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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

material that allows electric current to pass through
Deng Reply
material which don't allow electric current is called
Deng
insulators
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the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
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Is the ship moving at a constant velocity?
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The full note of modern physics
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introduction to applications of nuclear physics
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Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
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A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
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A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
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Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
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Samuel
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the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
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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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