"Hand-in question": While biking, the force of air resistance F (mass times length, per time- squared) appears to be positively related to the speed v (length per time) at which the bike travels and the cross-sectional area A (length-squared) of bike and biker. However, the force involves mass and hence cannot depend on v and A alone. Let the force also depend on the air density p (mass per length-cubed). Hence, the force F can be expressed as some multiplicative combination of v, A and p, that is F = kv" Aª p², for k E R. Find the values of r, y and z that result in the above equation being dimensionally consistent.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
"Hand-in question": While biking, the force of air resistance F (mass times length, per time-
squared) appears to be positively related to the speed v (length per time) at which the bike travels
and the cross-sectional area A (length-squared) of bike and biker. However, the force involves mass
and hence cannot depend on v and A alone. Let the force also depend on the air density p (mass
per length-cubed). Hence, the force F can be expressed as some multiplicative combination of v,
A and p, that is
F = kv" Aª p², for k E R.
Find the values of r, y and z that result in the above equation being dimensionally consistent.
Transcribed Image Text:"Hand-in question": While biking, the force of air resistance F (mass times length, per time- squared) appears to be positively related to the speed v (length per time) at which the bike travels and the cross-sectional area A (length-squared) of bike and biker. However, the force involves mass and hence cannot depend on v and A alone. Let the force also depend on the air density p (mass per length-cubed). Hence, the force F can be expressed as some multiplicative combination of v, A and p, that is F = kv" Aª p², for k E R. Find the values of r, y and z that result in the above equation being dimensionally consistent.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,