0.7 5.8 power  (Page 4/8)

A spark of static electricity, such as that you might receive from a doorknob on a cold dry day, may carry a few hundred watts of power. Explain why you are not injured by such a spark.

What is the cost of operating a 3.00-W electric clock for a year if the cost of electricity is $0.0900 per $\text{kW}\cdot \mathrm{h}$ ?

(a) What is the average power consumption in watts of an appliance that uses $5\text{.}\text{00 kW}\cdot \mathrm{h}$ of energy per day? (b) How many joules of energy does this appliance consume in a year?

(a) What is the average useful power output of a person who does $6\text{.}\text{00}\times {\text{10}}^6\text{J}$ of useful work in 8.00 h? (b) Working at this rate, how long will it take this person to lift 2000 kg of bricks 1.50 m to a platform? (Work done to lift his body can be omitted because it is not considered useful output here.)

A 500-kg dragster accelerates from rest to a final speed of 110 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts and horsepower if this takes 7.30 s?

(a) Find the useful power output of an elevator motor that lifts a 2500-kg load a height of 35.0 m in 12.0 s, if it also increases the speed from rest to 4.00 m/s. Note that the total mass of the counterbalanced system is 10,000 kg—so that only 2500 kg is raised in height, but the full 10,000 kg is accelerated. (b) What does it cost, if electricity is $0.0900 per $\text{kW}\cdot \mathrm{h}$ ?

(a) How long would it take a $1\text{.}\text{50}\times {\text{10}}^5$ -kg airplane with engines that produce 100 MW of power to reach a speed of 250 m/s and an altitude of 12.0 km if air resistance were negligible? (b) If it actually takes 900 s, what is the power? (c) Given this power, what is the average force of air resistance if the airplane takes 1200 s? (Hint: You must find the distance the plane travels in 1200 s assuming constant acceleration.)

Calculate the power output needed for a 950-kg car to climb a $\mathrm{2.00º}$ slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N. Explicitly show how you follow the steps in the Problem-Solving Strategies for Energy .

(a) Calculate the power per square meter reaching Earth’s upper atmosphere from the Sun. (Take the power output of the Sun to be $4\text{.}\text{00}\times {\text{10}}^{\text{26}}\text{W}\text{.})$ (b) Part of this is absorbed and reflected by the atmosphere, so that a maximum of $1\text{.}{\text{30 kW/m}}^2$ reaches Earth’s surface. Calculate the area in ${\text{km}}^2$ of solar energy collectors needed to replace an electric power plant that generates 750 MW if the collectors convert an average of 2.00% of the maximum power into electricity. (This small conversion efficiency is due to the devices themselves, and the fact that the sun is directly overhead only briefly.) With the same assumptions, what area would be needed to meet the United States’ energy needs $(1\text{.}\text{05}\times {\text{10}}^{\text{20}}\text{J})\mathrm{?}$ Australia’s energy needs $(5\text{.}4\times {\text{10}}^{\text{18}}\text{J)?}$ China’s energy needs $(6\text{.}3\times {\text{10}}^{\text{19}}\text{J)?}$ (These energy consumption values are from 2006.)