Physics 207: Lecture 2 Notes

1
Lecture 9

• Goals
• Describe Friction in Air (Ch. 6)
• Differentiate between Newtons 1st, 2nd and 3rd
  Laws
• Use Newtons 3rd Law in problem solving

Assignment HW4, (Chap. 6 7, due 10/5) 1st
Exam Thurs., Oct. 7th from 715-845 PM Chapters
1-7 in rooms 2103, 2141, 2223 Chamberlin Hall
2
Friction in a viscous mediumDrag Force Quantified

• With a cross sectional area, A (in m2),
  coefficient of drag of 1.0 (most objects), ?
  sea-level density of air, and velocity, v (m/s),
  the drag force is
• D ½ C ? A v2 ? c A v2 in Newtons
• c ¼ kg/m3
• In falling, when D mg, then at terminal
  velocity
• Example Bicycling at 10 m/s (22 m.p.h.), with
  projected area of 0.5 m2 exerts a force of 30
  Newtons
• At low speeds air drag is proportional to v but
  at high speeds it is v2
• Minimizing drag is often important

3
Newtons Third Law

• If object 1 exerts a force on object 2 (F2,1 )
  then object 2 exerts an equal and opposite force
  on object 1 (F1,2)
• F1,2 -F2,1

For every action there is an equal and opposite
reaction
IMPORTANT Newtons 3rd law concerns force
pairs which act on two different objects (not
on the same object) !
4
Force Pairs vs. Free Body Diagrams
Consider the following two cases (a falling ball
and ball on table), Compare and contrast Free
Body Diagram and Action-Reaction Force Pair
sketch
5
Free body diagrams
Ball Falls
For Static Situation N mg
6
Force Pairs
1st and 2nd Laws ? Free-body diagram Relates
force to acceleration 3rd Law ? Action/reaction
pairs Shows how forces act between objects
7
Example (non-contact)
Consider the forces on an object undergoing
projectile motion
Question By how much does g change at an
altitude of 40 miles? (Radius of the Earth 4000
mi)
8
Note on Gravitational Forces
Newton also recognized that gravity is an
attractive, long-range force between any two
objects. When two objects with masses m1 and m2
are separated by distance r, each object pulls
on the other with a force given by Newtons law
of gravity, as follows
9
Cavendishs Experiment
F m1 g G m1 m2 / r2 g G m2 / r2 If we
know big G, little g and r then will can find m2
the mass of the Earth!!!
10
Example (non-contact)
Consider the force on a satellite undergoing
projectile motion 40 km above the surface of the
earth
Compare g G m2 / 40002 g G m2 /
(400040)2 g / g / (400040)2 / 40002
0.98
11
A conceptual question A flying bird in a cage

• You have a bird in a cage that is resting on your
  upward turned palm.  The cage is completely
  sealed to the outside (at least while we run the
  experiment!).  The bird is initially sitting at
  rest on the perch.  It decides it needs a bit of
  exercise and starts to fly. Question How does
  the weight of the cage plus bird vary when the
  bird is flying up, when the bird is flying
  sideways, when the bird is flying down?
• Follow up question
• So, what is holding the airplane up in the sky? 

12
Static Friction with a bicycle wheel

• You are pedaling hard and the bicycle is speeding
  up.
• What is the direction of the frictional force?
• You are breaking and the bicycle is slowing down
• What is the direction of the frictional force?

13
Exercise Newtons Third Law
A fly is deformed by hitting the windshield of a
speeding bus.
v
The force exerted by the bus on the fly is,

1. greater than
2. equal to
3. less than

that exerted by the fly on the bus.
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Exercise 2Newtons Third Law
Same scenario but now we examine the
accelerations
A fly is deformed by hitting the windshield of a
speeding bus.
v
The magnitude of the acceleration, due to this
collision, of the bus is

1. greater than
2. equal to
3. less than

that of the fly.
15
Exercise 3Newtons 3rd Law

• Two blocks are being pushed by a finger on a
  horizontal frictionless floor.
• How many action-reaction force pairs are present
  in this exercise?

1. 2
2. 4
3. 6
4. Something else

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Force pairs on an Inclined plane
Forces on the block
Normal means perpendicular
Normal Force
Friction Force
f
mg sin q
q
y
mg cos q
q
q
x
Block weight is mg
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Force pairs on an Inclined plane
Forces on the block (equilibrium case)
Normal Force
Friction Force
f mN
y
Forces on the plane
q
x
18
Force pairs on an Inclined plane
Forces on the block (non equilibrium case)
Normal Force
Friction Force
f
y
Forces on the plane
q
x
19
Example Friction and Motion

• A box of mass m1 1 kg is being pulled by a
  horizontal string having tension T 40 N. It
  slides with friction
• (mk 0.5) on top of a second box having mass
  m2 2 kg, which in turn slides on a smooth
  (frictionless) surface.
• What is the acceleration of the second box ?
• 1st Question What is the force on mass 2 from
  mass 1?
• (A) a 0 N (B) a 5 N (C) a 20 N
  (D) cant tell

slides with friction (mk0.5 )
T
m1

a ?
m2
slides without friction
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ExampleSolution

• First draw FBD of the top box

N1
m1
fk mKN1 mKm1g
T
m1g
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ExampleSolution

• Newtons 3rd law says the force box 2 exerts on
  box 1 is equal and opposite to the force box 1
  exerts on box 2.

Action
Reaction
f1,2 mKm1g 5 N
f2,1 -f1,2
m1
m2
(A) a 0 N (B) a 5 N (C) a 20 N
(D) cant tell
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ExampleSolution

• Now consider the FBD of box 2

N2
f2,1 mkm1g
m2
m1g
m2g
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ExampleSolution

• Finally, solve Fx ma in the horizontal
  direction

mK m1g m2a
2.5 m/s2
f2,1 mKm1g
m2
24
Home Exercise Friction and Motion, Replay

• A box of mass m1 1 kg, initially at rest, is
  now pulled by a horizontal string having tension
  T 10 N. This box (1) is on top of a second box
  of mass m2 2 kg. The static and kinetic
  coefficients of friction between the 2 boxes are
  ?s1.5 and mk 0.5. The second box can slide
  freely (frictionless) on an smooth surface.
• Compare the acceleration of box 1 to the
  acceleration of box 2 ?

a1
friction coefficients ms1.5 and mk0.5
T
m1

a2
slides without friction
m2
25
Home Exercise Friction and Motion, Replay in the
static case

• A box of mass m1 1 kg, initially at rest, is
  now pulled by a horizontal string having tension
  T 10 N. This box (1) is on top of a second box
  of mass m2 2 kg. The static and kinetic
  coefficients of friction between the 2 boxes are
  ?s1.5 and mk 0.5. The second box can slide
  freely on an smooth surface (frictionless).
• If no slippage then the maximum frictional force
  between 1 2 is
• (A) 20 N (B) 15 N (C) 5 N (D) depends
  on T

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Home ExerciseFriction and Motion
N
fS ? ?S N ?S m1 g 1.5 x 1 kg x 10 m/s2
which is 15 N (so m2 cant break free)
fS
T
m1 g

• fs 10 N and the acceleration of box 1 is
• Acceleration of box 2 equals that of box 1, with
  a T / (m1m2) and the frictional force f is
  m2a
• (Notice that if T were in excess of 15 N then it
  would break free)

a1
friction coefficients ms1.5 and mk0.5
T
m1

a2
slides without friction
m2
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Recap

• Wednesday Review for exam