Math  /  Geometry

QuestionDoes this acceleration seem large to you?
70. Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. 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). (a) Show that θ\theta (as defined as shown) is a 12.0m/s12.0-\mathrm{m} / \mathrm{s} turn of radius 30.0 m (as in a race).

Studdy Solution
Find θ\theta by taking the arctangent:
θ=tan1(0.4898) \theta = \tan^{-1}(0.4898)
θ26.0 \theta \approx 26.0^\circ
The angle θ\theta for a 12.0m/s12.0 \, \text{m/s} turn of radius 30.0m30.0 \, \text{m} is approximately:
26.0 \boxed{26.0^\circ}

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