Friction and EquilibriumFriction and Equilibrium

Friction ForcesFriction ForcesWhen two surfaces are in contact, friction When two surfaces are in contact, friction forces oppose relative motion or forces oppose relative motion or impending motion.impending motion.

PPFriction forcesFriction forces are are parallel parallel to the surfaces in to the surfaces in contact and contact and opposeoppose motion or impending motion or impending motion.motion.

Static Friction:Static Friction: No No relative motion.relative motion.

Kinetic Friction:Kinetic Friction: Relative motionRelative motion.

22 N N

Friction and the Normal Friction and the Normal ForceForce

4 N4 N

The force required to overcome The force required to overcome staticstatic or or kinetic kinetic friction is proportional to the friction is proportional to the

normal force, normal force, nn.

fk = knfk = knfs = snfs = sn

nn

12 12 NN

6 N6 N

nn8 N8 N

4 N4 N

nn

Friction forces are independent of Friction forces are independent of area.area.

44 NN 44 NN

If the total mass pulled is constant, the If the total mass pulled is constant, the same force (4 N) is required to overcome same force (4 N) is required to overcome friction even with twice the area of friction even with twice the area of contact.contact.For this to be true, it is essential that For this to be true, it is essential that ALL other variables be rigidly controlled.ALL other variables be rigidly controlled.

Friction forces are independent of Friction forces are independent of temperature, provided no temperature, provided no

chemical or structural variations chemical or structural variations occur.occur.

44 NN 4 N4 N

Heat can sometimes cause surfaces to Heat can sometimes cause surfaces to become deformed or sticky. In such become deformed or sticky. In such cases, temperature can be a factor.cases, temperature can be a factor.

Friction forces are independent of Friction forces are independent of speed.speed.

2 2 NN2 2 NN

The force of kinetic friction is the The force of kinetic friction is the same at same at 5 m/s5 m/s as it is for as it is for 20 m/s20 m/s. . Again, we must assume that there Again, we must assume that there are no chemical or mechanical are no chemical or mechanical changes due to speed.changes due to speed.

5 m/s5 m/s 20 20 m/sm/s

The Static Friction ForceThe Static Friction Force

However, when we use the following However, when we use the following equation, we refer only to the equation, we refer only to the maximummaximum value of static friction and value of static friction and simply writesimply write::

FS = S FNFS = S FN

When an attempt is made to move an When an attempt is made to move an object on a surface, static friction object on a surface, static friction slowly increases to a slowly increases to a MAXIMUM MAXIMUM valuevalue.

FN

Fs

FA

W

Constant or Impending Constant or Impending MotionMotion

For motion that is For motion that is impendingimpending and for and for motion at motion at constant constant speed, the speed, the resultant force is zero and resultant force is zero and F = 0F = 0. . (Equilibrium)(Equilibrium)

PFs

P – Fs = 0

Rest

PFk

P – Fk = 0

Constant Speed

Here the Here the weightweight and and normal forcesnormal forces are balanced and do not affect are balanced and do not affect motion.motion.

Friction and AccelerationFriction and Acceleration

When P is greater than the maximum Fs the resultant force produces acceleration.

Note that the kinetic friction force Note that the kinetic friction force remains constant even as the velocity remains constant even as the velocity increases.increases.

PFk

Constant Speed

Fk = kFNFk = kFN

a

EXAMPLE 1:EXAMPLE 1: If If kk = 0.3 = 0.3 and and ss = = 0.50.5, what horizontal pull , what horizontal pull PP is is required to just start a required to just start a 250-N250-N block moving?block moving?

1. Draw sketch and free-1. Draw sketch and free-body diagram as body diagram as shown.shown.

2. List givens and label 2. List givens and label what is to be found:what is to be found:

kk = 0.3; = 0.3; ss = 0.5; = 0.5; W = W = 250 250 NN

Find: Find: P = ? P = ? to just to just startstart

3. Recognize for impending motion:3. Recognize for impending motion: P – fP – fss = 0= 0

nffss

PP

WW++

EXAMPLE 1(Cont.):EXAMPLE 1(Cont.): ss = 0.5 = 0.5, , W = 250 NW = 250 N. . Find Find PP to overcome to overcome ffs s (max)(max). Static . Static friction applies.friction applies.

4. To find P we need to 4. To find P we need to know know ffs s , which is:, which is:

5. To find5. To find

nn::

nfs

P

250 N

+

For this case:For this case: P – f P – fss = 0= 0

ffss = = ssnn n = ?n = ?

FFyy = = 00 nn – W = – W = 00

WW = = 250 N250 N n = n = 250 250 NN

(Continued)(Continued)

EXAMPLE 1(Cont.):EXAMPLE 1(Cont.): ss = 0.5 = 0.5, , WW = 250 N = 250 N. Find . Find PP to overcome to overcome ffs s (max)(max). Now we know . Now we know nn = = 250 N250 N..

7. For this case7. For this case: P – fs = 0

6. Next we find6. Next we find ffss from:from:ffss = = ssn n = = 0.5 (250 0.5 (250 N)N)

P = fP = fss = = 0.5 (250 N)0.5 (250 N)

P = 125 NP = 125 N

This force (This force (125 N125 N) is needed to ) is needed to just startjust start motion. Next we consider motion. Next we consider P P needed for needed for constant speedconstant speed..

nfs

P

250 N

+

ss = 0.5 = 0.5

EXAMPLE 1(Cont.):EXAMPLE 1(Cont.): If If kk = 0.3 = 0.3 and and ss = = 0.50.5, what horizontal pull , what horizontal pull PP is required to is required to move with move with constant speedconstant speed? ? (Overcoming (Overcoming kinetickinetic friction) friction)

FFyy = m = maayy = = 00

nn - W = 0 - W = 0 nn = W = W

Now: fNow: fkk = = kkn n = = kkWW

FFxx = = 0; 0; P - fP - fkk = = 0 0

P = fP = fk k = = kkWW

P = P = (0.3)(250 N)(0.3)(250 N) P = 75.0 NP = 75.0 N

fk

nP

mg+

kk = 0.3 = 0.3

The Normal Force and The Normal Force and WeightWeight

The normal force is NOT always equal to the weight. The following are examples:

300

P

m

n

W

Here the normal force is less than weight due to upward component of P.

Pn

W

Here the normal force is equal to only the compo- nent of weight perpendi- cular to the plane.

Summary: Important Points to Summary: Important Points to Consider When Solving Friction Consider When Solving Friction

Problems.Problems.

• The maximum force of static The maximum force of static friction is the force required to friction is the force required to just start just start motion.motion.

s sf nn

fs

P

W

Equilibrium exists at that instant:Equilibrium exists at that instant:

0; 0x yF F 0; 0x yF F

Summary: Important Points (Cont.)Summary: Important Points (Cont.)

• The force of The force of kinetic frictionkinetic friction is that is that force required to maintain force required to maintain constant motionconstant motion..

k kf n

• Equilibrium exists if speed is Equilibrium exists if speed is constant, but constant, but ffkk does does notnot get get larger as the speed is increased.larger as the speed is increased.

0; 0x yF F 0; 0x yF F

nfk

P

W

Summary: Important Points (Cont.)Summary: Important Points (Cont.)

• Choose an Choose an xx or or yy-axis along the -axis along the direction of motion or impending direction of motion or impending motion.motion.

fk

nnPP

WW++

kk = 0.3 = 0.3

The The FF will be will be zero zero along the along the x-x-axisaxis and along the and along the y-axisy-axis..

0; 0x yF F 0; 0x yF F

In this figure, we In this figure, we have:have:

SummarySummary

Static Friction: No relative motion.

Kinetic Friction: Relative motion.

fk = knfk = knfs ≤ snfs ≤ sn

Procedure for solution of equilibrium problems is the same for each case:

0 0x yF F 0 0x yF F