ES2501: Statics/Unit 24-1: Friction Related Problems Introduction Friction – force of resistance against motion or impending motion on and tangent the contact surface of two bodies. Classification of friction: against relative motion Fluid friction Friction Kinetic friction Dry friction Static friction Theories of friction: Several theories exist. For examples: against impending relative motion studied in Statics Impact between two rough surfaces causes friction bonding force between two surfaces causes friction

ES2501: Statics/Unit 24-2: Friction Related Problems Law of Dry Friction Friction exists on the contact surface If B moves or has impending motion relative to A B A Case 1: In Motion ------ Kinetic friction Case 2: Impending Motion ------ static friction Direction of motion relative to A Direction of impending motion trlstivr to A B B Normal pressure of A on B Kinetic Friction of A on B Normal Pressure of A on B Static Friction of A on B static friction coefficient Kinetic friction coefficient Magnitude: Magnitude: Direction: Opposite to the direction of the impeding motion Direction: Opposite to the direction of motion Maximum static friction --- a limit . Not necessarily the true static friction

ES2501: Statics/Unit 24-3: Friction Related Problems Angle of Static Friction Static friction can be characterized by either the static friction coefficient of the angle of static friction Direction of the impeding motion Maximum static Friction Normal Pressure Resultant of friction and pressure Materials of contact Metal on ice 0.03-0.05 Wood on wood 0.30-0.70 Leather on wood 0.20-0.50 Leather on metal 0.30-0.60 Aluminum on Aluminum 1.10-1.70

ES2501: Statics/Unit 24-4: Friction Related Problems Example 1: Find the friction force when F=5N and 10N, respectively. FBD: Equilibrium equations: Case 1: Case 2: Note: gives the limit but not true static friction; gives true kinetic friction, satisfied Not-satisfied Static friction Kinetic friction in motion

ES2501: Statics/Unit 24-5: Friction Related Problems Example 2: Three concrete pipes of weight W and radius r are stacked on the ground. Determine the minimum static friction coefficient such that the pile doesn’t collapse. A B C FBD and Equilibrium equations: A C B

ES2501: Statics/Unit 24-6: Friction Related Problems Example 3: A wedge of an angle is used to split a log. Find the splitting force when the wedge is hit by P and the force to keep the wedge in the position in the log. FBD and Equilibrium equations: A Load Friction To advance normal force Wedge angle Splitting force generated by P Force required to keep wedge in position

ES2501: Statics/Unit 24-7: Friction Related Problems Example 3: Friction on flat belts Proof: Small T1 can hold large T2