# Question: The forces acting on Einstein and the bicycle Fig 2

The forces acting on Einstein and the bicycle (Fig. 2 of the Insight 8.1, Stability in Action) are the total weight of Einstein and the bicycle (mg) at the center of gravity of the system, the normal force (N) exerted by the road, and the force of static friction (fs) acting on the tires due to the road.

(a) If Einstein is to maintain balance, should the tangent of the lean angle θ(tan θ) be (1) greater than, (2) equal to, or (3) less than fs/N?

(b) The angle θ in the picture is about 11o. What is the minimum coefficient of static friction between the road and the tires?

(c) If the radius of the circle is 6.5 m, what is the maximum speed of Einstein’s bicycle?

(a) If Einstein is to maintain balance, should the tangent of the lean angle θ(tan θ) be (1) greater than, (2) equal to, or (3) less than fs/N?

(b) The angle θ in the picture is about 11o. What is the minimum coefficient of static friction between the road and the tires?

(c) If the radius of the circle is 6.5 m, what is the maximum speed of Einstein’s bicycle?

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