# 2.2 Power  (Page 4/8)

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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.

## 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.

$2×{\text{10}}^{-\text{10}}$

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 ${\text{10}}^{\text{11}}$ observable galaxies, the average brightness of which is somewhat less than our own galaxy.

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

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

$149 (a) What is the average power consumption in watts of an appliance that uses $5\text{.}\text{00 kW}\cdot h$ 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 $6\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.20em}{0ex}}\text{J}$ 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) $\text{208 W}$ (b) 141 s 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) 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 (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 $\text{kW}\cdot h$ ?

(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 $8\text{.}\text{00}×{\text{10}}^{4}\phantom{\rule{0.20em}{0ex}}\text{J}$ run a pocket calculator that consumes energy at the rate of $1\text{.}\text{00}×{\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}\text{W}$ ?

(a) $9\text{.}\text{46}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{J}$

(b) $2\text{.}\text{54 y}$

(a) How long would it take a $1\text{.}\text{50}×{\text{10}}^{5}$ -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 $2.00º$ 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: $m=\text{950 kg}$ , $\text{slope angle}\phantom{\rule{0.25em}{0ex}}\theta =2.00º$ , $v=3.00 m/s$ , $f=\text{600 N}$

Identify unknowns: power $P$ of the car, force $F$ that car applies to road

Solve for unknown:

$P=\frac{W}{t}=\frac{\text{Fd}}{t}=F\left(\frac{d}{t}\right)=\text{Fv},$

where $F$ is parallel to the incline and must oppose the resistive forces and the force of gravity:

$F=f+w=\text{600 N}+\text{mg}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta$

Insert this into the expression for power and solve:

$\begin{array}{lll}P& =& \left(f+\text{mg}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \right)v\\ & =& \left[\text{600 N}+\left(\text{950 kg}\right)\left({\text{9.80 m/s}}^{2}\right)\text{sin 2º}\right]\left(\text{30.0 m/s}\right)\\ & =& \text{2.77}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}W\end{array}$

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

(a) Calculate the power per square meter reaching Earth’s upper atmosphere from the Sun. (Take the power output of the Sun to be $4\text{.}\text{00}×{\text{10}}^{\text{26}}\phantom{\rule{0.25em}{0ex}}\text{W}\text{.}\right)$ (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 $\left(1\text{.}\text{05}×{\text{10}}^{\text{20}}\phantom{\rule{0.25em}{0ex}}\text{J}\right)?$ Australia’s energy needs $\left(5\text{.}4×{\text{10}}^{\text{18}}\phantom{\rule{0.25em}{0ex}}\text{J)?}$ China’s energy needs $\left(6\text{.}3×{\text{10}}^{\text{19}}\phantom{\rule{0.25em}{0ex}}\text{J)?}$ (These energy consumption values are from 2006.)

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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