Transcript Slide 1

Problems with more than one object,
Connected
Objects move together : same speed and same
Magnitude of acceleration
mA
mB
FRICTION
Contact force and friction – Figure 5.10
•We need to re-examine
problems we formerly did
as “ideal”.
•We need to be able to find
frictional forces given the
mass of the object and the
nature of the surfaces in
contact with each other.
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The microscopic view of friction – Figure 5.11
•A surface will always have
imperfections, your
perception of them
depends on the
magnification.
•The coefficient of friction
will reveal how much force
is involved.
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DEMONSTRATION
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Friction changes as forces change – Figure 5.12
•Forces from static friction increase as force increases while
forces from kinetic friction are relatively constant.
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No dependence on surface area – Figure 5.13
•The normal force determines friction and the normal
force depends only on mass.
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Relation Between Normal Force and Maximum Static-Friction Force
When the maximum magnitude of the static-friction force can be
represented as proportional to the magnitude of the normal force,
the two are related by a constant μs called the coefficient of static
friction:
fs ≤ μsn
The equality sign holds only when the applied force parallel to the
surface has reached the critical value at which motion is about to
start.
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Relation Between Normal Force and kinetic-Friction Force
fk =μkn
For any given pair of surfaces, the coefficient of kinetic
friction is usually less than the coefficient of static friction.
As a result, when sliding starts, the friction force usually
decreases.
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A person pushes on a stationary 125 N box with 75 N
at 30o below the horizontal, as shown in the figure.
The coefficient of static friction between
the box and the horizontal floor is 0.80.
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a) Make a free body diagram of the box
b) What is the normal force on the box?
c) What is the friction force on the box?
d) What is the largest friction force?
e) The person now replaces his push with a 75 N pull at
30o above the horizontal. Find the normal
force on the box in this case.
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F
y
 m ay
y
n
a=0
Fcos30o
w
30o
F
f
Fsin30o
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x
Horizontal plane
• 3) Force at an angle + friction
q
A force Fa of 15 N making an angle of 35o from the horizontal
is applied to a block with mass m=6kg, on a table with friction
force Ff opposing the motion of the block of 5.2 N magnitude.
The block was originally at rest when the force was applied.
Draw a FBD and find the acceleration of the block and its
position after it travels for 5 seconds from the origin
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FBD
There is no motion in the y
Direction (the block does not jump !!!)
Fy = 0 N
Hence:
Normal force N = w+Fsin(q)
Normal force
N
y
m
Ff
Fa,
Fa,x
q
Fa applied force
y
W weight
Motion along x:
Fa,x – Ff = m ax
x
ax = (15N cos (35o) -5.2N)/6kg
Fx = Fcos(q)
Fy = Fsin(q)
ax = 1.18 m/s2
x = xo + voxt + (1/2) axt2
x = (1/2)(1.18m/s2)(5s)2
x = 14.77 m
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a?
n?
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Forces in fluids – Figure 5.18
•This topic is fully developed in advanced courses.
•Conceptually, observe the drag as objects fall through
“thicker” liquids.
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Elastic forces – Figure 5.19
•Springs or
other elastic
material will
exert force
when stretched
or
compressed.
Fspr = -kx
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You find that if you hang a 1.25 kg weight from a
vertical spring, it stretches 3.75 cm .
What is the force constant of this spring in N/m?
How much mass should you hang from the
spring so it will stretch by 8.13 cm from its
original, unstretched length?
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• A surgeon is using material from a donated heart to repair
a patient's damaged aorta and needs to know the elastic
characteristics of this aortal material. Tests performed on a
16.0 cm strip of the donated aorta reveal that it stretches
3.75 cm when a 1.50 N pull is exerted on it.
•
What is the force constant of this strip of aortal material?
• If the maximum distance it will be able to stretch when it
replaces the aorta in the damaged heart is 1.14cm what is
the greatest force it will be able to exert there?
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