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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.

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Problems&Exercises

The Crab Nebula (see [link] ) pulsar is the remnant of a supernova that occurred in A.D. 1054. Using data from [link] , calculate the approximate factor by which the power output of this astronomical object has declined since its explosion.

A supernova explosion.
Crab Nebula (credit: ESO, via Wikimedia Commons)
2 × 10 10 size 12{2 times "10" rSup { size 8{-"10"} } } {}
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Suppose a star 1000 times brighter than our Sun (that is, emitting 1000 times the power) suddenly goes supernova. Using data from [link] : (a) By what factor does its power output increase? (b) How many times brighter than our entire Milky Way galaxy is the supernova? (c) Based on your answers, discuss whether it should be possible to observe supernovas in distant galaxies. Note that there are on the order of 10 11 size 12{"10" rSup { size 8{"11"} } } {} observable galaxies, the average brightness of which is somewhat less than our own galaxy.

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A person in good physical condition can put out 100 W of useful power for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time: (a) How many people would it take to run a 4.00-kW electric clothes dryer? (b) How many people would it take to replace a large electric power plant that generates 800 MW?

(a) 40

(b) 8 million

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What is the cost of operating a 3.00-W electric clock for a year if the cost of electricity is $0.0900 per kW h size 12{"kW" cdot h} {} ?

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A large household air conditioner may consume 15.0 kW of power. What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per kW h size 12{"kW" cdot h} {} ?

$149

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(a) What is the average power consumption in watts of an appliance that uses 5 . 00 kW h size 12{5 "." "00 kW" cdot h} {} of energy per day? (b) How many joules of energy does this appliance consume in a year?

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(a) What is the average useful power output of a person who does 6 . 00 × 10 6 J size 12{6 "." "00" times "10" rSup { size 8{6} } " 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) 208 W

(b) 141 s

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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?

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(a) How long will it take an 850-kg car with a useful power output of 40.0 hp (1 hp = 746 W) to reach a speed of 15.0 m/s, neglecting friction? (b) How long will this acceleration take if the car also climbs a 3.00-m-high hill in the process?

(a) 3.20 s

(b) 4.04 s

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(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 kW h size 12{"kW" cdot h} {} ?

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(a) What is the available energy content, in joules, of a battery that operates a 2.00-W electric clock for 18 months? (b) How long can a battery that can supply 8 . 00 × 10 4 J size 12{8 "." "00" times "10" rSup { size 8{4} } " J"} {} run a pocket calculator that consumes energy at the rate of 1 . 00 × 10 3 W size 12{1 "." "00" times "10" rSup { size 8{-3} } " W"} {} ?

(a) 9 . 46 × 10 7 J size 12{9 "." "46" times "10" rSup { size 8{7} } " J"} {}

(b) 2 . 54 y size 12{2 "." "54" times "10" rSup { size 8{7} } " J"} {}

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(a) How long would it take a 1 . 50 × 10 5 size 12{1 "." "50" times "10" rSup { size 8{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.)

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Calculate the power output needed for a 950-kg car to climb a 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 .

Identify knowns: m = 950 kg size 12{m="950"`"kg"} {} , slope angle θ = 2.00º , v = 3.00 m/s , f = 600 N size 12{f="600"`N} {}

Identify unknowns: power P size 12{P} {} of the car, force F size 12{F} {} that car applies to road

Solve for unknown:

P = W t = Fd t = F d t = Fv , size 12{P= { {W} over {t} } = { { ital "Fd"} over {t} } =F left ( { {d} over {t} } right )= ital "Fv",} {}

where F size 12{F} {} is parallel to the incline and must oppose the resistive forces and the force of gravity:

F = f + w = 600 N + mg sin θ size 12{F=f+w="600 N"+ ital "mg""sin"θ} {}

Insert this into the expression for power and solve:

P = f + mg sin θ v = 600 N + 950 kg 9.80 m/s 2 sin 2º ( 30.0 m/s ) = 2.77 × 10 4 W alignl { stack { size 12{P= left (f+ ital "mg""sin"θ right )v} {} #size 12{ {}= left ["600 N"+ left ("950 kg" right ) left (9 "." "80 m/s" rSup { size 8{2} } right )"sin2"° right ] \( "30" "." "0 m/s" \) } {} #=2 "." "77" times "10" rSup { size 8{4} } `W {} } } {}

About 28 kW (or about 37 hp) is reasonable for a car to climb a gentle incline.

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(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 . 00 × 10 26 W . ) (b) Part of this is absorbed and reflected by the atmosphere, so that a maximum of 1 . 30 kW/m 2 reaches Earth’s surface. Calculate the area in 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 . 05 × 10 20 J ) ? size 12{ \( 1 "." "05" times "10" rSup { size 8{"20"} } " J" \) ?} {} Australia’s energy needs ( 5 . 4 × 10 18 J)? size 12{ \( 5 "." 4 times "10" rSup { size 8{"18"} } " J" \) ?} {} China’s energy needs ( 6 . 3 × 10 19 J)? size 12{ \( 6 "." 3 times "10" rSup { size 8{"19"} } " J" \) ?} {} (These energy consumption values are from 2006.)

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Questions & Answers

the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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