(g) In designing a new wheel with the same diameter and same ride duration as before it is proposed that the wheel's angular speed should not be constant but instead should take the form of 10 dt = 0.00049365 +0.5 in rad/sec during the first half of the ride when the rider is ascending and 10 = 0.017895 t-0.1882 in rad/sec during the second half, when the rider is descending. dt Determine the total angular displacement of the wheel between the time intervals of t = 250 sec and t = 600 sec. Also calculate the total curved distance that the rider travels between the times of t = 150 sec and t =720 sec.
(g) In designing a new wheel with the same diameter and same ride duration as before it is proposed that the wheel's angular speed should not be constant but instead should take the form of 10 dt = 0.00049365 +0.5 in rad/sec during the first half of the ride when the rider is ascending and 10 = 0.017895 t-0.1882 in rad/sec during the second half, when the rider is descending. dt Determine the total angular displacement of the wheel between the time intervals of t = 250 sec and t = 600 sec. Also calculate the total curved distance that the rider travels between the times of t = 150 sec and t =720 sec.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
With reference to the attached scenario and questions:
The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation.
Transcribed Image Text:(g) In designing a new wheel with the same diameter and same ride duration as before it is
proposed that the wheel's angular speed should not be constant but instead should take
the form of
de
dt
de
= 0.00049365 t0.5 in rad/sec during the first half of the ride when the rider is ascending and
= 0.017895 t-0.1882 in rad/sec during the second half, when the rider is descending.
dt
Determine the total angular displacement of the wheel between the time intervals of t = 250
sec and t = 600 sec. Also calculate the total curved distance that the rider travels between
the times of t = 150 sec and t =720 sec.
de
(h) To make the ride more exciting it is proposed that the wheel should ascend in such a way
that the rate of change of 0 with respect to t follows an exponential model of the form dt
aekt during the first quarter of the ride and debe-mt during the second quarter with a, b,
m and k all being constants. The same patterns are followed during the second half of the
ride. The wheel diameter and ride duration still unchanged.
Suggest possible values for the constants mentioned and use them to evaluate the angle through
which a rider goes between the time intervals of t =100 sec and of t =300 sec
Transcribed Image Text:Scenario
As a junior employee of a fairground and amusement company providing safe entertainment for
the public, you have been assigned to the design and build team responsible to create various
rides and fun activities at a theme park.
Your employer wishes to build a giant wheel similar to the one shown in Figure 1
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Can you please answer question H on the attached image. I think this got missed off the previous answer.
Thanks
Transcribed Image Text:(g) In designing a new wheel with the same diameter and same ride duration as before it is
proposed that the wheel's angular speed should not be constant but instead should take
the form of
de
dt
de
= 0.00049365 t0.5 in rad/sec during the first half of the ride when the rider is ascending and
= 0.017895 t-0.1882 in rad/sec during the second half, when the rider is descending.
dt
Determine the total angular displacement of the wheel between the time intervals of t = 250
sec and t = 600 sec. Also calculate the total curved distance that the rider travels between
the times of t = 150 sec and t =720 sec.
de
(h) To make the ride more exciting it is proposed that the wheel should ascend in such a way
that the rate of change of 0 with respect to t follows an exponential model of the form dt
aekt during the first quarter of the ride and debe-mt during the second quarter with a, b,
m and k all being constants. The same patterns are followed during the second half of the
ride. The wheel diameter and ride duration still unchanged.
Suggest possible values for the constants mentioned and use them to evaluate the angle through
which a rider goes between the time intervals of t =100 sec and of t =300 sec
Solution
by Bartleby ExpertRecommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
