Chapter Objectives Chapter Outline Introduce the concept of dry friction Chapter Outline Characteristics of Dry Friction Problems Involving Dry Friction

8.1 Characteristics of Dry Friction is a force occurring between two objects on the contact surface to resist the objects from separation is acting along the contact surface is in the opposite direction of the object’s motion can be classify as Fluid Friction and Coulomb Friction

8.1 Characteristics of Dry Friction Fluid friction occurs on the surface with fluid, i.e. gas or liquid depends on velocity and viscosity Coulomb friction occurs between two dry contact surface or Dry friction

8.1 Characteristics of Dry Friction Theory of Dry Friction Consider the result from the force P on the object with the weight W on a rough surface There are perpendicular forces ∆Nn and frictional forces ∆Fn along the contact surface For equilibrium, the sum of the perpendicular force ∆Nn is equal to the weight W and the sum of the frictional force ∆Fn is equal to the force P

8.1 Characteristics of Dry Friction Theory of Dry Friction The friction occurs on the contact surface, which is rough, and hence creating a resultant force ∆Rn from ∆Fn and ∆Nn For equilibrium the force N and F occur, which are the results from ∆Fn and ∆Nn , respectively The resultant forces F and N locate at the centroid

8.1 Characteristics of Dry Friction Theory of Dry Friction Impending Motion (just before the motion occurs) The force P is increased, then the force F will also increase until the fore F reach its limit called (Limiting) static frictional force “Fs ” Fs is directly proportional to N, which is Fs = μsN μs is the statics friction coefficient The angle Φs between Rs and N is called the angle of static friction

8.1 Characteristics of Dry Friction Theory of Dry Friction Typical Values of μs Contact Materials Coefficient of Static Friction μs 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

8.1 Characteristics of Dry Friction Theory of Dry Friction Motion Once the force P become greater than Fs, and object will start to move then then the frictional force will slightly reduce, which is less than the static frictional force Fs, the is friction when an object is in motion is called kinetic frictional force (Fk) Afterwhich an object will not be in equilibrium and will have acceleration Fk = μkN, in which μk is less then μs by 25%

8.1 Characteristics of Dry Friction Theory of Dry Friction F is static frictional force when in equibrium F is limiting static frictional force occurs at the peak of equilibrium F is kinetic frictional force when there is motion

8.2 Problems Involving Dry Friction Equilibrium unknown = equilibrium equations The friction must be less than F ≤ μsN, other wise the motion will occur Must test for friction at every point (i.e. A and C) to test equilibrium

Example 8.1 The uniform crate has a mass of 20kg. If a force P = 80N is applied on to the crate, determine if it remains in equilibrium. The coefficient of static friction is μ = 0.3.

Solution Resultant normal force NC act a distance x from the crate’s center line in order to counteract the tipping effect caused by P. 3 unknowns to be determined (F, NC, x) by 3 equations of equilibrium.

Solution

Example 8.2 When the bed of the dump truck is raised to an angle 25 degree the vending machine will begin to slide off the bed. Determine the static coefficient of friction between a vending machine and the surface of the truck bed.

Solution Equilibrium y’ x’