Chapter 6
Force and Motion–II
Friction


Friction forces are essential:
o
Picking things up
o
Walking, biking, driving anywhere
o
Writing with a pencil
o
Building with nails, weaving cloth
But overcoming friction forces is also important:
o
o
Efficiency in engines
(20% of the gasoline used in an automobile goes to counteract
friction in the drive train)
o
Roller skates, fans
o
Anything that we want to remain in motion
Friction

Two types of friction

The static frictional force:
o
The opposing force that prevents an object from moving
o
Can have any magnitude from 0 N up to a maximum
o

Once the maximum is reached, forces are no longer in equilibrium
and the object slides
The kinetic frictional force:
o
The opposing force that acts on an object in motion
o
Has only one value
o
Generally smaller than the maximum static frictional force
Friction
There are two types of frictional force:
1) Force of static friction: 𝒇𝒔 .
Static friction acts to keep the object from moving
If F increases, so does 𝒇𝒔
If F decreases, so does 𝒇𝒔
𝒇𝒔 ≤ 𝝁𝒔 𝑵
𝒇𝒔 = 𝝁𝒔 𝑵
𝝁𝒔 ∶ 𝑪𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕 𝒐𝒇 𝒔𝒕𝒂𝒕𝒊𝒄 𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏
2) Force of kinetic friction: 𝒇𝒌
Acts when the object is in motion
𝒇𝒌 = 𝝁𝒌 𝑵
𝝁𝒌 ∶ 𝑪𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕 𝒐𝒇 𝒌𝒊𝒏𝒆𝒕𝒊𝒄 𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏
Note: Force of static friction greater than Force of kinetic friction.
Friction
Figure 6-1
Friction

Microscopic picture: surfaces are bumpy

Friction occurs as contact points slide over each other



Two specially prepared metal surfaces can cold-weld together and
become impossible to slide, because there is so much contact between
the surfaces
Greater force normal to the contact
plane increases the friction because
the surfaces are pressed together
and make more contact
Sliding that is jerky, due to the
ridges on the surface, produces
squeaking/squealing/sound
Figure 6-2
Friction

The properties of friction
1. If the body does not move, then the applied force and
frictional force balance along the direction parallel to the
surface: equal in magnitude, opposite in direction
2. The magnitude of fs has a maximum fs,max given by:
Eq. (6-1)
3. where μs is the coefficient of static friction. If the
applied force increases past fs,max, sliding begins.
Friction

The properties of friction
3. Once sliding begins, the frictional force decreases to fk
given by:
Eq. (6-2)
where μk is the coefficient of kinetic friction.


Magnitude FN of the normal force measures how strongly
the surfaces are pushed together
The values of the friction coefficients are unitless and must
be determined experimentally
Friction
Example 1: A constant force of magnitude of 50 N is applied to move a 10kg stationary box over a frictionless floor of 𝝁𝒌 = 𝟎. 𝟏𝟐 . Calculate:
1) The acceleration.
2) The speed of the box after 2 s.
Solution:
1)
𝑭 = 𝒎𝒂
𝐹 − 𝑓𝑘 = 𝑚𝑎
𝑓𝑘 = 𝜇𝑘 𝑛
𝐹 − 𝜇𝑘 𝑛 = 𝑚𝑎
𝑛 = 𝑚𝑔
𝐹 − 𝜇𝑘 𝑚𝑔 = 𝑚𝑎
∴𝑎=
𝐹−𝜇𝑘 𝑚𝑔
𝑚
=
2) 𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕
50−(0.12×10×9.8)
10
𝑣𝑖 = 0
= 3.82
𝑚
𝑠2
𝑎 = 3.82
𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 ⟹ 𝑣𝑓 = 0 + 3.82 × 2 = 7.65
𝑚
𝑠
𝑚
𝑠2
Friction
Example 2: A constant force of magnitude of 20 N is applied, at angle of 𝜽 = 𝟑𝟎° above the horizontal,
to move a body of mass 4 kg on a frictionless table of 𝝁𝒌 = 𝟎. 𝟐. Calculate:
1) The normal force on the box.
2) The acceleration of the box.
Solution:
1) The normal force on the box is:
𝑛 + 𝐹 sin 𝜃 − 𝑊 = 0 ⟹ 𝑛 = 𝑊 − 𝐹 sin 𝜃
⟹ 𝑛 = 𝑚𝑔 − 𝐹 sin 𝜃 = 4 × 9.8 − 20 sin 30°
= 29.2 𝑁
2)
𝑭𝒙 = 𝒎𝒂
𝐹 cos 𝜃 − 𝑓𝑘 = 𝑚𝑎
𝐹𝑦 = 0
𝑓𝑘 = 𝜇𝑘 𝑛
𝐹 cos 𝜃 − 𝜇𝑘 𝑛 = 𝑚𝑎
𝐹 cos 𝜃 − 𝜇𝑘 𝑛 = 𝑚𝑎
∴𝑎=
𝐹 cos 𝜃−𝜇𝑘 𝑛
𝑚
=
(20 cos 30° )−(0.2×29.2)
4
= 2.87
𝑚
𝑠2
Uniform Circular Motion

Recall that circular motion requires a centripetal
acceleration
Eq. (6-17)
Examples You are a passenger:
o
o
For a car, rounding a curve, the car accelerates toward the center of
the curve due to a centripetal force provided by the inward
friction on the tires. Your inertia makes you want to go straight
ahead so you may feel friction from your seat and may also be
pushed against the side of the car. These inward forces keep you in
uniform circular motion in the car.
For a space shuttle, the shuttle is kept in orbit by the gravitational
pull of Earth acting as a centripetal force. This force also acts on
every atom in your body, and keeps you in orbit around the Earth.
You float with no sensation of force, but are subject to a centripetal
acceleration.
Uniform Circular Motion

Centripetal force is not a new kind of force, it is simply an
application of force
Eq. (6-18)

For the puck on a string, the
string tension supplies the
centripetal force necessary to
maintain circular motion
Figure 6-8
Uniform Circular Motion
Answer: (a) accel downward, FN upward
(b) accel upward, FN upward
(c) the magnitudes must be equal for the motion to be uniform
(d) FN is greater in (b) than in (a)
Uniform Circular Motion
Example 1: A car of weight 1000 N moves in a circular path of radius 25
m. If the speed of the car is 𝟏𝟒 𝒎/𝒔, determine the centripetal force on
the car.
Solution:
𝐹𝑐 =
𝑚𝑣 2
𝑟
∵ 𝑊 = 𝑚𝑔
⟹𝑚=
𝐹𝑐 =
𝑊
𝑔
𝑊
𝑔
𝑣2
𝑟
=
1000
9.8
.142
25
= ⋯ 𝑁 (𝐻. 𝑊. )
Summary
Friction

Opposes the direction of motion or
attempted motion

Static if the object does not slide

Static friction can increase to a
maximum
Eq. (6-1)

Kinetic if it does slide
Eq. (6-2)
Summary
Uniform Circular Motion

Centripetal acceleration required to
maintain the motion
Eq. (6-17)

Corresponds to a centripetal force
Eq. (6-18)

Force points toward the center of
curvature