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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

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
Collins Reply
What is thermal heat all about
Abel Reply
why uniform circular motion is called a periodic motion?.
Boniface Reply
when a train start from A & it returns at same station A . what is its acceleration?
Mwdan Reply
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
~\
Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
Worku Reply
what are the types of radioactivity
Worku
what is static friction
Golu Reply
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
Muhammed Reply
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
Eboh Reply
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
Subi Reply
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
yusuf Reply
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
syed Reply
definition of mass of conversion
umezurike Reply
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
please send the answer
Boniface
the range of objects and phenomena studied in physics is
Bethel Reply
I don't know please give the answer
Boniface
Practice Key Terms 4

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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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