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"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.

"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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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"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.
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