AP Physics Chapter 6

1
AP Physics Chapter 6

• Force and Motion II

2
AP Physics

• Turn in Chapter 5 Homework, Worksheet Lab
  Report
• Take Quiz 6
• Lecture
• QA

3
Review on Chapter 5

• Newtons Second Law ?F ma
• Newtons Third Law Action and Reaction Forces
• Forces

• Weight
• Normal Force
• Tension
• Apparent Weight

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Four Fundamental (Basic) Forces in Nature

• Gravitational Force
• Electromagnetic Force
• Strong (Nuclear) Force
• Weak (Nuclear) Force

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Gravitational Force

• Gravity or Weight (Gravitational force Earth
  pulling on objects around it) W

• Gravitational force always exist, but value of g
  can be different at different location.

• On surface of earth, g 9.81 m/s2.
• Higher elevation, smaller g.
• Higher latitude, larger g.

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Electromagnetic Force

• Almost all other forces we encounter in daily
  life are electromagnetic force in nature.

• Electric force F
• Magnetic force F
• Tension (pull, string) T
• Push F
• Normal (support) N (not to be confused with
  Newton, the unit of force)
• Friction ƒ (ƒs or ƒk)

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Strong (Nuclear) Force

• Holds protons and neutrons within the nucleus
• Exist in very short distance only (? 10-15 m)
• Stable nucleus

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Weak (Nuclear) Force

• Also holds protons and neutrons within the
  nucleus
• Also very short range (? 10-15 m)
• Not strong enough. Protons and neutrons can
  escape ? nuclear reaction
• Unstable nucleus

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Relative Strength of Forces
Electromagnetic
Gravitational
Weak
Strong
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Force at Distance

• Contact force

• Force giver and receiver must be in contact
• Tension, push, normal force, friction,

• Field force / Distant force

• Force giver and receiver do not have to be in
  contact
• Gravity, electric force, magnetic force,

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Unification of Forces

• Electromagnetic and weak forces have been unified
  into (understood as) one force Electroweak force
• It is believed that all four forces are different
  aspects of a single force.

• Grand Unification Theories (GUTs) and
  Supersymmetric theories
• Not yet successful

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Friction

• Friction force opposing relative motion or
  tendency of relative motion between two rough
  surfaces in contact

• Smooth surface ? No friction
• No normal force ? No friction

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Two kinds of frictions

• Static friction

• ?s coefficient of static friction
• Static friction force is not constant, it has a
  maximum.

• Kinetic (or sliding) friction

• ?k coefficient of kinetic friction
• Kinetic friction force is constant.

• ? is a constant depending on the properties of
  the two surfaces

• ? 0 when one of the surfaces is smooth
  (frictionless.)
• ?s gt ?k for same surfaces.
• ? has no unit.

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ExampleWhat happens to the frictional force as
you increase the force pushing on a table on the
floor?
But what if the applied force increases just
slightly?
Table not moving yet. Static friction increases
as applied force increases. fs Fapp
?sN

Once table is moving, a smaller constant kinetic
friction. fk lt fs, max




0
?sN
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Is friction always opposite to motion?
When you step on the pedal
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1
7
5
2
3
6
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Example

• A trunk with a weight of 220N rests on the floor.
  The coefficient of static friction between the
  trunk and the floor is 0.41, while the
  coefficient of kinetic friction is 0.32.
• a). What is the minimum magnitude for a
  horizontal force with which a person must push on
  the trunk to start in moving?
• b) Once the trunk is moving, what magnitude of
  horizontal force must the person apply to keep it
  moving with constant velocity?
• c) If the person continued to push with the force
  used to start the motion, what would be the
  acceleration of the trunk?

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Solution
W
Similarly,
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Solution
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Example Pg135-57

• The coefficient of kinetic friction in between
  the incline and the block is 0.20, and angle ? is
  60o. What is the acceleration of the block if
• a) It is sliding down the slope and
• b) It has been given an upward shove and is
  still sliding up the slope?

?
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Solution
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Solution (2)
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Practice

• An 11 kg block of steel is at rest on a
  horizontal table. The coefficient of static
  friction between block and table is 0.52.
• What is the magnitude of the horizontal force
  that will just start the block moving?
• What is the magnitude of a force acting upward
  60o from the horizontal that will just start the
  block moving?
• If the force acts down at 60o from the
  horizontal, how large can its magnitude be
  without causing the block to move?

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Solution
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Solution (2)

• c)

Similarly to Part b), we have
Another approach is to use the same equation as
in b) but change the angel to 60o.
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Practice Pg133-21

• Block B in the diagram weighs 711 N. The
  coefficient of static friction between block and
  horizontal surface is 0.25. Find the maximum
  weight of block A for which the system will be
  stationary?

30o
B
A
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Solution Pg133-21
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Drag Force

• Drag Force

• C drag constant (not a true constant)
• ? density of fluid (air or liquid)
• A cross-sectional area of object moving in
  fluid
• v speed of object relative to fluid

Source fluid in relative motion pushing on
object Direction opposing relative motion of
object relative to fluid, same direction as
relative motion of fluid
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Terminal velocity
Initially, v small ? D
small
W _____ D
gt
Fnet
downward
downward
? a
? v
increases
Increases
? D
Eventually, D ___ W
0
? Fnet

? v
0
constant
? a
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Practice Pg133-33Calculate the ratio of the
drag force on a jet flying with a speed of 1000
km/h at an altitude of 10 km to the drag force on
a prop-driven transport flying at half the speed
and half the altitude. The density of air is
0.38 kg/m3 at 10 km and 0.67 kg/m3 at 5.0 km.
Assume that the airplanes have the same effective
cross-sectional area and the same drag
coefficient C.
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Review Uniform Circular Motion and Centripetal
Acceleration
, where

• Direction of acceleration is always toward the
  center of circle (or circular arc)
• ? Centripetal

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Centripetal Force

• Centripetal force is in general not a single
  physical force rather, it is in general the net
  force.
• Do not draw centripetal force on force diagram
  (Free Body Diagram)

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Examples of centripetal forces
Rear View

• Rounding a curve in a car

• Flat curve

Static friction provides the centripetal force
(when no skidding)
Max velocity w/o skidding

• Banked curve

a component of Normal force (net force)
No friction

• Orbiting the Earth (Sun or other object)

• Gravity

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Example Pg138-87A car weighing 10.7 kN and
traveling at 13.4 m/s attempts to round an
unbanked curve with a radius of 61.0 m. a) What
force of friction is required to keep the car on
its circular path?b) If the coefficient of
static friction between the tires and road is
0.35, is the attempt at taking the curve
successful?
Yes, successful.
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Practice Pg135-50A banked circular highway
curve is designed for traffic moving at 60 km/h.
The radius of the curve is 200 m. Traffic is
moving along the highway at 40 km/h on a rainy
day. What is the minimum coefficient of friction
between tires and road that will allow cars to
negotiate the turn without sliding off the road?
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Practice Pg134-45 (Modified wording)A student
of weight 667 N rides a steadily rotating Ferris
wheel (the student sits upright). At the highest
point, the apparent weight of the student is 556
N. (a) Does the student feel light or heavy
there? (b) What is the apparent weight at the
lowest point? If the wheels speed is doubled,
what is the apparent weight at the (c) highest
point and (d) lowest point?
a) Wapp lt W ? Feel light
Top
Bottom
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Practice Pg134-45 (Modified wording)A student
of weight 667 N rides a steadily rotating Ferris
wheel (the student sits upright). At the highest
point, the apparent weight of the student is 556
N. (a) Does the student feel light or heavy
there? (b) What is the apparent weight at the
lowest point? If the wheels speed is doubled,
what is the apparent weight at the (c) highest
point and (d) lowest point?
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Practice Pg139-107A certain string can
withstand a maximum tension of 40 N without
breaking. A child ties a 0.37 kg stone to one
end and, holding the other end, whirls the stone
in a vertical circle of radius 0.91 m, slowly
increasing the speed until the string breaks.
a) Where is the stone on its path when the
string break?b) What is the speed of the stone
as the string breaks?

• a) In order to keep the same speed, and
  therefore the same centripetal force, the tension
  required is largest when the rock is at the
  bottom.

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Practice Pg133-29Two blocks (m 16 kg and M
88 kg) are not attached to each other. The
coefficient of static friction between the blocks
is ?s 0.38, but the surface beneath the larger
block is frictionless. What is the minimum
magnitude of the horizontal force F required to
keep the smaller block from slipping down the
larger block?
m
F
m
M
M
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Practice A little girl of mass m1 10 kg sits
on a slab of mass m2 20 kg on a frozen lake.
Between girl and slab, the coefficient of static
friction is 0.60, and the coefficient of static
friction between the sled and lake is 010. The
sled is pulled forward by a horizontal force F.
What is the maximum magnitude of F such that the
girl stays on the sled?
m1
F
m2
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Practice (Continued)