ES 2501 StaticsUnit 24 1 Friction Related Problems

ES 2501: 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: Friction Fluid friction Dry friction against relative motion Kinetic friction Static friction Theories of friction: against impending Several theories exist. relative motion For examples: Impact between two rough studied in Statics surfaces causes friction bonding force between two surfaces causes friction

ES 2501: Statics/Unit 24 -2: Friction Related Problems Law of Dry Friction B A Case 1: In Motion ------ Kinetic friction B Kinetic Friction of A on B Direction of motion relative to A Normal Pressure of A on B Kinetic friction coefficient Magnitude: Direction: Opposite to the direction of motion Friction exists on the contact surface If B moves or has impending motion relative to A Case 2: Impending Motion ------ static friction B Static Friction of A on B Direction of impending motion trlstivr to A Normal pressure of A on B static friction coefficient Magnitude: Direction: Opposite to the direction of the impeding motion Maximum static friction --- a limit. Not necessarily the true static friction

ES 2501: 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

ES 2501: Statics/Unit 24 -4: Friction Related Problems Example 1: Find the friction force when F=5 N and 10 N, respectively. FBD: Equilibrium equations: Case 2: Case 1: Note: gives the limit but not true static friction; gives true kinetic friction, Not-satisfied Static friction Kinetic friction in motion

ES 2501: 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. FBD and Equilibrium equations: A B C

ES 2501: 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 normal force Wedge angle Splitting force generated by P To advance Force required to keep wedge in position

ES 2501: Statics/Unit 24 -7: Friction Related Problems Example 3: Friction on flat belts Proof: Small T 1 can hold large T 2