Newton’s Third Law of Motion
Physics 111
Lecture 9 (Walker: 5.4-5)
Forces always come in pairs, acting on
different objects:
Newton’s Third Law
Free Body Diagram
Solving 2-D Force Problems
Weight & Gravity
If Object 1 exerts a force F on Object 2,
then Object 2 exerts a force –F on Object 1.
These forces are called action-reaction pairs.
Alternate Wording:
Sept. 21, 2009
“For every action there is an equal and opposite reaction.”
r
r
FA on B = − FB on A
Quiz Wednesday - Chaps. 3 & 4
Lecture 9
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Question
Lecture 9
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Applying Newton’s Laws
• Assumptions
– Objects behave as particles
Small car is pushing large truck that has a dead battery.
Mass of truck is much larger than mass of car. Which of
the following statements is true?
• can ignore rotational motion (for now)
a. Car exerts force on truck, but truck doesn’t exert force on
car.
b. Car exerts a larger force on truck than truck exerts on car.
c. Car exerts the same force on truck as truck exerts on car.
d. Truck exerts a larger force on car than car exerts on truck.
e. Truck exerts a force on car, but car doesn’t exert a force
– Masses of strings or ropes are negligible
– Interested only in the forces acting on the
object
• can neglect reaction forces
• Start with a Free Body Diagram
on truck.
Lecture 9
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Lecture 9
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Free Body Diagram (FBD)
Example of a free-body diagram:
• Diagram that shows all force vectors acting
on the object of interest. How to construct:
– Draw object as a dot (point particle)
– Replace everything that touches object with
appropriate force vectors
– Add weight vector (always points straight down)
– Choose a convenient coordinate system
– Resolve force vectors into components
Lecture 9
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Example 5-4
A box of mass m1=10.0 kg rests on a floor next to a box of mass
m2=5.00 kg. If you push box 1 with a horizontal force of
magnitude F=20.0N in the positive x-direction,
(a) what is the acceleration of the boxes;
(b) What is the magnitude of contact force F1? Of F2 ?
Drawing Force Vectors
Lecture 9
Lecture 9
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Lecture 9
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N
F
W
FBD Combined
Boxes
N1
F1
y
N2
F
W1
FBD Box 1
Moving a Satellite (Deep Outer Space)
F2
x
W2
FBD Box 2
Only x acceleration in each case (y forces cancel)
Combined Boxes: ax = F/(m1+m2) = 20N/15kg = 1.33 m/s2
Box 1: a1x = ax = (F - F1)/m1 so 1.33 m/s2 = (20N - F1)/10kg
Thus F1 = 6.7 N
Box 2: a2x = ax = F2/5kg so 1.33 m/s2 = F2/5kg
Thus F2 = 6.7 N (as expected from Third Law !!)
Lecture 9
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Lecture 9
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2D Newton’s 2nd Law Problems
• Draw FBD and choose good coordinate system
• Get force components: Fx = Fcosθ; Fy = Fsinθ
• Use Newton 2nd Law
∑ F = ma
in component form (treat x & y separately)
∑F
x
∑F
= ma x
y
= ma y
• ax or ay may be zero
Lecture 9
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Lecture 9
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F2 = 41N @ 52° CCW from x-ax
F2x = F2 cos 52° = 25.2 N
Finding Acceleration
• ax = Fx/m = 51.2N / 940kg = 0.054 m/s2
• ay = Fy/m = 32.3N / 940kg = 0.034 m/s2
F2y = F2 sin 52° = 32.3 N
F1x = 26 N
F1y = 0
a = a x2 + a 2y = 0.064m / s 2
Net force: Fx = F1x + F2x
= 26 N + 25.2 N = 51.2 N
θ a = arctan⎜⎜
Fy = 32.3 N
F = Fx2 + Fy2 = 60.5 N
⎛ Fy ⎞
⎟⎟ = 32.2°
⎝ Fx ⎠
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⎛ ay ⎞
⎟⎟ = 32.2°
⎝ ax ⎠
• Note, also, a = Fnet/m and the angle of the
acceleration is same as net force angle
θ = arctan⎜⎜
Lecture 9
Newton proposed that every object in the universe attracts every
other object with a force that has the following properties:
The falling box is pulled toward
Earth by long-range force of
gravity. The gravitational pull on an
object on or near the surface of
the Earth is called weight, for which
we use the symbol W.
W = mg
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Newton’s Law of Gravity*
Weight
Weight force is the entire Earth
pulling on an object. Weight acts
equally on objects at rest or in
motion. The weight vector always
points vertically downward, and it
can be considered to act at the
center of mass of the object.
Lecture 9
1. The force is inversely proportional to the square of the distance
between the objects.
2. The force is directly proportional to the product of the masses
of the two objects.
W
g = 9.80 N/kg = 9.80 m/s2 down
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Lecture 9
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The Earth’s Gravitation*
Newton’s Law of Gravity*
F1 on 2
What is the gravitational force on an object of mass m at
the surface of the Earth? The center of the Earth is one
Earth radius (RE) away, so that is the distance r:
mm
= F2 on 1 = G 1 2 2
r
G = 6.673 × 10−11 N m /kg 2
2
Therefore,
r is distance between mass
m1 and mass m2.
where
Direction of force on m1 is
toward m2; direction of
force on m2 is toward m1
(third law pair ! )
GM E
RE2
g = 9.80 N/kg = 9.80 m/s2
Lecture 9
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Lecture 9
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Weight & Free Fall
Earth Gravitation vs. Altitude*
The acceleration of gravity decreases
slowly with altitude:
GM E
g ( h) =
( RE + h) 2
GM E
g (0) =
= 9.83 m/s 2
RE 2
Lecture 9
g=
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Weight of box of mass m is
W = mg
g = 9.80 N/kg = 9.80 m/s2 down
∑ Fy = −mg
By Newton’s 2nd Law
m
may = -mg
ay = -g = -9.80 m/s2
y
Lecture 9
W
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Apparent Weight
Apparent Weight
Your perception of your weight is based on the contact
forces between your body and your surroundings.
Elevator not accelerating:
Wa=mg
If your surroundings are
accelerating, your
apparent weight may
be more or less than
your actual weight.
Elevator accelerates up:
Wa> mg
Elevator accelerates down:
Wa< mg
Force felt from contact with the floor (or a scale,
etc.) in an accelerating system.
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Apparent Weight
(Example 5.7 from Walker)
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Weight Components on Inclined Surface
m = 5.0 kg
a) Wa (at rest)?
b) Wa ?
(a =2.5m/s2 up)
c) Wa ?
(a =3.2 m/s2
down)
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Lecture 9
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Force Component Down Inclined Plane
• Forces acting on the object:
– The normal (support)
force acts perpendicular
to the plane
– The gravitational force
acts straight down
• Choose coordinate system
with x along the incline and
y perpendicular to incline
• Replace the force of gravity
with its components
Acceleration Down Inclined Plane
• Newton’s 2nd law:
∑ Fx = mg sin θ = max
∑ Fy = 0
• From 1st equation:
a x = g sin θ
• Check special cases to
see that answer makes
sense:
θ = 90o
θ = 0o
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End of Lecture 9
z Before the next lecture, read Walker
Chapter 5, 5.7; Chapter 6, 6.1 - Kinetic Friction
z Homework Assignment #5b should be
submitted using WebAssign by 11:00 PM on
Thursday, Sept. 24.
Lecture 9
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What is acceleration
in each of these cases?
Lecture 9
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