(c) Find an equation relating tan(0) with the speed of the bicycle v, radius r, and acceleration due to gravity, g. Hint: equate the vector decomposition of F (1) and (2) to your results from part (b)-(3) and (4). To type your equations, you can enter Greek letters by selecting the MathType popup button (red radical) in the answer box. For Greek letters, press the right-facing arrow next to the alpha ( a) symbol. tan(8) = (d) Based on your answer for (c), if the bicycle is vertical (0 = 0°), will it be able to traverse the curve while maintaining balance? O yes O no Why? (e) Calculate e for a 12 m/s turn of radius 28.5 m.

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter6: Applications Of Newton's Laws
Section: Chapter Questions
Problem 70P: Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. To...
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1.
Free-body diagram
YA
0
W
F
F
f
X
CG
W
F = sum of
N and f
N=W
Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in the figure.
To be stable, the force exerted by the ground must be on a line going through the center of gravity. The
force on the bicycle wheel can be resolved into two perpendicular components: friction parallel to the
road (this must supply the centripetal force) and the vertical normal force (which must equal the weight
of the system).
Transcribed Image Text:1. Free-body diagram YA 0 W F F f X CG W F = sum of N and f N=W Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in the figure. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components: friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the weight of the system).
(c) Find an equation relating tan(0) with the speed of the bicycle v, radius r, and acceleration due to
gravity, g. Hint: equate the vector decomposition of F (1) and (2) to your results from part (b)-(3) and
(4).
To type your equations, you can enter Greek letters by selecting the MathType popup button
(red radical) in the answer box. For Greek letters, press the right-facing arrow next to the alpha (
a) symbol.
tan(0) =
(d) Based on your answer for (c), if the bicycle is vertical (8=0°), will it be able to traverse the curve
while maintaining balance?
O yes
O no
Why?
(e) Calculate for a 12 m/s turn of radius 28.5 m.
0=
degrees
Transcribed Image Text:(c) Find an equation relating tan(0) with the speed of the bicycle v, radius r, and acceleration due to gravity, g. Hint: equate the vector decomposition of F (1) and (2) to your results from part (b)-(3) and (4). To type your equations, you can enter Greek letters by selecting the MathType popup button (red radical) in the answer box. For Greek letters, press the right-facing arrow next to the alpha ( a) symbol. tan(0) = (d) Based on your answer for (c), if the bicycle is vertical (8=0°), will it be able to traverse the curve while maintaining balance? O yes O no Why? (e) Calculate for a 12 m/s turn of radius 28.5 m. 0= degrees
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