Question

You are pushing against a door while your body is slanted. The door is made of smooth ice and has zero friction. The floor though, is made of rough sandpaper and has coefficients of friction μ_s and μ_k, both of which are non-zero.

Model yourself as a uniform one-dimensional rod of mass M and length L. Your body makes angle θ relative to the ground.

You know: M, L, θ, μ_s, μ_k, g (also remember that there is no friction between the door and you)

Part A: If you are stationary without slipping, determine the magnitude of normal force exerted on you by the wall.

Part B: Now you try leaning more horizontal so that your feet get closer and closer to slipping on the floor. What is the smallest angle θ_smallest relative to the ground without slipping?

Answer 1

suppose length of rod = L your weight (M*g) act at mid point L/2 - No N1 = normal force between you and wall and there is no friction. N2 =normal force between you and floor and friction f By Newton's second law - - Na-Mg=0 N2=Mg (i) { Fx=0 N,- f = 0 normal force exerted on you by the wall- N, - f = 4N2) = Us(mg) Total torque about point A=0 (N2XL COBO) - (f ) Sino) - mg (cose) = 0 = Nz cose-mg Cono = f sino mg Caso-mac caso = Us Mg(sino) tano = tales o = tant' ( 2ms)