1. Free-body diagram X 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). (2) Express friction and normal force in terms of F and A

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Chapter6: Applications Of Newton's Laws
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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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(b) Write Newton's second law for the horizontal and vertical directions. Take rightward to be the +x-
direction and vertically upward to be +y-direction. Write your equations in terms of the normal force
N, friction f, mass m, and g.
✓ = mv²/r (3)
Fnet, x
✓=0 (4)
Fnet,y E
(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) =
V
(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 10.5 m/s turn of radius 32 m.
8=
degrees
Transcribed Image Text:(b) Write Newton's second law for the horizontal and vertical directions. Take rightward to be the +x- direction and vertically upward to be +y-direction. Write your equations in terms of the normal force N, friction f, mass m, and g. ✓ = mv²/r (3) Fnet, x ✓=0 (4) Fnet,y E (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) = V (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 10.5 m/s turn of radius 32 m. 8= degrees
1.
Free-body diagram
YA
F
X
CG
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).
(a) Express friction and normal force in terms of F and 8.
Transcribed Image Text:1. Free-body diagram YA F X CG 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). (a) Express friction and normal force in terms of F and 8.
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