Download Chapter 4 Force and Motion

DYNAMICS
Force
Mass and Weight
Newton’s Laws
“If I have been able to see further, it was only because I stood on
the shoulders of giants.”—Isaac Newton
Chapter 4
Force and Motion:
Dynamics
In chapters 2 and 3 we described motion in terms of position,
velocity, and acceleration. We didn’t consider the causes of
motion.
In chapter 4, we begin our investigation of the causes of
motion.
4.1 Force
The grade school definition—a force is a push or a pull—works
OK here too.
Forces have both magnitude and direction, so forces are
vector quantities.
In our diagrams, we will show that a force is exerted on an
object by “connecting” it to that object:
F
Later, it will matter where the force acts on the body, but
don’t worry about that yet.
Don’t draw forces like this:
F
The top ten reasons why I insist you draw forces emanating
from the object…
F
10. To be consistent with Physics 23.
9. I’m the dictator here!
That’s enough reasons for me.
4.2 Newton’s* First Law of Motion
Why study Newton’s laws? We use them to solve an
enormous number of real-world problems. Most of the first
half of your text is applications of Newton’s laws.
Matter has inertia. An object at rest “wants” to stay at rest.
A moving object “wants” to keep moving.
There are lots of different ways to state Newton’s first law.
Here’s one: an object at rest remains at rest unless acted on
by a nonzero net force,
force and an object moving with a uniform
speed in a straight line continues that motion unless acted on
by a nonzero net force.
*If Galileo discovered this, why is it Newton’s law?
Newton’s laws are valid only in inertial (non-accelerated)
reference frames.
The earth is (approximately) such a reference frame.
4.3 Mass
We already defined mass (chapter 1). In the context of this
chapter, mass is the measure of the inertia of a body (a
measure of its resistance to a change in its state of motion).
Mass and weight are different, but you already know that…
You may not realize there are two different kinds of mass.*
*Which are, to the best of our ability to measure, the same.
4.4 Newton’s Second Law of Motion
It is an experimental observation that a net force applied to
an object causes the object to accelerate, with the
acceleration directly proportional to the force.
Mathematically:
OSE:
F = m a .
This equation cannot be derived; it is a postulate that our
experience suggests always works in macroscopic inertial
reference frames.
The SI unit of force is the newton:
1 kg
1 newton = 1 N =
.
2
1 m/s
A note on nomenclature and abbreviations—
a unit named after a person is written in lowercase
newton
joule
ohm
watt
but abbreviated in uppercase
N
J
 (uppercase Greek letter)
W.
The English unit of force is the pound. To help your intuition get going, a
force of 1 pound is equal to a force of 4.45 newtons.
Remember that a component version of an OSE is also an
OSE, so the following are equally valid
F = m a
F = m a
F = m a
x
x
r
r
z
z
.
The summation sign on the left hand side is necessary
because the net force—the sum of all forces acting—produces
the acceleration.
The net force produces a single acceleration, not a collection
of accelerations which sum to a net acceleration.
Example 4-2. What net force is required to bring a 1500 kg
car to rest from a speed of 100 km/h within a distance of 55 m.
What’s in your toolbox now? Kinematics, plus Newton’s second
law. Newton’s second law requires an acceleration, so…
…you know the kinematics problem-solving drill…
Vi=100 km/h
xi=0 m
Vf=0
a=?
D=55 m
xf=55 m
x
Vi=100 km/h
Vf=0
a=?
xi=0 m
xf=55 m
x
D=55 m
OSE:

v2x = v20x + 2ax  x - x0 

0 = +Vi2 + 2  -a  +D  - +0  
0 = Vi2 - 2aD
Vi2
a =
2D
this is the magnitude; the figure
shows the direction
Time now for something different…
…a force problem.
OSE:
F
x
-Fnet  = m -a
a
= m ax
Fnet
m
x
Fnet = m a
 Vi2 
Fnet = m 

2D


h
 100 km 1000 m





h
km
3600s
Fnet = 1500 kg 

2  55m




Fnet = 1.1 104 N this is the magnitude; the figure
shows the direction
There is a new litany for force problems. Not surprisingly, it is
called the “Litany for Force Problems.”
It may appear to be something new, but many of the steps
correspond to steps in the Litany for Kinematics.
4.5 Newton’s Third Law of Motion
“For every action, there is an equal and opposite reaction...”
That’s probably the way you’ve heard it before.
“Action” and “reaction” refer to forces.
A “better” way to phrase this law: if object A exerts a force on
object B, then object B exerts and equal and opposite force on
object A.
“Wait a minute…
F = m a
…if for every force, there is another equal and opposite
force, shouldn’t the sum of all forces be zero and
therefore motion impossible?”
The forces in Newton’s second law are all the forces exerted
by other objects on the object in question.
The “equal and opposite” forces in Newton’s third law are
forces on different objects. Only the forces on the object in
question go into Newton’s second law.
Let me do a couple of demonstrations of Newton’s third law…
try to identify the action-reaction pairs.
If object A exerts a force on object B, then object B exerts and
equal and opposite force on object A.
More examples:
(http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
identify all the actionreaction pairs
Example:
(http://hyperphysics.phy-astr.gsu.edu/hbase/incpl.html#c1)
Let’s just look at the “rope” connecting the two masses. We
will learn how to solve this problem soon.
This example introduces the concept of “tension.” Read about
on page 86 of your text.
Newton’s third law gives us one new OSE:
Fab = -Fba
How to remember the order of the subscripts: we will be
particularly interested on the forces ON an object. Forces on
come first. Therefore, you may write (if you wish)
Fon
a by b
= -Fon
b by a
4.6 Weight
The Force of Gravity and the Normal Force
On earth, the weight of an object is the gravitational force
exerted on the object by the earth. If the object has mass m,
the magnitude of weight is always mg:
W = mg, down
In the inclined plane picture we saw a
couple of slides back, the weight of the
object on the plane is m1g, and the weight
of the hanging object is m2g. Both are
directed “down.”
Caution: this picture violates at least one of the rules in our litany for
force problems.
We also saw this picture a few slides back.
Don’t confuse the
abbreviation N for
newtons with N for
normal force!
The combined 250 N mass exerts a downward force on the
scale. The scale exerts an equal and opposite force upward.
The contact force resulting from an object pushing on a
surface is always parallel to, or “normal” to, the surface;
hence the term “normal force.”
Normal force example: the table exerts an
upward force on the lamp. The force is
normal to the surface of the table.
Normal force example: the ramp exerts
a force on the block. The force is
normal to the surface of the ramp.
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7-9 M-Th room 208 Norwood.
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