farmer uses a tractor to pull a 150 kg bale of hay up a 15° incline to the barn at a steady 5.0 km/h . The coefficient of kinetic friction between the bale and the ramp is 0.45. What is the tractor's power output?

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Textbook Question

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?

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Textbook Question

A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s . During the same time interval, a 30 kg greyhound can go from rest to 20 m/s . What is the average power output of each? Average power over a time interval ∆t is ∆E/∆t .

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Textbook Question

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. (b) 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.

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Textbook Question

(I) An 85-kg football player traveling 5.0 m/s is stopped in 1.0 s by a tackler.

(b) What average power is required to stop him?

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Textbook Question

Some electric power companies use placement of water to store energy. Water is pumped from a low reservoir to a high reservoir. To store the energy produced in 1.0 hour by a 180-MW electric power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is 380 m above the lower one. Water has a mass of 1.00 x 10³ kg for every 1.0m³ ( 1MW = 10⁶ W).

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Textbook Question

(II) Energy may be stored by pumping water to a high reservoir when demand is low and then releasing it to drive turbines (Fig. 20–15) during peak demand. Suppose water is pumped to a lake 105 m above the turbines at a rate of 1.00 x 10⁵ kg/s for 10.0 h at night.

(a) How much energy (kWh) is needed to do this each night?

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Textbook Question

(b) If all this energy is released during a 14-h day, at 75% efficiency, what is the average power output?

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Textbook Question

A bicylist of mass 75 kg (including the bicycle) can coast down a 5.0° hill at a steady speed of 12 km/h. Pumping hard, the cyclist can descend the hill at a speed of 32 km/h. Using the same power, at what speed can the cyclist climb the same hill? Assume the force of friction is proportional to the square of the speed v; that is, F𝒻ᵣ = bv² , where b is a constant.

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Textbook Question

III) The position of a 280-g object is given (in meters) by x = 4.0t³ - 8.0t² - 44t, where t is in seconds.

(c) 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?

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Textbook Question

Water flows slowly over a dam at the rate of 320 kg/s and falls vertically 88 m before striking the turbine blades. Calculate

(b) the rate at which mechanical energy is transferred to the turbine blades, assuming 55% efficiency.

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