Engineering Fundamentals

Saeed Moaveni

Chapter 8 Time and Time-Related Parameters - all with Video Answers

Educators

Chapter Questions

01:00

Problem 1

Create a calendar showing the beginning and the end of daylight saving time for the years $2009-2016$.

Heather Zimmers

Numerade Educator

02:12

According to the Department of Transportation analysis of energy consumption figures for 1974 and 1975 , observation of daylight saving time in the month of April in the years of 1974 and 1975 saved the country an estimated energy equivalent of 10,000 barrels of oil each day. Estimate how much energy is saved in the United States or your country due to observing daylight saving time in the current year.

Anand Jangid

Numerade Educator

01:24

Problem 3

Is there a need for a country near the equator to observe daylight saving time? Explain.

Km Neeraj

Numerade Educator

01:50

Problem 4

Besides energy savings, what are other advantages that observation of daylight saving time may bring?

Rodger Claar

Numerade Educator

00:45

Problem 5

Every year all around the world we celebrate certain cultural events dealing with our past. For example, in Christianity, Easter is celebrated in the spring and Christmas is celebrated in December; in the Jewish calendar, Yom Kippur is celebrated in October; and Ramadan, the time of fasting, is celebrated by Muslims according to a lunar calendar. Briefly discuss the basis of the Christian, Jewish, Muslim, and Chinese calendars.

Zachary Warner

Numerade Educator

03:48

Problem 6

In this problem you are asked to investigate how much water a leaky faucet wastes in one week, one month, and one year. Perform an experiment by placing a container under a leaky faucet and actually measure the amount of water accumulated in an hour (you can simulate a leaky faucet by just partially closing the faucet). You are to design the experiment. Think about the parameters that you need to measure. Express and project your findings in gallons/day, gallons/week, gallons/month, and gallons/year. At this rate, how much water is wasted by $10,000,000$ households with leaky faucets. Write a brief report to discuss your findings.

Caleb Miller

Numerade Educator

01:35

Problem 7

Next time you are putting gasoline in your car, determine the volumetric flow rate of the gasoline at the pumping station. Record the time that it takes to pump a known volume of gasoline into your car's gas tank. The flow meter at the pump will give you the volume in gallons, so all you have to do is to measure the time. Investigate the size of the storage tanks in your neighborhood gas station. Estimate how often the storage tank needs to be refilled. State your assumptions.

Justin Swantek

Numerade Educator

00:33

Problem 8

You are to investigate the water consumption in your house, apartment, or dormitory-whichever is applicable. For example, to determine bathroom water consumption, time how long it normally takes you to shower. Then place a bucket under the showerhead for a known period of time. Determine the total volume of water used when you take a typical shower. Estimate how much water you use during the course of a year just by showering. Identify other activities where you use water and estimate your amount of use.

Harsh Gadhiya

Numerade Educator

02:07

Problem 9

Using the concepts discussed in this chapter, measure the volumetric flow rate of water out of a drinking fountain.

Chai Santi

Numerade Educator

02:20

Problem 10

Convert the following speed limits from miles per hour (mph) to kilometers per hour $(\mathrm{km} / \mathrm{h})$ and from feet per second $(\mathrm{ft} / \mathrm{s})$ to meters per second $(\mathrm{m} / \mathrm{s})$. Think about the relative magnitude of values as you go from $\mathrm{mph}$ to $\mathrm{ft} / \mathrm{s}$ and as you go from $\mathrm{km} / \mathrm{h}$ to $\mathrm{m} / \mathrm{s}$. You may use Microsoft Excel to solve this problem.

Susan Hallstrom

Numerade Educator

03:05

Problem 11

Most car owners drive their cars an average of 12,000 miles a year. Assuming a 20 miles/gallon gas consumption rate, determine the amount of fuel consumed by 150 million car owners on the following time basis:
a. average daily basis
b. average weekly basis
c. average monthly basis
d. average yearly basis
e. over a period of ten years
Express your results in gallons and liters.

Charles Carter

Numerade Educator

03:21

Problem 12

Calculate the speed of sound for the U.S. standard atmosphere using, $c=\sqrt{k R T}$, where $c$ represents the speed of sound in $\mathrm{m} / \mathrm{s}, k$ is the specific heat ratio for air $(k=1.4)$, and $R$ is the gas constant for the air $(R=$ $286.9 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ ) and $T$ represents the temperature of the air in Kelvin. The speed of sound in atmosphere is the speed at which sound propagates through the air. You may use Excel to solve this problem.

Erika Bustos

Numerade Educator

01:25

Problem 13

Express Equation (8.5), the traffic density, in terms of number of vehicles per mile.

Carson Merrill

Numerade Educator

01:01

Problem 14

Express the angular speed of the earth in $\mathrm{rad} / \mathrm{s}$ and rpm.

Prabhu Ramji

Numerade Educator

00:45

Problem 15

What is the magnitude of the speed of a person at the equator due to rotational speed of the earth.

Mayukh Banik

Numerade Educator

10:06

Problem 16

Calculate the average speed of the gasoline exiting a nozzle at a gas station. Next time you go to a gas station, measure the volumetric flow rate of the gas first, and then measure the diameter of the nozzle. Use Equation (8.12) to calculate the average speed of the gasoline coming out of the nozzle. Hint: First measure the time that it takes to put so many gallons of gasoline into the gas tank!

Sriparna Bhattacharjee

Numerade Educator

01:33

Problem 17

Measure the volumetric flow rate of water coming out of a faucet. Also determine the average velocity of water leaving the faucet.

Chai Santi

Numerade Educator

05:02

Problem 18

Determine the speed of a point on the earth's surface in $\mathrm{ft} / \mathrm{s}, \mathrm{m} / \mathrm{s}, \mathrm{mph}, \mathrm{km} / \mathrm{h}$. State your assumptions.

Gopesh Vishwakarma

Numerade Educator

00:11

Problem 19

Into how many time zones are the United States and its territories divided?

Michelle Nguyen

Numerade Educator

00:46

Problem 20

Estimate the rotational speed of your car wheels when you are traveling at $60 \mathrm{mph}$.

Zulfiqar Ali

Numerade Educator

01:05

Problem 21

Determine the natural frequency of a pendulum whose length is $5 \mathrm{~m}$.

Nishant Kumar

Numerade Educator

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Problem 22

Determine the spring constant for Example $8.1$ if the system is to oscillate with a natural frequency of $5 \mathrm{~Hz}$.

Lainey Roebuck

Numerade Educator

03:17

Problem 23

Determine the traffic flow if 100 cars pass a known location during $10 \mathrm{~s}$.

Kush Khamesra

Numerade Educator

03:06

Problem 24

A conveyer belt runs on 3 -in. drums that are driven by a motor. If it takes $6 \mathrm{~s}$ for the belt to go from zero to the speed of $3 \mathrm{ft} / \mathrm{s}$, calculate the final angular speed of the drum and its angular acceleration. Assume constant acceleration.

Sheh Lit Chang

University of Washington

02:31

Problem 25

Chinook, a military helicopter, has two three-blade rotor systems, each turning in opposite directions. Each blade has a diameter of approximaterly $41 \mathrm{ft}$. The blades can spin at angular speeds of up to $225 \mathrm{rpm}$. Determine the translational speed of a particle located at the tip of a blade. Express your answer in $\mathrm{ft} / \mathrm{s}, \mathrm{mph}$, $\mathrm{m} / \mathrm{s}$, and $\mathrm{km} / \mathrm{h}$.

Jay Patel

Numerade Educator

01:01

Problem 26

Consider the piping system shown in the accompanying figure. The speed of water flowing through the 4-in.-diameter section of the piping system is $3 \mathrm{ft} / \mathrm{s}$. What is the volume flow rate of water in the piping system? Express the volume flow rate in $\mathrm{ft}^{3} / \mathrm{s}, \mathrm{gpm}$, and $\mathrm{L} / \mathrm{s}$. For the case of steady flow of water through the piping system, what is the speed of water in the 3 -in.-diameter section of the system?

Narayan Hari

Numerade Educator

02:15

Problem 27

Consider the duct system shown in the accompanying figure. Air flows through two 8 -in.-by-10-in. ducts that merge into a 18-in.-by-14-in. duct. The average speed of the air in each of the $8 \times 10$ ducts is $30 \mathrm{ft} / \mathrm{s}$. What is the volume flow rate of air in the $18 \times 14$ duct? Express the volume flow rate in $\mathrm{ft}^{3} / \mathrm{s}, \mathrm{ft}^{3} / \mathrm{min}$, and $\mathrm{m}^{3} / \mathrm{s}$. What is the average speed of air in the $18 \times 14$ duct?

Anand Jangid

Numerade Educator

02:26

Problem 28

A car starts from rest and accelerates to a speed of $60 \mathrm{mph}$ in $20 \mathrm{~s}$. The acceleration during this period is constant. For the next 20 minutes the car moves with the constant speed of $60 \mathrm{mph}$. At this time the driver of the car applies the brake and the car decelerates to a full stop in $10 \mathrm{~s}$. The variation of the speed of the car with time is shown in the accompanying diagram. Determine the total distance traveled by the car and the average speed of the car over this distance. Also plot the acceleration of the car as a function of time.

Allison Knapp

Numerade Educator

03:41

Problem 29

The drum of a clothing dryer is turning at a rate of 1 revolution every second when you suddenly open the door of the dryer. You noticed that it took $1.5$ seconds for the drum to completely stop. Determine the deceleration of the drum. State your assumptions.

Willis James

Numerade Educator

01:34

Problem 30

A drill bit is turning at a rate of 1200 revolutions per minute when you suddenly stop it by turning off the power. If the deceleration of the bite is $40 \mathrm{rad} / \mathrm{s}^{2}$, how long would it take for the bit to completely stop?

Zulfiqar Ali

Numerade Educator

02:43

Problem 31

On a gusty windy day, the blades of a wind turbine are turning at a rate of 200 revolutions per minute when suddenly the brakes are applied to stop the turbine to avoid failure. If the brakes cause a deceleration of 2 $\mathrm{rad} / \mathrm{s}^{2}$, how long would it take for the blades of the wind turbine to come to rest?

Marshall Styczinski

Numerade Educator

03:20

Problem 32

A plugged dishwasher sink with the dimensions of $2 \mathrm{ft}$ $\times 1.5 \mathrm{ft} \times 1 \mathrm{ft}$ is being filled with water from a faucet with an inner diameter of $1 \mathrm{in}$. If it takes 35 seconds to fill the sink to its rim, estimate the volumetric flow of water coming out of the faucet. What is the average velocity of water coming out of the faucet?

Prabhat Tyagi

Numerade Educator

01:53

Problem 33

Imagine the plug in the sink described in Problem $8.32$ leaks. If it now takes 40 seconds to fill the sink to its rim, estimate the volumetric flow rate of the leak.

Gregory Higby

Numerade Educator

02:15

Problem 34

A rectangular duct with dimensions of 12 in $\times 14$ in delivers conditioned air to a room at a rate of 1000 $\mathrm{ft}^{3} / \mathrm{min}$. What should be the size of a circular duct if the average air velocity inside the duct is to remain the same?

Anand Jangid

Numerade Educator

01:32

Problem 35

The tank shown in the accompanying figure is being filled by Pipes 1 and 2 . If the water level is to remain constant, what is the volumetric flow rate of water leaving the tank at 3 ? What is the average velocity of the water leaving the tank?

Sriparna Bhattacharjee

Numerade Educator

01:36

Problem 36

Imagine that the water level in Problem $8.35$ rises at a rate of $0.1 \mathrm{in} / \mathrm{s}$. Knowing the diameter of the tank is $6 \mathrm{in}$., what is the average velocity of the water leaving the tank?

Kratika Bhadauria

Numerade Educator

01:48

Problem 37

If it takes a bicyclist 20 seconds to reach a speed of $10 \mathrm{mph}$ from rest, what is her acceleration? For the next 10 minutes, she moves at the constant speed of $10 \mathrm{mph}$, and at this time, she applies her brakes, and the bicycle decelerates to a full stop in 4 seconds. What is the total distance travelled by the bicyclist? Determine the average speed of the cyclist during the first 20 seconds, 620 seconds, and 624 seconds.

Penny Riley

Numerade Educator

05:56

Problem 38

An object is dropped from the roof of a high-rise building at a distance of $450 \mathrm{ft}$. Prepare a table similar to Table $8.3$ showing the speed and acceleration of the object and the distance travelled by the object as a function of time.

Landon Basham

Numerade Educator

02:33

Problem 39

Solve Problem $8.38$ for a situation in which the object is given an initial vertical upward velocity of $4 \mathrm{ft} / \mathrm{s}$. Again, prepare a table similar to Table $8.3$ showing the speed and acceleration of the object and the distance travelled by the object as a function of time.

Gus Steppen

Numerade Educator

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Problem 40

Determine the natural frequency of the system given in Example $8.1$ if its mass is doubled.

Lainey Roebuck

Numerade Educator

01:15

Problem 41

The period of oscillation for a pendulum on Earth is 2 seconds. If the given pendulum oscillates with a period of $4.9$ seconds on the surface of the Moon, what is the acceleration due to gravity on the Moon's surface? Express your answer in both SI and U.S. Customary units.

Ajay Singhal

Numerade Educator

01:06

Problem 42

What is the period of oscillation of the pendulum given in Problem $8.40$ on Mar's surface? Given $g_{\text {Earth }}=9.81$ $\mathrm{m} / \mathrm{s}^{2}$ and $\mathrm{g}_{\mathrm{Mars}}=3.70 \mathrm{~m} / \mathrm{s}^{2}$.

Zhaojie Xu

Numerade Educator

01:43

Problem 43

The power to an electric motor running at a constant speed of $1600 \mathrm{rpm}$ is suddenly turned off. It takes 10 seconds for the motor to come to rest. What is the deceleration of the motor? How many turns does the motor make before it stops. State your assumptions.

Lisa Tarman

Numerade Educator

02:23

Problem 44

The 2009 World Record for the $100-\mathrm{m}$ sprint is $9.58$ seconds and belongs to a Jamaican runner named Usain Bolt. Assuming constant acceleration, determine the speed of Mr. Bolt at distances of $10 \mathrm{~m}, 20 \mathrm{~m}, 30 \mathrm{~m}$, $\ldots, 80 \mathrm{~m}, 90 \mathrm{~m}$, and $100 \mathrm{~m}$.

Melissa Munoz

Numerade Educator

00:47

Problem 45

The 1994 men's pole vault World Record of $6.14 \mathrm{~m}$ belongs to Mr. Sergey Bubka of Ukraine. If the pole vault mat has the dimensions of $6.0 \mathrm{~m} \times 8.0 \mathrm{~m} \times 0.8 \mathrm{~m}$, what is the vertical speed of the vaulter (Mr. Bubka) right before he strikes the mat?

Manuel Santana

Numerade Educator

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Problem 46

A typical household of four people consume approximately 80 gallons of water per day. Express the annual consumption rate of a city with a population of 100,000 people. Express your answer in gallons per year, $\mathrm{ft}^{3}$ per year, liters per year, and $\mathrm{m}^{3}$ per year.

Sarah Parrigin

Numerade Educator

05:09

Problem 47

The American Society of Heating, Ventilating, and Air Conditioning Engineers (ASHRAE) sets the standard for outdoor air requirement for ventilation purposes. For example, for a gymnasium, an outdoor air requirement of $20 \mathrm{cfm}$ (cubic feet per minute) per person is required. What is the total volume of the outdoor air that must be introduced into a gym during a 12-hour period if on average 30 people are using the gym every minute? Express your answer in $\mathrm{ft}^{3}$, liters, and $\mathrm{m}^{3}$.

P Krishnamurthy

Numerade Educator

00:41

Problem 48

Lake Mead near the Hoover Dam, which is the largest man-made lake in the United States, contains $28,537,000$ acre-foot of water (an acre-foot is the amount of water required to cover 1 acre to a depth of 1 foot). Express this water volume in gallons and $\mathrm{m}^{3}$.

David Collins

Numerade Educator

02:15

Problem 49

Within the next 10 to 15 years, wind turbines with rotor diameters of $180 \mathrm{~m}$ are anticipated to be developed and installed in Europe. If the blades of such turbines turn at a rate of 5 revolutions per minute, what is the speed of a point located at a tip of a blade? Express your answer in $\mathrm{ft} / \mathrm{s}, \mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h}$, and $\mathrm{mph}$.

Vysakh M

Numerade Educator

01:38

Problem 50

The design fluid (typically water and antifreeze) flow rate through a solar hot-water heater system is $0.02$ $\mathrm{gpm} / \mathrm{ft}^{2}$. If a system runs continuously for 3 hours and makes use of two solar panels (each $4 \mathrm{ft} \times 8 \mathrm{ft}$ ), what is the total volume of the fluid that goes through the collector during this period? Express your answer in gallons, $\mathrm{ft}^{3}$, liters, and $\mathrm{m}^{3}$.

Averell Hause

Carnegie Mellon University