Newton's Laws of Motion

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Newton's Laws of Motion

• Dr. Robert MacKay

Clark College, Physics
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Introduction

• Newtons 3 laws of motion
• 1. Law of inertia
• 2. Net Force mass x acceleration
• ( F M A )
• 3. Action Reaction
• Newtons Universal Law of Gravity

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Isaac Newton 1642-1727
Isaac Newton 1689
Knighted by Queen Anne 1705
Isaac Newton 1702
Isaac Newton 1726
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Other topics

• Why do objects accelerate?
• Why do objects not accelerate?
• Forces in Balance (Equilibrium)
• Forces out of Balance
• Friction
• Air resistance
• Terminal Velocity

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Law of inertia (1st Law)

• Every object continues in its state of rest, or
  of uniform motion in a straight line, unless it
  is compelled to change that state by forces
  impressed upon it.
• acceleration 0.0 unless the objected is acted
  on by an unbalanced force

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Law of inertia (1st Law)

• Inertia (The intrinsic tendency of an object to
  resist changes in motion)
• Mass is a measure of an objects inertia
• Mass is also a measure of the amount of an
  objects matter content. (i.e. protons,
  neutrons, and electrons)
• Weight is the force upon an object due to gravity

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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

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Newtons Law of Action Reaction (3rd Law)

• You can not touch without being touched

For every action force there is and equal and
oppositely directed reaction force
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

M2.0 kg
F?
FM A 2.0 kg x 6.0 m/s2 12.0 Newtons
12.0 N
A 6.0 m/s2
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An object experiences a net force and exhibits an
acceleration in response. Which of the following
statements is always true? (a) The object moves
in the direction of the force. (b) The
acceleration is in the same direction as the
velocity. (c) The acceleration is in the same
direction as the force. (d) The velocity of the
object increases.
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

M2.0 kg
F6.0 N
AF / M ? m/s2
A ?
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

M?
F 10.0 N
M F/A ? kg
A 20.0 m/s2
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

M 8.0 kg
F ? N
FM A ? N
A 10.0 m/s2
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

A 10.0 m/s2
FM A ? N
M 8.0 kg
F ? N F weight
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Weight
m 6.0 kg

• W m g
• g 10 m/s2

weight is the force due to the gravitational
attraction between a body and its planet
W ?
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• Question 1 A force of 45 N pulls horizontally on
  a 15 kg
• crate resting on a level
  frictionless surface. (Actually the crate
• has real good tiny wheels) What is
  the acceleration of the crate?
• 3.0 m/s/s
• 30.0 m/s/s
• 60.0 m/s/s
• 0. 33 m/s/s

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Question 2 A 15.0 kg crate is in contact with a
30.0 kg crate on a level
frictionless surface as shown. If the 15.0 kg
mass is pushed with a force of 45.0 N
what is the acceleration of the two
masses? A. 1.0 m/s/s
B. 1.5 m/s/s C. 2.0
m/s/s D. 3.0 m/s/s
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Question 3 A 15.0 kg crate is in
contact with a 30.0 kg crate on a
level frictionless surface as shown. If the 15.0
kg mass is pushed with a force of
45.0 N what is the force that the
15.0 kg mass exerts on the 30.0 kg mass?
15 N 6 28 20 N 2
9 25 N 1 4
30 N 12 57
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Weight

• W m g

8.0 kg
W ?
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A baseball of mass m is thrown upward with some
initial speed. A gravitational force is exerted
on the ball (a) at all points in its motion (b)
at all points in its motion except at the highest
point (c) at no points in its motion
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

F 150.0 N
M 5.0 kg
D 120.0 N
Net Force ?
A ? m/s2
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

F 150.0 N
M 5.0 kg
D?
Net Force ?
A 20.0 m/s2
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Newtons 2nd Law

• Net Force Mass x Acceleration
• F M A

F 150.0 N
M 5.0 kg
D?
Net Force ?
A 0.0 m/s2
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Which of the following statements is most
correct? (a) It is possible for an object to
have motion in the absence of forces on the
object. (b) It is possible to have forces on an
object in the absence of motion of the object.
(c) Neither (a) nor (b) is correct. (d) Both
(a) and (b) are correct.
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An object experiences no acceleration. Which of
the following cannot be true for the object? (a)
A single force acts on the object. (b) No forces
act on the object. (c) Forces act on the object,
but the forces cancel.
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QUICK QUIZ 5.3
(end of section 5.5)
On Earth, where gravity is present, an
experiment is performed on a puck on an air
hockey table, with negligible friction. A
constant horizontal force is applied to the puck
and its acceleration is measured. The experiment
is performed on the same puck in the far reaches
of outer space where both friction and gravity
are negligible. The same constant force is
applied to the puck and its acceleration is
measured. The pucks acceleration in outer space
will be a) greater than its acceleration on
Earth, b) less than its acceleration on Earth, c)
exactly the same as its acceleration on Earth, d)
infinite since neither friction nor gravity are
holding it back?
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Given q160 degrees q245 degrees T3200 N
(45 lbs) Find T1 and T2
X Y T1
-T1cos(q1) T1sin(q1) T2 T2cos(q2)
T2sin(q2) T3 0 -200N R
0 0
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T
30 kg
F 200 N
20 kg
Find A T
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T
30 kg
20 kg
Find a T
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T
30 kg
Friction80 N (mk 0. 27)
20 kg
Find a T
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Newtons 2nd Law

• Friction depends
• on surfaces in contact (roughness)
• contact force pushing surfaces together

Friction ?
F 130.0 N
M 5.0
A 0.0 m/s2
Net Force ?
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FnetP-fK
P
fs,maxmsN
fKmKN
f
fs,max
fKmKN
kinetic friction
(sliding friction)
Static friction
F
Applied ForceStatic frictional force Ffs
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Air ResistanceForce

• Depends on
• velocity
• Air density
• Shape and aerodynamics of object

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Terminal Velocity

• When air resistance force balances an objects
  weight

Air Drag
Acceleration 0.0 gt Terminal velocity
w
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Terminal Velocity
Acceleration 0.0 gtTerminal velocity
Air Drag
Air Drag
80 kg
10 kg
w
w
which has the greatest force of air resistance?
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Not Terminal Velocity
Acceleration ?
Air Drag 240N
80 kg
W ?
which has the greatest force of air resistance?
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Not Terminal Velocity
Acceleration ?
Air Drag 240N
80 kg
x
W 800 N
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Not Terminal Velocity
Acceleration ?
Air Drag 240N
SF m a 800N - 240N 80kg a 560N80kg a a7.0
m/s2 Down
80 kg
x
W 800 N
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Which encounters the greater force of air
resistance

• A falling elephant, or
• 2. A falling feather?

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1. A falling elephant, or 2. A falling
feather?
Which encounters the greater force of air
resistance
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Newtons 2nd Law Free Body diagrams
A rock in Free Fall
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Newtons 2nd Law Free Body diagrams
A rock in Free Fall
w
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Free Body diagrams
A rock At the top of its parabolic trajectory (no
air resistance)
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Free Body diagrams
A rock At the top of its parabolic trajectory (no
air resistance)
w
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Newtons 2nd Law Free Body diagrams
A rock in Free Fall
w
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Newtons 2nd Law Free Body diagrams
A rock Falling with air resistance
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Newtons 2nd Law Free Body diagrams
A rock Falling with air resistance
R
w
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Newtons 2nd Law Free Body diagrams
A rock on a string
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Newtons 2nd Law Free Body diagrams
A rock on a String
T
For the FBD is acceleration, a, up or down ?
w
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Newtons 2nd Law Free Body diagrams
A rock sliding without friction
Vo
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Newtons 2nd Law Free Body diagrams
A rock sliding without friction
N
w
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Newtons 2nd Law Free Body diagrams
A rock sliding with friction
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Newtons 2nd Law Free Body diagrams
y
A rock sliding with friction
N
Fk
x
w
Wmg
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A rock or car sliding with friction
y
N
Fk
x
w
Wmg
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A rock or car sliding with friction
y
N
Fk
x
w
Wmg
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1. Sketch the problem 2. Draw a FBD with all
forces 3. Label x and y axes 4. Resolve
vectors into components 5. Use to help solve
the problem 6. Think
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Elevator
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50. A boy pulls on a box of mass 30 kg with a
Force of 25 N in the direction shown. (a) What
is the acceleration of the box? (b) What is
the normal force? (ignore friction)
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50. A boy pulls on a box of mass 30 kg with a
Force of 25 N in the direction shown. (a) What
is the acceleration of the box? (b) What is
the normal force? (ignore friction)
Fy25sin(30)12.5N
N
Fx25cos(30)21.7N
w
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50. A boy pulls on a box of mass 30 kg with a
Force of 25 N in the direction shown. (a) What
is the acceleration of the box? (b) What is
the normal force? (sliding WITH friction)
Fy25sin(30)12.5N
N
fmkN
Fx25cos(30)21.7N
w
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A car coasting without friction
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A car coasting without friction
y
N
Wmg
x
wmg
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A car coasting without friction
y
WxWsinq
N
WyWcosq
q
wy
wx
Wmg
x
wmg
q
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A car coasting without friction
y
WxWsinq
N
WyWcosq
Wmg
wy
wx
x
wmg
q
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A rock or car sliding without friction
WxWsinq
y
WyWcosq
N
Wmg
wy
wx
x
wmg
q
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A rock sliding with friction
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A rock sliding with friction
y
N
Fk
Wmg
x
wmg
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A rock or car sliding without friction
y
WxWsinq
N
Fk
WyWcosq
wy
q
wx
Wmg
x
wmg
q
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A rock or car sliding without friction
y
WxWsinq
N
Fk
WyWcosq
Wmg
wy
wx
x
wmg
q
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A rock or car sliding without friction
WxWsinq
y
WyWcosq
N
Fk
wy
wx
x
wmg
q
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A rock or car sliding without friction
WxWsinq
y
N
Fk
wy
wx
x
wmg
q
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1. Sketch the problem 2. Draw a FBD with all
forces 3. Label x and y axes 4. Resolve
vectors into components Use to help solve the
problem 5. Think
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Atwoods Machine
m1
m2
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Atwoods Machine
T
m1
x
T
m1g
m2
-x
-m2g
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a 1 x g
If m1m2m a0 T2m2/(2m) Tmg
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Find the acceleration a And the tension T in the
cord connecting the two blocks
y
F80 N
m14.0 kg
m2 6.0 kg
µk0.0
x
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Find the acceleration a And the tension T in the
cord connecting the two blocks
y
N1
N2
T
T
F80 N
F80 N
m14.0 kg
m2 6.0 kg
w2
w1
µk0.0
x
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Find the acceleration a And the tension T in the
cord connecting the two blocks
y
F80 N
m14.0 kg
m2 6.0 kg
µk0.30
x
90
Find the acceleration a And the tension T in the
cord connecting the two blocks
N1
N2
T
T
F80 N
Fk2
m14.0 kg
m2 6.0 kg
Fk1
w2
w1
µk0.30
N1m1g Fk1 0.3m1g
N2m2g Fk2 0.3m2g