# 7.7 Power  (Page 4/8)

 Page 4 / 8

## Conceptual questions

Most electrical appliances are rated in watts. Does this rating depend on how long the appliance is on? (When off, it is a zero-watt device.) Explain in terms of the definition of power.

Explain, in terms of the definition of power, why energy consumption is sometimes listed in kilowatt-hours rather than joules. What is the relationship between these two energy units?

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.)

Why does earth exert only a tiny downward pull?
hello
Islam
Why is light bright?
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
thanks so much. i undersooth well
what is physics
is the study of matter in relation to energy
Kintu
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
what is power?
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
hi
Godfred
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
how can I read physics...am finding it difficult to understand...pls help
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju
I have a exam on 12 february
what is velocity
Jiti
the speed of something in a given direction.
Ju