Friction

Frictional ForcesFrictional Forces Friction has its basis in surfaces that are not completely smooth:

Static Friction

•Static friction keeps an object from starting to move when a force is applied.

•Static frictional force has a maximum value, but may take on any value from zero to the maximum,

Static FrictionStatic Friction

5/29

Static Frictional ForcesStatic Frictional Forces

(6-2)

where

(6-3)

Kinetic Friction

Fpush > fk = kn

Kinetic FrictionKinetic Friction

Kinetic friction: the friction experienced by surfaces sliding against one another

Kinetic frictional force depends on the normal force:

(6-1)

Constant is called the coefficient of kinetic friction.

kinetic friction is independent of relative speed of the surfaces, and of their area of contact.

Kinetic Friction and SpeedKinetic Friction and Speed

Coefficients of FrictionCoefficients of Friction

Typically, s>kfs max = sFn fk = kFnfs sFn

Horizontal Retarding Friction

xk

a

g

A cruise-ship passenger uses a shuffleboard cue to push a shuffleboard disk of mass 0.40 kg horizontally along the deck, so that the disk leaves the cue at a speed of 8.5 m/s. The disk then slides a distance of 8.0 m.

What is the coefficient of kinetic friction between the disk and deck?

0 0y yneta F

nF mg

xnet k k nF f F

k xmg ma x ka g2 2

0 02 ( )x x xv v a x x 2

2

4.516 /

9.8 /0.46

k

m s

m s

m = 0.40 kg

v0x = 8.5 m/s

x = 8.0 m

x0 = 0

vx = 0

220

2

8.54.516

2 2 8.0x

x

mv s ma

sx m

0 0

Friction ACT1

a. F1>F2 b. F1=F2 c. F1<F2

d. Need to know brick areas to answer

You push two identical bricks across a tabletop with constant speed v. Which Case, as shown above, requires more force Fn?

Suppose a 20 kg object is sliding down a 50o inclined plane. If µk = 0.4 between the plane surface and the object, what is the object’s acceleration down the plane? How long will it take the object to slide 5.0 m if it starts from rest?.

y-axis: cos cosn w mg

||x-axis: F = F

sin

sin cos

net k

net k

net k

f

F w n

F mg mg

sin coskma mg mg

k||F

F

Inclined Plane Friction

2 2

(sin cos )

9.8 (sin 50 0.4cos50 ) 4.99

k

o o

a g

m mas s

Friction with Component of Tension

0ynet n yF F T mg

Two children sitting on a sled at rest in thesnow ask you to pull them. You oblige by pullingon the sled’s rope, which makes an angle of 40°with the horizontal. The children have acombined mass of 45 kg, and the sled has amass of 5.0 kg. The coefficient of kinetic friction is k=0.15. Find the acceleration of the sled and children if the rope tension is 140 N.

cosnet x k xF ma T f ma

2

cos 140 cos 40 602.63

50

ok

x

T f N N masm kg

cosxT T sinyT T

sinnF T mg

sin (50 )(9.8 / ) 140 sin(40 ) 400onF mg T kg N kg N N

0.15 400 60k k nf F N N

Antilock Brakes

Antilock Brakes

22 2 0

0 2 and 0, so 2

vv v a x v x

a

A car is traveling at 30 m/s along a horizontal road. The coefficients of friction are s=0.50 and k=0.40.(a) What is the braking distance xa with antilock brakes?(b) What is the braking distance xb if the brakes lock?

and a s b ka g a g

2 20

2

(30 m/s)91.7 m

2 2(0.5)(9.81 m/s )as

vx

g

2 20

2

(30 m/s)114.7 m

2 2(0.4)(9.81 m/s )bk

vx

g