Physics 2211: Lectures 911

1
Physics 2211 Lectures 9-11

• Friction Static, Kinetic, Rolling
• Drag
• Motion on Inclined Planes
• Many Examples

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Friction Static, Kinetic, Rolling
Friction acts to (try to) prevent
slipping Friction always acts parallel to
surface of contact. Friction always acts
perpendicular to the normal force.
N
F
ma
W
Opposite to slipping motion
3
Magnitude of Kinetic (Sliding) Friction
Experiment shows that
Magnitude of kinetic friction force
Magnitude of Normal force
Coefficient of Kinetic Friction
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Application of Newtons 2nd Law to Sliding
Friction
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Inclined Plane with Friction

• Always begin with the free-body diagram

ma
N
?KN
?
mg
?
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Inclined plane with Friction
x mg sin ?????KN ma
y N - mg cos ? 0
N mg cos ?
N
?KN
ma
?
mg
?
mg cos ??
mg sin ??
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Static Friction is Just like Kinetic Friction
Except
There is no magic formula for the magnitude of
the static friction force!
Static No Motion
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Static Friction
No. There is a maximum value of the static
friction force.
If you continue to increase F, sliding motion
begins
9
Graph of Friction force f vs. Applied Force FA
f ?SN
f ?KN
f
f FA
FA
10
N
FMAX
?SN
mg
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Rolling friction
coefficient of rolling friction
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Friction force vs. Applied Force
f
?SN
?KN
f FA
FA
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A 50 kg steel file cabinet sits in the back of a
dump truck. The trucks bed, also made of steel,
is slowly tilted. What is the size of the static
friction force on the cabinet when the bed is
tilted 20 degrees? At what angle will the file
cabinet begin to slide?
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Static Friction on An Inclined Plane
N
f
?
mg
The applied force is the component of the
weight parallel To the plane.
Therefore, the static friction force will vary
with angle.
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N
y
f
x
?
mg
Assess!
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N
y
f
x
?
mg
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A horizontal force P 12 N pushes on a M 6 kg
mass that slides on a frictionless surface. Due
to friction, a smaller mass (m 4 kg) stays
fixed with respect to the larger mass. What is
the force that m exerts on M?
1 4.8 N to the right 2 4.8 N to the
left 3 6.1 N to the right
4 6.1 N to the left 5 7.2 N to the
left 6 7.2 N to the left
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Drag
A force experienced by a body that moves through
air.
Experiment shows that to a good approximation,
Unit vector that points in the direction of the
velocity of the body
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Throw a ball upward vertically
Drag decreases as the ball slows down
Drag increases as the ball speeds up slows
Drag opposes the weight as it falls
Drag adds to the weight as it rises
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Terminal velocity
At the terminal velocity, the drag force
balances the force of gravity.
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Drop a particle from rest (v 0)
As the speed (and thus drag) increases, the
slope decreases
Slope approaches zero as v approaches terminal
velocity
Without drag, v - at
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1 25 m 2 45 m 3 120 m 4
136 m 5 230 m
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No mass!
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a
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M
3M
q
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Words to the Wise
Study the Worked Examples In Section 5.6 of
Knight
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Recap
Friction
Next Lecture
Motion in a Plane Knight Chapter 6