Physics 121

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Physics 121
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4. Motion and Force Dynamics
4.1 Force 4.2 Newtons First Law of Motion 4.3
Mass 4.4 Newtons Second Law of Motion 4.5
Newtons Third Law of Motion 4.6 The Force of
Gravity and Weight 4.7 Applications of Newtons
Laws 4.8 Applications involving Friction 4.9
The art and science of problem solving
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4.1 Force
A force is a push or a pull A force is that
which causes a body to accelerate
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Example 4.1
You see an object moving towards the East with a
constant speed of 3 m/s. What can you say about
the force acting on it?
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Solution 4.1
The force (or net force to be precise) must be
zero. The keyword is acceleration. The
acceleration of the object is given to be zero.
(Neither speed nor the direction is changing).
If there is no acceleration then there cannot be
a net force. So you see, motion without force
is possible but acceleration without force is
impossible!
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Example 4.2
The term net force simply means the resultant
or unbalanced force. (a) What is the net force
acting on the object shown? (b) Would you expect
this object to accelerate?
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Solution 4.2
(a) The net force is 4 units to the right (b)
This object will accelerate towards the right
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4.2 Newtons First Law
In the absence of external forces, an object at
rest remains at rest and an object in motion
continues in motion with a constant velocity
(that is with a constant speed in a straight line)
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Newtons First Law (in English)
When no force acts on an object, the acceleration
of the object is zero
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4.3 Mass
The mass of an object depends on how much stuff
is in the object. The mass of a given object is
the same on Earth, under water, and on the
moon! The tendency of an object to resist
acceleration is called inertia. The greater the
mass of an object the greater the inertia. In
other words, the mass of an object is a measure
of its inertia and vice-versa.
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4.4 Newtons Second Law
The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to its mass F ma
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Newtons Second Law . . . In English

• F ma
• Acceleration is greater if the force is greater
• and
• Acceleration is smaller if the mass is greater

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Example 4.3 . . . 0 to 60 in 3 seconds!

• Explain two different ways to design a car in
  order for it to go from 0 to 60 in 3 seconds.

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Solution 4.3 . . . 0 to 60 in 3 seconds!
There is a right way and a wrong way to go about
this and, by golly, I am going to show you the
right way! 1. Design a bigger engine in order
to apply a greater force. The downside of this
is that it will cost you! 2. Take a tin can (in
order to reduce the mass) and paint it red
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4.5 Newtons Third Law
When two objects interact, the force exerted by
object 1 on object 2 is equal in magnitude but
opposite in direction to the force exerted by
object 2 on object 1 F12 -F21
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Newtons Third Law . . . in English
Action and reaction are equal and
opposite Action You stand on a skateboard and
throw a ball Reaction The ball pushes you
back! Note Action and reaction act on different
objects and so cannot cancel each other.
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Example 4.4 . . . Head-on Collision
A big truck slams into a Neon. Which statement is
most nearly correct A. Force of truck on neon
equals the force of Neon on truck B. Force of
truck on neon far exceeds the force of Neon on
truck C. Force of truck on Neon is much less than
the force of Neon on truck D. Neither
experiences any force because the equal and
opposite forces cancel each other out
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Solution 4.4 . . . Head-on Collision
A. Force of truck on neon equals the force of
Neon on truck Note Do not confuse force with
damage (acceleration). The same force will
cause a tremendous amount of acceleration on the
puny Neon.
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4.6 The Force of Gravity and Weight
The weight of an object is the attractive force
of gravity acting on it Acceleration due to
gravity Near the surface of the Earth, the
attractive force of gravity accelerates objects
at the rate of approximately 9.8 m/s2
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Example 4.5 . . . weight of a crate
(a) What are the units of weight? (b) What is
the weight of a 5 kg crate?
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Solution 4.5 . . . weight of a crate
(a) Weight is a force (of gravity) so the units
would be newtons.
A newton is a kg m / s2. A force of 1 N will
cause a 1 kg mass to accelerate at the rate of 1
m / s2.
(b) F ma Fg mg (g stands for a due
to gravity) Fg (5)(9.8) Fg 49 N
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Example 4.6 . . . Moon walk
Object P weighs the same on the Moon as object Q
does on Earth. Identify the correct
statement A. Mass of P is more than the mass of
Q B. Mass of P is less than the mass of Q C. Mass
of P on the Moon is more than its mass on
Earth D. Weight of P on the Moon is more than the
weight of Q on Earth
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Solution 4.6 . . . Moon walk
A. Mass of P is more than the mass of Q. In
fact, mass of P must be 6 times the mass of Q
because gM 1/6 gE Note Mass never changes.
Mass is mass is mass. (Unless you break the
object in two!). Weight changes if the
acceleration due to gravity changes.
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4.7 Applications of Newtons Laws
We will present situations from daily life and
apply Newtons Laws to answer questions about
forces and motion. This will aid us in
comprehending the material learned so far.
Practice makes perfect!
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Example 4.7 . . . The sun also rises!
What is the tension in the string (T) if the mass
of the Van Gogh painting is 2 kg and the price is
37 million dollars? A. 10 N B. 15 N C. 20 N D.
40 N
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Solution 4.7 . . . The sun also rises!

• T sin 45 T sin 45 20 N
• T 14 N

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Example 4.8 . . . Slippery when wet

• What is a in m/s2 if there is no friction?

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Solution 4.8 . . . Slippery when wet
What is a in m/s2 if there is no friction?

• F ma
• mg sin ? ma
• a g sin ?
• a 5 m/s2

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4.8 Applications involving Friction
Frictional forces resist the motion of objects.
They can arise when one surface rubs against
another, or an object encounters resistance as it
moves through air, water, and other media.
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Example 4.9 . . . Calculate ?
You apply a 30 N force on a 5 kg crate to push it
horizontally across a factory floor. The speed
of the crate increases at the rate of 1.5 m/s
every second. What is the coefficient of
friction?
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Solution 4.9 . . . Calculate ?
Fnet ma F - f (5)(1.5) 30 - f 7.5 f 22.5 N
f ? n 22.5 (?) (49) ? 0.46
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All about friction . . .
Static friction must be overcome in order to
start the motion fs ? ?s n Kinetic friction must
be overcome in order to maintain the motion.
fk ?k n n normal
reaction or the force that the surface exerts
perpendicularly on the object ?s and ?k are the
respective coefficients of friction and depend on
the nature of the surfaces. ?s is slightly
greater than ?k .
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Example 4.10 . . . Who wins?
Calculate the acceleration and tension if ? 0.1
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Solution 4.10 . . . Who wins?
Apply F ma to each mass individually
20-T 2a .(1) T 30 sin 30 30 cos 30(0.1)
3a (2)
Now solve (1) and (2) for a and T
a 0.5 m/s2 T 19 N
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Thats all folks!