Download dynamics - moorsscience

Dynamics
Mechanics is the branch of physics that is
concerned with the analysis of the action of
forces on matter or material systems.
Dynamics is the branch of mechanics that is
concerned with the effects of forces on the
motion of a body or system of bodies,
especially of forces that do not originate
within the system itself.
Why are Forces Important?
• Forces help to describe much of what
occurs in our Universe. For example, we
know that if we push a box with a certain
amount of force, it will move.
• In chemistry, intermolecular and
intramolecular forces help describe why
different elements react with each other
and what happens at the subatomic level.
• A force is defined by a push or a pull
one object exerts on another and is
measured in units of Newtons (N)
• 1 Newton is defined as the magnitude
of force required to accelerate a 1.0 kg
mass at a rate of 1.0 m/s2.
• Forces are vector quantities
(magnitude and direction). They are
denoted as Fx (for example the force of
gravity is denoted Fg)
Examples of Forces
• Force of Gravity (Fg)
- Direction always toward centre of attracting
mass
-
Earth attracts us we attract earth
Applied Force (Fa)
-Contact action force applied by one object to the
other
Fa
not really in contact, repulsion of nuclei
Normal Force (FN)
-Perpendicular to and provided by a supporting
surface
FN
Once again due to repulsion of nuclei, normal forces can be very small or very large
FN
Frictional Force (Ff)
- Direction of frictional force generally opposes
motion and is caused by particles of both
objects being attracted to each other
(intermolecular forces)
V
Ff (Frictional Force)
Other forces include the force of tension, FT,
and the force of compression, Fc.
The Four Fundamental Forces
Each of the examples of forces
mentioned can be divided into the four
fundamental forces of our Universe.
1. Strong Interaction: The strong
interaction or strong force is the
attractive force that holds protons and
neutrons together in a nucleus.
2. Electromagnetic force: The force that
exists between charged particles (repulsion
or attraction). This force is transmitted by
electric fields. Magnetic fields are linked to
electric fields (as are electricity and
magnetism) so it is called the
electromagnetic force.
3. Gravitation or gravity is the attractive force
that exists between all matter.
4. The weak interaction (often called the
weak force or sometimes the weak
nuclear force) is an interaction between
elementary particles involving neutrinos
or antineutrinos that is responsible for
certain kinds of radioactive decay.
All About Newton’s Laws
Newton’s First Law of Motion
Every object continues in its state of rest, or
uniform motion in a straight line unless acted
upon by an unbalanced force.
Constant velocity of the car
The car will continue to travel at the same speed
at which it is going unless an external force is
applied to it. For example, the force on wheels
caused by brakes!
Newton’s first law discusses a property
of matter known as inertia.
Inertia is the property of matter that
causes a body to resist changes in its
state of motion. The amount of inertia an
object possesses depends directly on its
mass.
Think about a hockey puck on ice
(which is basically frictionless). It will
continue to glide at practically the
same speed until it is hit by a stick or
hits the boards.
Forces Thinking Exercise
In groups of two or three:
Think of as many examples of uses
or dangers of Newton’s first law. If
there is a danger then state what
counteractive measures are taken.
Newton’s Second Law of Motion
When an unbalanced force acts on an
object, the object will accelerate in the
direction of the unbalanced force. The
acceleration of the object is directly
proportional to the size of the force and
inversely proportional to the mass of the
object.
Demonstrate this with spring loaded cars, with roller bladed students, (can be done as part of third law as well)
From Newton’s Second Law, we can
arrive at the conclusion that the
acceleration of an object is equivalent to
its net force divided by mass.
F
a
m
or
F  ma
Mass is the quantity of matter in a body.
Free Body Diagrams
Newton’s Second Law utilizes a quantity called the net force on an
object. Forces are vector quantities and if more than one force
acts on an object then the forces can be added (summed). The
sum of these forces is called the net force or resultant force. This
force is symbolized as shown below.


 F F net

FR


F total F sum
Free Body Diagrams
A free body diagram (FBD) shows all of the forces acting on a
object. All forces are shown as a pull on the object.
Draw free body diagrams of the following situations:
pushing against a stationary chair

FN


Ff
Fa

Fg
Newton’s Third Law of Motion
If object A exerts a force on object B,
then object B exerts a force equal in
magnitude but opposite in direction on
object A.
These two forces are called action
reaction pairs.
“For every action force there is an equal
and opposite reaction force.”
Let’s take someone pushing a wall for
example. When you (object A) push on a wall
(object B) Newton’s Third Law dictates that
the wall (object B) should push back on you
(object A).
Think about this concept. If there was
no force pushing back on you, then
essentially you would feel nothing
and would be able to go through the
wall (as there would no force pushing
back on you).
Now what would be the reaction force to
that of the force of gravity on a man
standing on Earth?
Fg
FM
The reaction force to
the force of gravity
(Earth pulling down on
the man) is the force of
the man pulling up on
Earth!
Name the reaction pair to the forces
below.
a) Bill pushes [S] on Mike.
b) Jenny pulls westward on the rope.
c) Mack pushes a spring down.
d) Sue hits a tennis ball up.
e) The Sun attracts Earth towards it.
f) John experiences friction while sliding
[NW] on the hardwood floor.
g) Proton A repels proton B left.
h) Ana falls and hits the ground.
Fanyan and Atif each pull on a rope so that
they slide towards each other, on ice, with a
constant velocity (Assume rope is massless)
Fanyan
Atif


FN
FN




Ff
FT
FT
Ff


Fg
Fg
The ground pushes up on Fanyan and
Fanyan pushes down on the ground.
Earth pulls down on Fanyan and Fanyan
pulls upwards on Earth.
Fanyan pulls the rope left and the rope
pulls Fanyan right.
The ground attracts Fanyan to the right
and Fanyan attracts the ground to the
left.
Draw a sketch of the following systems
(underlined items) then draw individual free
body diagrams. State action reaction force
pairs (some reaction forces may not be
present in your system)
a) A box sits on the ground, is pushed by
Sohaib and remains stationary.
b) A ball falls with a constant velocity.
c) Greg holds on to Ian who holds on to a
rope.
d) Alison sits and remains on a rough box
that is being pushed west by a spring.
Newton's Third Law at a Traffic Intersection
Ernie McFarland
University of Guelph
Many physics students seem to have the
impression that physics is something found only
in textbooks; therefore it is particularly nice to
show them physics phenomena in the "real"
world. I recently noticed an interesting example
of Newton's third law at a traffic intersection on
campus, and students are quite intrigued by it.
What happened to the lines? There are traffic lights at this intersection, and each day
hundreds of cars stop just to the left of the fines. When the light turns green, the cars
accelerate to the right (Fig. 2). To achieve this acceleration, the car tires exert a
backward force on the road (to the left in the photograph), and by Newton's third law,
the road exerts a forward force on the tires, i.e., on the car. At this particular
intersection, the top layer of pavement is poorly bonded to the underlying layers, and
the backward force on the road under the tires has actually caused the top layer to slide
to the left, as seen from the photo, leading to the unusual bends in the painted fines.
Figure 1 shows part of a road
at the intersection, from the
curb and gutter in the
foreground (bottom of
photograph) to the center of
the road (top). The white
lines painted on the road
show a rather unusual
pattern -indeed, it looks as if
the road-painters went
berserk! However, the lines
were straight when originally
painted, eventually assuming
the shape in the photograph.
The Force of Gravity
Earth is surrounded by a gravitational force
field. This means that every mass, no
matter how large or small feels a force
pulling it directly towards the center of
Earth. The force field is measured in N/kg.
All objects on Earth have the same ratio of
force to mass (demonstrate with spring
scale). At Earth’s surface this ratio is 9.81
N/kg [down] The magnitude of this ratio
decreases as one moves farther from Earth.
The gravitational field strength at Earth’s surface can be
denoted by “g”. 6400 km above Earth’s surface the field
strength has decreased to 2.45 N/kg [down] (12800 km
above 1.09 N/kg).
Mass is defined as the quantity of matter in an object
(kg). The standard kilogram of comparison is a Pt-Ir bar
in France. The mass of an object is constant
everywhere. Mass is measured with a balance.
Weight is defined as the force of gravity acting on an
object (N). The weight of an object is variable and
depends on the size of the “other mass”. For example a
person’s weight on the moon is less than his/her weight
on earth. Weight is measured with a scale.


Fg  m g
Gravitational field strength (N/kg)
Acceleration due to gravity (m/s2)
g is a variable quantity!
Text problems
LAW OF UNIVERSAL GRAVITATION
Gm1m2
FG 
2
r
FG gravitational force (in two directions)
G
r
m1
m2
universal gravitation constant
6.67x10-11 Nm2/kg2
distance between the objects
mass of the larger object
mass of smaller object
at the Earth’s surface . . .
Gm1m2
m2 g 
2
r
Gm1
g 
2
r
All objects at the same distance from a
large object experience the same
acceleration due to gravity.
Text problems
Calculate the gravitational field strength of all of
the planets and the Sun if you were on the
surface of each. G = 6.67 x 10-11 Nm2/kg2
Force of Gravity Problems
David (62 kg) stands on a scale in an elevator.
Determine the reading on the scale in each of the
following situations.
a)The elevator is at rest.
b)The elevator is moving with a constant velocity
upwards.
c) The elevator is moving with a constant velocity
downwards.
d) The elevator is accelerating at 2 m/s2 [up].
e) The elevator is accelerating at 7 m/s2 [down].
worksheet
+ is up

FS

Fg



FR  FS  Fg


ma  F S  F g
m  62 kg
N
g  9.81
kg
When dealing with forces
we will treat acceleration
due to gravity as a scalar
quantity. “g” is used in
many forces which do not
have a downward
direction. The direction of
the force will be
determined by the student
by calculation or analysis.
a, b, c) The acceleration is 0 in each of these situations.



FR  FS  Fg
0  Fs  mg
Fs  mg
Fs  608.2 N up 
Since the scale is pushing up on the rider with a force
of 608.2 N the scale will read a weight of 608.2 N
d) The acceleration is +2 m/s2.



FR  FS  Fg
ma  Fs  mg
Fs  ma  mg
Fs  62(2  9.81)
Fs  733.2 N up 
d) The acceleration is -7 m/s2.



FR  FS  Fg
ma  Fs  mg
Fs  ma  mg
Fs  62(7  9.81)
Fs  174.2 N up 
Normal Forces
When an object rests on a flat surface (parallel to the
ground) the normal force of the surface is equal and
opposite to the force of gravity on the object. This
balance also applies to situations when the object is
accelerating parallel to the ground (height remains the
same). These situations are encountered often and as a
result people often think the force of gravity and the
normal force are equal and opposite. Surfaces are, in
fact, capable of a wide range of forces. Surfaces are
capable of changing an object’s velocity very quickly and
thus exert forces much larger than force of gravity on the
same object. The following example will illustrate this
point.
worksheet
Alison (55 kg) jumps off a 30 m building and lands in
mud! She compresses the mud 20 cm while coming to
rest.
a)What velocity did she hit the mud with?
b)What was Alison’s acceleration in the mud?
c) What was the mud’s normal force on Alison?
mud

air
+ is up

Fg
FN

Fg
a)
ma   mg
d  30 m
N
g  9.81
kg
v1  0
a  g
v  v  2ad
in air


FR Fg
2
2
2
1
v  2(9.81)( 30)
2
2
Therefore Alison hits
the mud with a velocity
of 24.26 m/s [down].
m
v2  24.26
s
a)
Alison’s acceleration must
first be calculated.
in mud



FR FN Fg

ma  F N  mg
d  0.2 m
m
v1  24.26
s
v2  0
v  v  2ad
2
2
2
1



FR FN Fg
v v

a
ma  F N  mg
2d
2 
0  (24.26)
a
F N  ma  mg
2(0.2)

m
F

55
(
1471

9
.
81
)
N
a  1471 2
s

2
2
2
1
F N  81440 N [up ]
Superhero Matt (60 kg) jumps upward with an initial
velocity of 40 m/s to catch a basketball. He miscalculates and finds himself embedded in ceiling 50 cm.
The ceiling is 15 m high. What normal force did the
ceiling exert on Supehero Matt.
FRICTION
Textbook: 96-108
Questions: p. 97 #13, p. 98 #4, p. 100 #16, p. 103 #16,
p. 105 #79, p. 106 #10, p. 107 #18
The force of friction (Ff) is the resistance to motion because of
the interaction of the object with its surroundings (gas, liquid,
solid). Forces of friction are very important because they
allow things to move or stop. On a molecular level friction
involves the electrostatic forces between atoms or molecules
where the surfaces are in contact. There are two types of
friction. Static friction (Fs) occurs when an object is stationary
while kinetic friction (Fk) occurs when an object is moving. There
are different types of friction such as sliding, rolling and fluid
friction. For each of these types there are also static and kinetic
forms.
Friction follows these two empirical laws.
1. It is proportional to the normal force.
2. It is approximately independent of the area of contact over wide
limits.
When a stationary object is acted upon by an unbalanced
force that increases so too does static friction (and the
object does not move). When the static frictional force
reaches a maximum it grows no longer and the object
begins to move. The frictional force often decreases at this moment
since the coefficient of kinetic friction is generally lower than the
coefficient of static friction.
Kinetic frictional forces do change with increasing velocity but
not that dramatically. We will treat kinetic friction as being
independent of an object’s velocity. Both coefficients of friction
(kinetic and static) are dimensionless constants that are generally
less than one in value.