6. 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 system's weight). Free-body diagram CG F = sum of N and f (a) Show that 0 (as defined in the figure) is related to the speed V and radius of curvature r of the turn in the same way as for an ideally banked roadway- N= w that is, 0 = tan¬' v² / rg -1

6. 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 system's weight). Free-body diagram CG F = sum of N and f (a) Show that 0 (as defined in the figure) is related to the speed V and radius of curvature r of the turn in the same way as for an ideally banked roadway- N= w that is, 0 = tan¬' v² / rg -1

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

6. Part of riding a bicycle involves leaning at the correct angle when making a
Free-body diagram
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-
N
w
friction parallel to the road (this must supply the centripetal force), and
the vertical normal force (which must equal the system's weight).
F = sum of
w
N and f
(a) Show that 0 (as defined in the figure) is related to the speed V and radius
N = w
f
of curvature r of the turn in the same way as for an ideally banked roadway-
that is, o = tan¬' v² / rg
(b) Calculate 0 for a 12.0 m/s turn of radius 30.0 m (as in a race).

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