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Friction
Announcements:
•  CAPA homework due next Tuesday,10pm.
•  Clicker scores thru Wed, Feb 15 are now
on D2L.
•  Exam solutions will be available on D2L
today.
•  The 14 (70%) multiple choice will be
scanned and graded today. Hope to grade
everything over the weekend.
•  Will start talking about Energy + Work next
week. (Chap. 7)
Web page:
http://www.colorado.edu/physics/phys1110/phys1110_sp12/
Clickers Thru Feb 15
Extra Credit Problem
Dick and Jane stand on a platform of negligible
weight, as shown in the figure. Dick weighs 500
N and Jane weighs 400 N. Jane is supporting
some of her weight on the end of the rope she is
holding. What is the downward force she is
exerting on the platform?
Tension is the same everywhere
T
T
T
Force down on the platform =
500 N + 400 N –T
Force pulling up on the platform =
2T
The platform is not moving so these
are equal so 900 N = 3T
So T = 300 N
Downward
force
Jane
exerts
on
the
platform
is
400N
(down)
–
300N
(Up)
=
100N
Friction
Friction occurs when two materials
slide past one another
On a microscopic level, molecules
in one material form bonds with
molecules in the other material
Friction acts parallel to the surface
(perpendicular to the normal force).
Friction only acts to oppose motion
Not enough friction!
4
Friction
Experiments have found two main types of sliding friction
Static friction is the force exerted when the two objects
are not in motion relative to each other (no slipping)
Kinetic friction is the force exerted when the two
objects are in motion relative to each other (slipping)
Force of kinetic friction is
v
It depends on
which depends
m
on the materials and on the
normal force N which is the force
pushing the materials together.
is the coefficient of kinetic friction
m
Static friction
Formula for static friction is similar:
.
The static friction will oppose forces which try to slide one
object across another. However, once the maximum
possible static friction force
is exceeded the
object will “break loose” and start moving.
If the block is not moving then:
m
is the coefficient of static friction
m
Static and Kinetic Friction
Start with object at rest feeling a normal force of N
Start applying a force perpendicular to N.
Force of friction
Up to a force of µsN static friction prevents movement
After movement starts, frictional force is reduced to µkN.
kinetic friction
Applied force
Clicker question 1
Set frequency to BA
A stationary block sits on an inclined plane. The
coefficient of static friction is µS = 0.2. The normal, gravity,
and static friction force are shown. Which set of relations
applies to this situation?
N
F
f
A.
B.
C.
mg
θ
Clicker question 2
Set frequency to BA
A stationary block sits on an inclined plane. The coefficient of static
friction is µs = 0.2. If the angle of the plane increases, eventually the
block begins to slide. Sliding will begin when… F
N
f
A.
B.
mg
C.
D. None of the above
The maximum possible static friction force is
. When the
opposing force exceeds this, the block will start sliding.
From the previous question we know
&
Combining these 3 equations gives
so
Cornering problem
A car is taking a corner with radius of 100 m at a speed of 56 mph
(25 m/s). On dry pavement the rubber/asphalt coefficient of static
friction is 0.8. Will the car hold the line or start skidding?
To solve this we can find the frictional force necessary to
keep the car from skidding and see if this is less than
Which direction is Free body diagram?
the acceleration?
since
Coordinate system:
along acceleration
direction is good
there will no skidding
Fluid resistance
Another type of force similar to friction is due to moving
through a medium like air or water called fluid resistance
Fluid resistance depends on the size and shape
of the object and the medium being traversed
The force direction is opposite the velocity with a magnitude
of approximately f = −kv − Dv 2 where the proportionality
constants depend on the object and medium
For small v, the kv term dominates when turbulence
is not a factor and is called viscous drag.
€
For larger v, the Dv2 term (called drag) dominates
and it is called quadratic drag.
Fluid resistance
f = −kv − Dv, 2so force increases with speed. If a constant force
is trying to increase the speed, at some point the resistance
will match that force and the speed will no longer increase
Falling objects experience a
constant force due to gravity and as
the speed increases the drag force
increases until balance is reached.
This speed is the terminal velocity.
Because the resistance force is not
Result for terminal
constant, acceleration is not constant
and so integral calculus is needed, but velocity:
-ma = -mg+ Dv2 ; when a = 0, we reached terminal velocity
Fluid resistance
At high speeds the force is
and it has been found
that
where ρ is the medium density, A is the
cross sectional area, and CD is the drag coefficient
(generally between 0.1 and 1)
Top submarine speed = 80 km/hr
where
Top airplane speed = 3500 km/hr
where
Terminal Velocity Examples
Falling object
Skydiver
75 kg 0.7 m2
Baseball (3.66cm radius)
Golf ball (2.1 cm radius)
Hail stone (0.5 cm radius)
Raindrop (0.2 cm radius)
Terminal velocity
60 m/s
134 mi/hr
33 m/s
74 mi/hr
32 m/s
72 mi/hr
14 m/s
31 mi/hr
9 m/s
20 mi/hr
Data from Serway, Physics for Scientists and Engineers,
Table 6.1. A drag coefficient C=0.5 is assumed, falling
through air.
Hailstone Terminal Velocity
Contributing to the danger of large hailstones is the fact
that they fall faster than small ones. That is, the terminal
velocity increases with the size of the hailstone. Assuming
the hailstones to be spherical and using a drag coefficient
of C = 0.5 gives the following :
Radius (cm)
v(m/s)
v(mi/hr)
.01
1.9
4.3
0.1
6.1
13.7
0.2
8.6
19.3
0.5
13.6
30.5
1.0
19.3
43.2
2.0
27.3
61
3.0
33.4
74.8
5.0
43.2
96.6
10.0
61
136
Dot (scalar) product
One type of vector multiplication is the dot product or
scalar product which produces a scalar from two vectors
where is the angle
between the two vectors
Also,
Note that
so
Dot (scalar) product
The dot product can be thought of as the
projection of one vector along another vector
y
x
But remember, the scalar product
returns a scalar, not a vector