Statics (MET 2214)
Prof. Simin Nasseri
Friction MET 2214Part 1Friction MET 2214Part 1
Statics (MET 2214)
Prof. Simin Nasseri
Objective
a) Understand the characteristics of dry friction.
b) Draw a FBD including friction.
c) Solve problems involving friction.
Statics (MET 2214)
Prof. Simin Nasseri
Types of Friction
Dry Friction
When the unlubricated surfaces of two solids are incontact under a condition of sliding or tendency to slide.
Fluid Friction
When adjacent layers in a fluid are moving at differentvelocities.
Internal Friction
When solid materials are subjected to cyclical loading.
Statics (MET 2214)
Prof. Simin Nasseri
Applications
In designing a brake system for abicycle, car, or any other vehicle, it isimportant to understand the frictionalforces involved.
For an applied force on the brakepads, how can we determine themagnitude and direction of theresulting friction force?
Statics (MET 2214)
Prof. Simin Nasseri
Consider pushing a box as shownhere.
How can you determine if it willslide, tilt, or stay in staticequilibrium?
What physical factors affectthe answer to this question?
Applications
Statics (MET 2214)
Prof. Simin Nasseri
Friction is defined as a force of resistanceacting on a body which prevents or retardsslipping of the body relative to a secondbody.
Experiments show that frictional forcesact tangent (parallel) to the contactingsurface in a direction opposing therelative motion or tendency for motion.
Characteristics Of Dry Friction
Statics (MET 2214)
Prof. Simin Nasseri
Characteristics Of Dry Friction
For a body to be in equilibrium, the following must be true:F = P, N = W, and W.x = P.h.
Statics (MET 2214)
Prof. Simin Nasseri
To study the characteristics of the friction force F, let us assumethat tipping does not occur (i.e., “h” is small or “a” is large).
Then we gradually increase the magnitude of the force P. Typically,experiments show that the friction force F varies with P, as shownin the right figure above.
Characteristics Of Dry Friction
Statics (MET 2214)
Prof. Simin Nasseri
The maximum friction force is attained just before the blockbegins to move (a situation that is called “impending motion”).
The value of the force is found using Fs = s N, where s iscalled the coefficient of static friction. The value of s dependson the materials in contact.
Once the block begins to move, the frictional force typicallydrops and is given by Fk = k N. The value of k (coefficientof kinetic friction) is less than s .
Characteristics Of Dry Friction
Statics (MET 2214)
Prof. Simin Nasseri
Determining s Experimentally
A block with weight W is placed on aninclined plane. The plane is slowly tilteduntil the block just begins to slip.
The inclination, s, is noted. Analysis ofthe block just before it begins to movegives (using Fs = s N): + Fy = N – W cos s = 0
+ FX = S N – W sin s = 0
Using these two equations, we get
s = (W sin s ) / (W cos s ) = tan sThis simple experiment allows us to findthe S between two materials in contact.
Statics (MET 2214)
Prof. Simin Nasseri
Problems Involving Dry Friction
Steps for solving equilibrium problems involving dry friction:
1. Draw the necessary free body diagrams. Make sure thatyou show the friction force in the correct direction (italways opposes the motion or impending motion).
2. Determine the number of unknowns. Do not assume F = S Nunless the impending motion condition is given.
3. Apply the equations of equilibrium and appropriatefrictional equations to solve for the unknowns.
Statics (MET 2214)
Prof. Simin Nasseri
Reading Quiz
A friction force always acts _____ to the contact surface.
A) normalB) at 45°
C) parallelD) at the angle of static friction
![MMj01855880000[1]](data/images/img17.gif)
Considering the forces acting on the block shown in the figure below. Ifthe pulling force (P) equals the friction force (Ffriction), which of thefollowing is true?
a) The block will remain stationary if the friction force is static.b) The block will accelerate if the friction force is kinetic.c) The block will move at constant velocity if the friction force is static.d) The block will begin to move if the friction force is static.
Statics (MET 2214)
Prof. Simin Nasseri
Impending Tipping versus Slipping
For a given W and h, how can wedetermine if the block will slidefirst or tip first?
In this case, we have fourunknowns (F, N, x, and P) andonly three E-of-E.
Statics (MET 2214)
Prof. Simin Nasseri
Impending Tipping versus Slipping
Hence, we have to make an assumption to give us anotherequation. Then we can solve for the unknowns using thethree E-of-E. Finally, we need to check if our assumptionwas correct.
Statics (MET 2214)
Prof. Simin Nasseri
Assume: Slipping occurs
Known: F = s N
Solve: x, P, and N
Check: 0 x b/2
Or
Assume: Tipping occurs
Known: x = b/2
Solve: P, N, and F
Check: F s N
Impending Tipping versus Slipping
Statics (MET 2214)
Prof. Simin Nasseri
Example
Given:A uniform ladder weighs 20lb. The vertical wall is smooth (nofriction). The floor is rough and s =0.8.
Find: The minimum force P needed tomove ( tip or slide) the ladder.
Plan:
a) Draw a FBD.
b) Determine the unknowns.
c) Make any necessary friction assumptions.
d) Apply E-of-E (and friction equations, if appropriate ) to solvefor the unknowns.
e) Check assumptions, if required.
Statics (MET 2214)
Prof. Simin Nasseri
There are four unknowns: NA, FA, NB, and P. Let us assume that theladder will tip first. Hence, NB = 0
FY = NA – 20 = 0 ; so NA = 20 lb
+ MA = 20 ( 3 ) – P( 4 ) = 0 ; so P = 15 lb
+ FX = 15 – FA = 0 ; so FA = 15 lb
P
20 lb
NB
4 ft
4 ft
3 ft
3 ft
NA
FA
A FBD of the ladder
Example
Statics (MET 2214)
Prof. Simin Nasseri
Now check the assumption.
Fmax = s NA = 0.8 * 20 lb = 16 lb
Is FA = 15 lb Fmax = 16 lb? Yes, hence our assumption of tipping iscorrect.
Remember that if you assume that the ladder slips first (F = s NA),and find NB and P, then your P would be 17lb and the situation atwhich P= 15lb happens before P=17, so the ladder tips first.
P
20 lb
NB
4 ft
4 ft
3 ft
3 ft
NA
FA
A FBD of the ladder
Example
Statics (MET 2214)
Prof. Simin Nasseri
Concept Quiz
1. A 100 lb box with wide base is pulled by a force P and s = 0.4.Which force orientation requires the least force to beginsliding?
A) P(A) B) P(B)
C) P(C) D) Can not be determined
P(A)
P(B)
P(C)
100 lb
2. A ladder is positioned as shown. Indicate thedirection of the friction force on the ladder at B.
A) B)
C) D)
A
B
Statics (MET 2214)
Prof. Simin Nasseri
Given: Drum weight = 100 lb, s =0.5 , a = 3 ft and b = 4 ft.
Find:The smallest magnitude of Pthat will cause impendingmotion (tipping or slipping)of the drum.
Plan:
a) Draw a FBD of the drum.
b) Determine the unknowns.
c) Make friction assumptions, as necessary.
d) Apply E-of-E (and friction equation as appropriate) to solve forthe unknowns.
e) Check assumptions, as required.
Example
Statics (MET 2214)
Prof. Simin Nasseri
There are four unknowns: P, N, F and x.
First, let’s assume the drum slips. Then the frictionequation is F = s N = 0.5 N.
X
3
4
5
1.5 ft
1.5 ft
100 lb
0
4 ft
F
A FBD of the drum:
P
N
Example
Statics (MET 2214)
Prof. Simin Nasseri
+ FX = (4 / 5) P – 0.5 N = 0
+ FY = N – (3 / 5) P – 100 = 0
These two equations give:
P = 100 lb and N = 160 lb
+ MO = (3 /5) 100 (1.5) – (4 / 5) 100 (4) + 160 (x) = 0
Check:x = 1.44 1.5 so OK!
Drum slips as assumed at P = 100 lb
X
3
4
5
1.5 ft
1.5 ft
100 lb
0
4 ft
F
A FBD of the drum:
P
N
Example
Statics (MET 2214)
Prof. Simin Nasseri
1. A 10 lb block is in equilibrium. What is themagnitude of the friction force betweenthis block and the surface?
A)0 lbB) 1 lb
C)2 lbD) 3 lb
Attention Quiz
A
S = 0.3
2 lb
2. The ladder AB is postioned as shown. What is thedirection of the friction force on the ladder at B.
A)B)
C) D)
B
Writing the equation of equilibrium along x, you will notice that friction forceis equal to the force applied or 2lb. The maximum friction force is (0.3)N =0.3(W) = 3lb which would exist when the block is on the verge of slipping.