Download Introduction to Mechanics Dynamics Forces Newton`s Laws

Introduction to Mechanics
Dynamics
Forces
Newton’s Laws
Lana Sheridan
De Anza College
Feb 17, 2016
Last time
• forces
• net force and equilibrium
• Newton’s first law
• intertia
Overview
• Newton’s second law
• mass and weight
• examples
• free-body diagrams
examples of a class of
between two objects.
molecules on the wall
Isaac Newton was able to articulate simple rules that govern
theclass of f
Another
way in which forces act and effect motion.
between two objects.
of attraction between
of this class of force.
the planets in orbit ar
that one electric char
force between an elec
of a field force is the f
The distinction be
have been led to beli
level, all the forces w
(field) forces of the ty
els for macroscopic ph
The only known fund
forces between object
forces between subato
tive decay processes.
Isaac Newton
and electromagnetic
Bridgeman-Giraudon/Art Resource, NY
Newton
English physicist and mathematician
Newton’s First Law
Newton I (as commonly stated)
An object in motion will stay in motion with constant velocity and
an object at rest will stay at rest, unless acted upon by a
(non-zero) net force.
An “object” for these purposes is something with mass.
Newton’s Second Law
Galileo also proposed the concept of acceleration, but Newton
realized:
acceleration ∝ net Force
(Remember net force is the sum of all the forces on an object)
If the net force on an object is doubled, the acceleration is twice as
big also.
Newton’s Second Law
Newton II
Fnet = ma
P
Fnet = i Fi where Fi are individual separate forces that we sum
to get the net force.
Newton’s Second Law
Newton II
Fnet = ma
P
Fnet = i Fi where Fi are individual separate forces that we sum
to get the net force.
Acceleration is directly proportional to the net force and in the
same direction. The constant of proportionality is the mass, m.
Alternatively, given a net force, the acceleration is inversely
proportional to the mass of the object.
We are assuming the mass of the object is constant.
Units of Force
Newton’s second law gives us units for force.
F
= ma
Newtons, N = (kg) (ms−2 )
1N = 1 kg m s−2 : on Earth’s surface there are roughly 10 N per
kg. Why?
Mass vs. Weight
mass, m
A measure of the amount of matter in an object. Also, a measure
of the inertia of an object, that is, its resistance to changes in its
motion.
weight
The force due to gravity on an object.
Weight is a force. It is measured in Newtons (N) as are all forces.
weight = mg
Weight depends on mass, m. The mass that appears in the
equation above is sometimes called the “gravitational mass”.
Mass is an amount of “stuff”, measured in kilograms (kg).
Mass and Inertia
Mass is also a measure of resistance to acceleration.
For a constant net applied force:
acceleration ∝
1
mass
The mass, m, in the equation F = ma is sometimes called “inertial
mass”.
Weight and acceleration
Let the weight of an object be written Fg .
Fg = mg
Mass in this equation is sometimes called “gravitional mass”.
Weight and acceleration
Let the weight of an object be written Fg .
Fg = mg
Mass in this equation is sometimes called “gravitional mass”.
We can find the acceleration of an object when the only force on it
is due to gravity:
Fg
mg
a=
=
=g
m
m
Weight and acceleration
Let the weight of an object be written Fg .
Fg = mg
Mass in this equation is sometimes called “gravitional mass”.
We can find the acceleration of an object when the only force on it
is due to gravity:
Fg
mg
a=
=
=g
m
m
As we would expect! This is because the inertial mass is the same
as the gravitational mass.
That is why all objects, no matter their mass, fall at the same rate
(with the same acceleration).
brief period of free fall. To decelerate your fall, must the force
exerted on you by the parachute be greater than, less than, or
equal to your weight?
Question
A hockey puck is acted on by one or more forces, as shown in
Figure A
5–19.
Rank the
fouriscases,
A, on
B, C,by
and
D, in
of the
hockey
puck
acted
one
ororder
more
forces, as shown.
magnitude
of
the
puck’s
acceleration,
starting
with
the
smallthe four cases, A, B, C, and D, in order of the magnitude of
est. Indicate ties with an equal sign.
Rank
the
puck’s acceleration, starting with the smallest. Ties are shown in
brackets.
3N
5N
3N
7N
A A, B, C, D
B
A
B D, C, C, A
C A, D, B, C
3N
3N
C
3N
D
▲ FIGURE
5–19 Conceptual Exercise 10
1
Walker, “Physics”, page .
D D, (B and C), A
brief period of free fall. To decelerate your fall, must the force
exerted on you by the parachute be greater than, less than, or
equal to your weight?
Question
A hockey puck is acted on by one or more forces, as shown in
Figure A
5–19.
Rank the
fouriscases,
A, on
B, C,by
and
D, in
of the
hockey
puck
acted
one
ororder
more
forces, as shown.
magnitude
of
the
puck’s
acceleration,
starting
with
the
smallthe four cases, A, B, C, and D, in order of the magnitude of
est. Indicate ties with an equal sign.
Rank
the
puck’s acceleration, starting with the smallest. Ties are shown in
brackets.
3N
5N
3N
7N
A A, B, C, D
B
A
B D, C, C, A
C A, D, B, C
3N
3N
C
3N
D
▲ FIGURE
5–19 Conceptual Exercise 10
1
Walker, “Physics”, page .
←
D D, (B and C), A
Newton’s Second Law Implications
Question. If an object with mass 16 kg is acted upon by two
forces, F1 = −(10N)i and F2 = (2N)i, what is the object’s
acceleration?
Newton’s Second Law Implications
Question. If an object with mass 16 kg is acted upon by two
forces, F1 = −(10N)i and F2 = (2N)i, what is the object’s
acceleration?
A − 21 ms−2 i.
B + 34 ms−2 i.
C − 34 ms−2 i.
D −2 ms−4 i.
Newton’s Second Law Implications
Question. If an object with mass 16 kg is acted upon by two
forces, F1 = −(10N)i and F2 = (2N)i, what is the object’s
acceleration?
A − 21 ms−2 i.
B
C
+ 34
− 34
ms−2 i.
ms−2 i.
D −2 ms−4 i.
←
Newton’s Second Law Implications
Question. If an object is not accelerating, can there be forces
acting on it?
A Yes.
B No.
C I don’t pay attention in class.
D I choose randomly because I’ve no idea what’s going on.
Newton’s Second Law Implications
Question. If an object is not accelerating, can there be forces
acting on it?
A Yes.
←
B No.
C I don’t pay attention in class.
X
D I choose randomly because I’ve no idea what’s going on.
X
Diagrams of Forces
We can draw pictures to aid our reasoning. This is always a good
idea.
The process will be to identify a system of interest. Something we
want to study. We will make a mathematical model of it.
Everything that is not part of the system, but interacts with it, is
part of the environment. We do not describe the environment
mathematically.
Diagrams of Forces
This is a physical picture.
(a) Sketch the forces
Physical picture
We need to identify the system we want to study. Here: the chair.
1
(b) Isolate the object of interest
Diagrams from Walker, “Physics”.
(c) Choose a convenient coordinate sy
at indicates each and every external force acting on a
ch is referred to as a free-body diagram. If we are
onal motion, as is the case in this and the next chapst as a point particle and apply each of the forces actas Figure 5–5 shows. Once the forces are drawn, we
d resolve each force into components. At this point,
pplied to each coordinate direction separately.
Diagrams of Forces
PROBLEM-SOLVING NOTE
External Forces
External forces acting on an object fall
into two main classes: (i) Forces at the
This is a physical picture, but point
nowof contact
we consider
the and
forces that act
with another object,
(ii) forces exerted by an external agent,
on the system (chair) from thesuchenvironment
(everything else).
as gravity.
(a) Sketch the forces
F
W
Physical picture
(c) Choose a convenient coordinate system
N
(d) Resolve forces into their components
N
Diagrams of Forces: Free-Body
Diagram
Physical picture
This is a free-body diagram. We represent the chair as a
point-particle (c)
with
force vectors pointing outward.
f interest
Choose a convenient coordinate system
(d) Resolve fo
y
N
W
N
Nx = 0
Ny = N
F
W
x
O
Free-body diagram
We also picked a coordinate system (x, y axes).
Wx = 0
Wy = –
Diagrams of Forces:NFree-Body Diagram
To analyze the forces, we must break them into components along
our chosen axes.
nate system
(d) Resolve forces into their components
y
N
W
x
Nx = 0
Ny = N
Wx = 0
Wy = –W
x
Fx = F cos θ
Fy =
–F sin θ
θ
F
object, which we will model as a particle. T
Diagrams of Forces
us isolate only those forces on the object and
analysis.
We can choose our system
to be more than one object. This is
three interacting objects, a monitor sitting on a table, on the Earth:
S
S
S
S
S
Fg ! FEm
S
S
FmE
a
1
Figure from Serway & Jewett.
S
Fg ! FEm
S
Fmt
S
n ! Ftm
n ! Ftm
b
nly those forces on the object and eliminate the
Force Diagrams
We could later refine our system into pieces. Here is a depiction of
the forces that act on a single object, the monitor.
S
S
S
n ! Ftm
Ftm
S
S
n ! Ftm
S
S
Fg ! FEm
S
S
Fg ! FEm
S
S
S
Fg ! FEm
Summary
• Newton’s second law
Homework
Walker Physics:
• Ch 5, onward from page 138. Problems: 1, 3, 5, 9