Question

A dancer is standing on one leg on a drawbridge that is about to open. The coefficients of static and kinetic friction between the drawbridge and the dancer's foot are μ_s and μ_k, respectively. n represents the normal force exerted on the dancer by the bridge, and F_g represents the gravitational force exerted on the dancer, as shown in the drawing. (Intro1 figure) For all the questions, we can assume that the bridge is a perfectly flat surface and lacks the curvature characteristic of most bridges

Part A

Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on one leg. What is the horizontal component of the friction force f?

Express your answer in terms of some or all of the variables n, μ_s, and/or μ_k.

Part B

(part 1 figure) The drawbridge then starts to rise. The dancer continues to stand on one leg. The drawbridge stops just at the point where the dancer is on the verge of slipping. What is the magnitude f of the frictional force now?

Express your answer in terms of some or all of the variables n, μ_s, and/or μ_s. The angle θ should not appear in your answer.

Part C

Then, because the bridge is old and poorly designed, it falls a little bit and then jerks. This causes the dancer to slide down the bridge. What is the magnitude f of the frictional force now?

Express your answer in terms of some or all of the variables n, μ_s, and/or μ_k. The angle θ should not appear in your answer.

Answer 1

Answer 2

since the surface is flat and there is no tendency ofmotion along the surface the frictional force is zero.