PHYS 170 - Chapter 8. 2 (Dry Friction ) and 8.3 ( Wedges) 2/2 / W / Cgravity , always point Procedures downward ) Vo P >(pulling ford , given. in question ) 1 FBD 2 Equations & unknowns L> Unknowns: P, N, Fp , x 4 Set up 3 equations, EFx=0, 2Fy=0, SM,= 0 4 4 unknowns - 3 equilibrium equations: 1 impending motion 4> Write down restrictions F & M3. N and x = = Ly identify possible scenarios & check restrictions F. Coppose direction of motion ) (normal ford , occurs DX distance away ) N Static Vs. Kinetic Friction F= M3.N Wedges , Tapping ( Motion ) NOTE . When the object is in equilibrium or for restrictions , write with _ signs FE MON and x' ? . When the equilibrium is about to break , we assume tipping or shipping occurs , write with equal sign : ? SLIPPING: F = MgN (check x? ) TIPPING: x = 2 (check if F S M S N Important Points about Dry Friction Procedures for Analysis · Friction is a tangential force that resist the movement of one surface relative to another . · If no sliding occurs, Ff : Ms . N. (Normal Force) coefficient of static friction . If sliding occurs at slow speed , FF max = M . N ( Normal Force ) coefficient of Kinetic friction · Draw FBD 4) assume frictional forces as unknown, unless it is stated impending motion or shipping occurs ~> # of unknowns - # of equilibrium equations = # of impending motion · Equations of Equilibrium & Friction W> EFx, EF4, EM around a point Example 8. 1 The uniform crate shown in Fig. 8-7a has a mass of 20 kg. If a force P = 80 Nis applied to the crate, determine if it remains in equilibrium. The coefficient of static friction is A4, = 0.3. P-80 N 0,8m IW 30 0.2 m F: W= 20kg x 9.8m/s2 = 196.IN 1 FBD . for rectangular objects the Normal force act distance or away and create counter - clockwise momentum ( counteract the tipping effect caused by P) · friction force oppose the direction of motion Unknowns: Ff, Nc, Dx Equations of Equilibrium : SF= 0 80 cos 30° N - F1 = 0 Px => F1 = 80 cos 30° = 69. 3N EFy = 0 80 sin 30? + W - Nc = 0 Py Nc = 80 sin 30° + 196 . ZN = 236.2N sub in EMp =0 (80 sin 30") (0. 4m) - (80 cos 30° N) (0.2m) + Nc (x) = 0 x= - 0.00 908m = - 9.08mm Example 8.2 It is observed that when the bed of the dump truck is raised to an angle of 8 = 25° the vending machines will begin to slide off the hed. Fig 8-82. Determine the static coefficient of friction between a vending machine and the surface of the truckbed.