Activity 4 (The Water Bender) To generate electricity in one of the towns in Republic City, the town uses hydroelectric power produced by spinning a water wheel. Suppose water benders bend water to rotate a water wheel (see figure to the right) at five revolutions per minute (rpm). When you start your stopwatch, three seconds later the point P on the rim of the water wheel is at its greatest height. As the engineer, you are to model the distance d (in feet) of the point P from the surface of the water in terms of time t, what the stopwatch reads in seconds. If d varies sinusoidally with t, and the radius (in feet), answer the following by underlining the correct word to complete the sentence and then supplying the correct measurements to sketch the graph of this situation: a. AMPLITUDE: the amplitude is how high the point travels above the (center / side) of the wheel. What is the distance of the amplitude? P b. PERIOD: One period of this graph is equivalent to (Point P/ radius) coming back to its original starting position. How long does it take point P to travel one revolution? c. HORIZONTAL SHIFT: to determine the phase shift of the graph, you need to know a high point, low point, and (amplitude / middle point) relating to the problem. How long did it take for point P to reach its highest point? d. VERTICAL SHIFT: The vertical shift is the distance from the (lowest point on the rim of the water wheel / surface of the water) to the center of the wheel. What is the vertical shift? Using the information above, sketch one cycle of the graph and then write the equation of the cosine and sine function. Which equation was easier to figure? Why? Graph: Equation using cosine function: Equation using sine function:
Activity 4 (The Water Bender) To generate electricity in one of the towns in Republic City, the town uses hydroelectric power produced by spinning a water wheel. Suppose water benders bend water to rotate a water wheel (see figure to the right) at five revolutions per minute (rpm). When you start your stopwatch, three seconds later the point P on the rim of the water wheel is at its greatest height. As the engineer, you are to model the distance d (in feet) of the point P from the surface of the water in terms of time t, what the stopwatch reads in seconds. If d varies sinusoidally with t, and the radius (in feet), answer the following by underlining the correct word to complete the sentence and then supplying the correct measurements to sketch the graph of this situation: a. AMPLITUDE: the amplitude is how high the point travels above the (center / side) of the wheel. What is the distance of the amplitude? P b. PERIOD: One period of this graph is equivalent to (Point P/ radius) coming back to its original starting position. How long does it take point P to travel one revolution? c. HORIZONTAL SHIFT: to determine the phase shift of the graph, you need to know a high point, low point, and (amplitude / middle point) relating to the problem. How long did it take for point P to reach its highest point? d. VERTICAL SHIFT: The vertical shift is the distance from the (lowest point on the rim of the water wheel / surface of the water) to the center of the wheel. What is the vertical shift? Using the information above, sketch one cycle of the graph and then write the equation of the cosine and sine function. Which equation was easier to figure? Why? Graph: Equation using cosine function: Equation using sine function:
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Transcribed Image Text:Activity 4 (The Water Bender)
To generate electricity in one of the towns in Republic City, the town uses
hydroelectric power produced by spinning a water wheel. Suppose water
benders bend water to rotate a water wheel (see figure to the right) at five
revolutions per minute (rpm). When you start your stopwatch, three seconds
later the point P on the rim of the water wheel is at its greatest height. As the
engineer, you are to model the distance d (in feet) of the point P from the surface
of the water in terms of time t, what the stopwatch reads in seconds. If d varies
sinusoidally with t, and the radius (in feet), answer the following by underlining
the correct word to complete the sentence and then supplying the correct
measurements to sketch the graph of this situation:
a. AMPLITUDE: the amplitude is how high the point travels above the (center / side) of the wheel.
What is the distance of the amplitude?
b. PERIOD: One period of this graph is equivalent to (Point P / radius) coming back to its original starting
position.
How long does it take point P to travel one revolution?
c. HORIZONTAL SHIFT: to determine the phase shift of the graph, you need to know a high point, low point,
and (amplitude / middle point) relating to the problem.
How long did it take for point P to reach its highest point?
d. VERTICAL SHIFT: The vertical shift is the distance from the (lowest point on the rim of the water wheel /
surface of the water) to the center of the wheel.
What is the vertical shift?
Using the information above, sketch one cycle of the graph and then write the equation of the cosine and sine
function. Which equation was easier to figure? Why?
Graph:
Equation using cosine function:
Equation using sine function:
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 20 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY