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№1 слайд![L Static Equilibrium and](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img0.jpg)
Содержание слайда: 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
№2 слайд![. Statics Recall Conditions](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img1.jpg)
Содержание слайда: 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)
№3 слайд![Static Equilibrium Examples](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img2.jpg)
Содержание слайда: Static Equilibrium Examples
№4 слайд![Static Equilibrium Examples](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img3.jpg)
Содержание слайда: Static Equilibrium Examples
№5 слайд![Example A beam AB of length .](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img4.jpg)
Содержание слайда: 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.
№6 слайд![](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img5.jpg)
№7 слайд![Example Stability and](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img6.jpg)
Содержание слайда: 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?
№8 слайд![. Friction Friction plays a](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img7.jpg)
Содержание слайда: 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)
№9 слайд![. . Origin of Friction Where](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img8.jpg)
Содержание слайда: 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.
№10 слайд![. . Measuring Frictional](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img9.jpg)
Содержание слайда: 3.2. Measuring Frictional Force
Experimentally, it is found that the limiting frictional force, Ff is proportional to the normal reaction force, N. Therefore:
№11 слайд![. Coefficient of friction,](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img10.jpg)
Содержание слайда: 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
№12 слайд![. . Static vs. Kinetic Forces](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img11.jpg)
Содержание слайда: 4.1. Static vs. Kinetic Forces of Friction
№13 слайд![. . Frictional Force does](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img12.jpg)
Содержание слайда: 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.
№14 слайд![Example A box of . kg sits on](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img13.jpg)
Содержание слайда: 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.
№15 слайд![Example Ladder Problem A](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img14.jpg)
Содержание слайда: 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.
№16 слайд![Example](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img15.jpg)
Содержание слайда: Example 5:
№17 слайд![CHECK LIST and READING](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img16.jpg)
Содержание слайда: 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
№18 слайд![Numerical Answers to Examples](/documents_6/ed38467e5ef24c36aac78e7cafbfcc2b/img17.jpg)
Содержание слайда: 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