of motion - texas a&m...
TRANSCRIPT
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Chap. 4: Newton’s Law
of Motion
Force; Newton’s 3 Laws; Mass and Weight
Free-body Diagram (1D)
Free-body Diagram (1D, 2 Bodies)
Free-body Diagram (2D)
Equilibrium
Frictional Force
Circular Motion / Rotation
1
And Chap.5 Applying Newton’s Laws (more examples)
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F
Who Wanted “Force”?
2
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What is Force?
an interaction between two objects
a push or a pull on an object; either a contact force
or a long-range force
Push up on an apple by hand; contact force
Pull down on an apple by earth; long-range force
a vector
it has both a magnitude and a direction
causes an acceleration on an object
2
2
m/s 8.9
; ˆ)m/s 8.9(ˆ)0(
gg
jig
jmgiF ˆ)(ˆ)0(g
y
g
g
v
v
4
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Newton’s Laws of Motion
Newton’s 3 Laws
Newton’s 1st Law
Law of inertia
“Mass” (kg) is a measure of the inertia of a body.
Newton’s 2nd Law
Dynamical analysis using Free-Body Diagram (FBD)
Newton’s 3rd Law
Action-reaction pair
m
Fa
5
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Newton’s Laws of Motion
Kinematics
(r, v, a)
Structure of Newtonian Mechanics
Inertial Reference Frame
(Newton’s 1st Law)
Action-Reaction
(Newton’s 3rd Law)
Mass
(m)
The Nature of Force The Nature of Object The Nature of Motion
F = m a
(Newton’s 2nd Law)
Kinematics
(r, v, a)
Kinematics
(r, v, a)
Kinematics
(r, v, a)
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Newton’s Laws of Motion
WHAT HAPPEN?
9
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Newton’s Laws of Motion
The force on a hokey puck
causes the acceleration
If the net force on a hokey
puck is zero (equilibrium),
the acceleration is zero.
0
0
a
F
11
Force: Acceleration/Equilibrium Acceleration
Kinetic Equations
(see Chap. 2 &3)
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Newton’s Laws of Motion
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Diagram to Understand Forces
The force of the starting
block on the runner has a
vertical component that
counteracts her weight and a
large horizontal component
that accelerate her.
Vector Nature
(see Chap. 1)
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Newton’s Laws of Motion
The two cases are identical as far as the acceleration of
the box is concerned. This demonstrates the VECTOR
NATURE of the force. FFFFF
321R
13
Force: Vector
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Newton’s Laws of Motion
1300 N
1300 N
90o
FFFF
21R
14
Similar to Fig. P4.37
Vector direction x-y coordinates
Find the magnitude of F2 and its direction relative
to F1.
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Newton’s Laws of Motion
1300 N
1300 N
90o
FFFF
21R
15
Similar to Fig. P4.37 x
y
yyy
xxx
FFR
FFR
21
21
?
?
01300
13000
Find the magnitude of F2 and its direction relative
to F1.
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Newton’s Laws of Motion
Find the tensions in each of three chains when the
weight of a car engine is W.
0321O)Point R(at
TTTF
17
Fig. 5.3
Also see Fig. E4.2
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Newton’s Laws of Motion
What is 2nd Law?
m
Fa
m
Fa
m
Fa
m
Fa
z
z
y
y
xx
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Newton’s Laws of Motion
y
x Impulsive Force “F ”
(for a short time
interval)
Top View
vk
(1) A hockey puck is initially
at rest on a flat ice surface.
(2) Then, it receives
a horizontal kick in
a direction of the
red arrow.
F = m a Change in velocity for non-zero F
[Quick Quiz] The motion of the puck
right after the kick is:
(a) Motion with constant velocity
(b) Motion with constant acceleration
(c) Motion with constant deceleration
(d) None of above 19
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Newton’s Laws of Motion
Which of the path 1-5 below would the puck most
closely follow after receiving the force?
y
x
Top View
A hockey puck is sliding
at constant velocity
on a flat ice surface
5 4 3
2
1
v0
Impulsive Force “F ”
(for a short time
interval)
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Newton’s Laws of Motion
vx2 = v0x
2 + 2 ax (x – x0)
x – x0 = 55 m
v0x = 28 m/s
Was: What is the acceleration?
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Newton’s Laws of Motion
Fxnet = m ax
x – x0 = 55 m
m = 1500 kg
Fxnet?
v0x = 28 m/s
Was: What is the acceleration?
Now: What is the net force?
26
vx2 = v0x
2 + 2 ax (x – x0)
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Newton’s Laws of Motion
vx2 = v0x
2 + 2 ax (x – x0)
Fxnet = m ax
x – x0 = 55 m
m = 1500 kg
Fxnet?
v0x = 28 m/s
Was: What is the acceleration?
Now: What is the net force?
vx2 = v0x
2 + 2 ax (x – x0) ax = 7.1 m/s2
SFx = m ax (1500 kg) x (7.1 m/s2)
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• If you exert a force on a body, the body always exerts a force (the “reaction”) back upon you.
• Figure 4.25 shows “an action-reaction pair.”
• A force and its reaction force have the same magnitude but opposite directions. These forces act on different bodies. [Follow Conceptual Example 4.8]
What is 3rd Law?
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Newton’s Laws of Motion
Which force is greater?
From Giancoli 3rd ed.
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Newton’s Laws of Motion
What is 3rd Law? (II)
Push forward
on a rocket
by gas
Push backward
on gas
by a rocket
Action and reaction forces have the same magnitude
but are opposite in direction.
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Newton’s Laws of Motion
[Quick Quiz] A massive truck collides head-on
with a small sports car.
1) Which vehicle experiences the greater force of
impact?
31
2) Which vehicle experiences the greater
acceleration?
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Newton’s Laws of Motion
A stonemason drags a marble block across
a floor by pulling on a rope attached to the
block. Why does the block move while the
stonemason remains stationary?
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Newton’s Laws of Motion
FP-G
Force on
Rope exerted
By Person
FR-P =10 N
Force on
Box exerted
By Rope
Assume the rope is massless.
At rest
x
What is the tension here?
0? 10? 20? Or else?
Quick Quiz
FB-R =10 N
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Newton’s Laws of Motion
Free-Body Diagram
jmgiF ˆ)(ˆ)0(g
y
g
g
v
v
Draw only force(s) on the apple
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Newton’s Laws of Motion
A hockey puck is sliding at a
constant velocity across a flat
horizontal ice surface. Which is
the correct free-body diagram?
[A]
44
Quick Quiz
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Newton’s Laws of Motion
Free-Body Diagram (1D)
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Newton’s Laws of Motion
Free-Body Diagram (1D) M
oti
on
y
m = 10.0 kg
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Find ay
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Newton’s Laws of Motion
ay = 0
Weight in Elevator
y
ay = 4.9 m/s2
49
m = 60 kg
Fg = mg = 588 N
SFy= m ay FN = ?
Example 5.9
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Newton’s Laws of Motion
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Weight on Planet
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Newton’s Laws of Motion
FBD (1B/1D 2B/1D) M
oti
on
y
54
Find ay
Motion
Find ax
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Newton’s Laws of Motion
Free-Body Diagram (x-axis)
Motion
55
P4.43, P4.54
e.g., 2 boxes sliding on desk (no friction)
Find acceleration and tension.
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Newton’s Laws of Motion
Find FP and FT
ax = 2.50 m/s2
FT FP
59
P4.43
Exercise
1) 1B 2B
2) Now a is given. Then you are asked to find forces.
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Newton’s Laws of Motion
2) Apply Newton’s 2nd law:
e.g., 2 boxes sliding on desk (no friction)
Find acceleration and tension.
Free-Body Diagram (x-axis) The rope has a mass …
60
1) Draw F.B.D.
identify all forces exerted on box1, rope and box2
separately.
FP = 40.0 N
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Newton’s Laws of Motion
Free-Body Diagram (y-axis)
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Newton’s Laws of Motion
Example 1: One paint bucket (mass m1) is hanging by
a massless cord from another paint
bucket (mass m2), also hanging by a
massless cord. The two buckets are pulled
upward with an acceleration by the
upper cord. Draw the free-body
diagram for each bucket. Determine the
tension on each code if a = 3.00 m/s2.
a
a
y
66
P4.57
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Newton’s Laws of Motion
Example 1: One paint bucket (mass m1) is hanging by
a massless cord from another paint
bucket (mass m2), also hanging by a
massless cord. The two buckets are pulled
upward with an acceleration by the
upper cord. Draw the free-body
diagram for each bucket. Determine the
tension on each code if a = 3.00 m/s2.
m1
m2 a
a
Fg1
Fg2
FT2
FT1
FT1
y
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Newton’s Laws of Motion
Acceleration?
Tension at the midpoint of the rope?
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P4.54
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Newton’s Laws of Motion
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Newton’s Laws of Motion
2)
e.g., Box sliding on desk (no friction)
Free-Body Diagram (2D)
1)
Motion
x
y
73
m = 10.0 kg
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Newton’s Laws of Motion
2) Apply Newton’s 2nd law:
m ax =
m ay (=0) =
e.g., Box sliding on desk (no friction)
1) Draw F.B.D -identify all forces exerted on the box.
FN
FG
FP Motion
x
y
FP cos(30.0o)
FP sin(30.0o) + FN m g
74
Free-Body Diagram (2D)
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Newton’s Laws of Motion
2) Apply Newton’s 2nd law:
10.0 ax =
10.0 (0) =
e.g., Box sliding on desk (no friction)
1) Draw F.B.D -identify all forces exerted on the box.
FN
FG
FP Motion
x
y
40.0 cos(30.0o)
40.0 sin(30.0o) + FN (10.0)(9.80)
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Free-Body Diagram (2D)
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Newton’s Laws of Motion
e.g., Box sliding on desk (no friction)
FN
FG
FP Motion
x
y
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Free-Body Diagram (2D)
Try E4.4
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Circular Motion
Free-Body Diagrams?