🗊Презентация Static Equilibrium and Friction

L10 – Static Equilibrium and Friction 1. Statics 2. Stability and Toppling 3. Friction and Force of Friction 4. Coefficient of Static Friction and coefficient of Kinetic Friction

1. Statics: Recall Conditions of Equilibrium For an object to be static, two conditions must be fulfilled: No resultant force in any direction ( Fup = Fdown, and Fright = Fleft) No resultant torque about any axis. (Moments acting to give a cw rotation= Moments acting to give an acw rotation)

Static Equilibrium Examples

Static Equilibrium Examples

Example 1: A beam AB of length 5.00 m, weight 200 N is supported horizontally by two vertical ropes x, y at A and B respectively. Calculate the tensions in the ropes if a man weighing 700 N stands on the beam at 2.00 m from A.

Example 2: Stability and toppling A 40.0 x 50.0 cm block sits on a rough plane. The inclination of the plane is increased gradually. 1) When will the block topple to the left? 2) At what angle of inclination will the block topple?

3. Friction Friction plays a dual role in our lives: Impedes motion of objects, causes abrasion On the other hand, without it, we could not walk, drive cars, climb ropes or use nails. Friction is a contact force that opposes the relative motion of two bodies In 1748, Euler made a distinction between static and kinetic friction. If an object does not move, then the applied force must be exactly equal (in magnitude) to the force of static friction. (if these are the only 2 forces acting in the direction of motion, of course)

3.1. Origin of Friction Where points of contact cause very high pressure, temporary bonding occurs. To slide the brick horizontally, some work must be done, lifting and deforming the surface.

3.2. Measuring Frictional Force Experimentally, it is found that the limiting frictional force, Ff is proportional to the normal reaction force, N. Therefore:

4. Coefficient of friction, μ You must distinguish between the coefficient of sliding (kinetic) friction μk and the coefficient of static friction μs. Generally μk < μs. E.g. for rubber on dry concrete, μs = 1.00 and μk = 0.8; on wet concrete, μs = 0.300 and μk = 0.250

4.1. Static vs. Kinetic Forces of Friction

4.2. Frictional Force does Work Friction does work: W = Ff d cosθ This energy becomes heat and sound and is usually not useful. Ff is an example of a dissipative force.

Example 3: A box of 2.00 kg sits on a rough slope. If μs = 0.200 and the angle of inclination is 20.0º, find force T if the box is just about to slide up the slope.

Example 4: Ladder Problem A uniform 6.00 m long ladder of 10.0 kg leans against a wall. The wall is smooth and the floor is rough. Draw a FBD. Find: a) The reaction force from the wall; b) N and Ff at ground; c) μs,min so that the ladder does not slide.

Example 5:

CHECK LIST and READING READING : Serway - Section 4.6 , Examples 4.8, 4.9 (pages 77-78) Section 8.2 – Example 8.3 (pages 178-179) Section 8.4 – Examples 8.5, 8.6 (pages 181-183) Adams and Allday - Sections: 3.5, 3.7, 3.25. At the end of this lecture you should State the 2 conditions for static equilibrium of a rigid body Understand the nature of friction and that it is a contact force proportional to the normal reaction force Understand the origin of the coefficient of static friction Be able to perform calculations to find the forces and torques acting on different bodies in a number of different situations of static equilibrium

Numerical Answers to Examples Ex. 1 : X = 0.520 kN, Y = 0.380 kN Ex. 2 : a) Block topples when CM is not supported. b) angle = 38.7 degrees Ex. 3 : T = 11.9 N Ex. 4 : a) R = 28.3 N b) N = 98.1 N, Ff = 28.3 N c) μs ≥ 0.289 Ex. 5 : a) T1 = (2.60)Mg, T2 = Mg, b) F = (3.28) Mg at 37.6 degrees from horizontal ‘x’ axis