Download HONORS Physics : Lecture 5 Notes

Honors Physics
Today’s Agenda



Newton’s 3 laws.
 How and why do objects move?
 Dynamics.
Textbook problems Chapter 4 59-80
You should also try answering 41-58
Honors Physics , Pg 1
The Fundamental Forces of our Universe

Any object with mass will have an attraction to another
object with mass Luckily it is VERY WEAK.
This is called the Gravitational Force (due to the large
mass of the earth)
Honors Physics , Pg 2
The Fundamental Forces of our Universe

Electromagnetic Force
Electric and magnetic forces
Forces that give objects their strength, their ability to
squeeze, stretch, or shatter
Very Large compared to the gravitational force
• Strong Nuclear Force
•Holds the particles in the nucleus together
•Strongest force (100 times stronger than electromagnetic)
• Weak Nuclear Force
•Radioactive decay of some nuclei (enough said)
Honors Physics , Pg 3
GUT
Grand Unified Theory



At one time in the history of our
universe (BIG BANG) all of the
forces could not be
differentiated due to the nature,
temperature, and pressure of
the universe. Therefore there
was only one force which ruled
the universe
Mathematical Models of the BIG
BANG theory
Based on some observations
between Electromagnetic and
the WEAK force yielding the the
combined Elecrtroweak Force
Honors Physics , Pg 4
See text: 5-1 and 5-2
Dynamics

Issac Newton (1643-1727) published Principia Mathematica
in 1687. In this work, he proposed three “laws” of motion:
Honors Physics , Pg 5
See text:pge 94
Newton’s First Law



An object subject to no external forces is at rest or moves
with a constant velocity if viewed from an inertial reference
frame.
If no forces act, there is no acceleration.
For Normal Folks- An object at rest remains at rest and an
object in motion remains in motion unless acted upon by an
external force.
The first statement can be thought of as the definition of
inertial reference frames.
An IRF is a reference frame that is not accelerating (or
rotating) with respect to the “fixed stars”.
If one IRF exists, infinitely many exist since they are
related by any arbitrary constant velocity vector!
Honors Physics , Pg 6
Is Cincinnati a good IRF?


Is Cincinnati accelerating?
YES!
Cincinnati is on the Earth.
The Earth is rotating.
What is the centripetal acceleration of Cincinnati?
4 sec,
2
T
=
1
day
=
8.64
x
10
2
v
 2 
aU 
  2R    R
R ~ RE = 6.4 x 106 meters .
T 
R




Plug this in: aU = .034 m/s2 ( ~ 1/300 g)
Close enough to 0 that we will ignore it.
Cincinnati is a pretty good IRF.
Honors Physics , Pg 7
See text: pge 93 and 4.2
Newton’s Second Law...

What is a force?
A Force is a push or a pull.
A Force has magnitude & direction (vector).
Adding forces is like adding vectors.(next chapter)
a
a
F1
F1
FNET = ma
FNET
F2
F2
Honors Physics , Pg 8
Newton’s Second Law

For any object a= FNET /m
The acceleration a of an object is proportional to the
net force FNET acting on it and inversely proportional to
the objects mass m

For any object, FNET = S F = ma. The constant of
proportionality is called “mass”, denoted m.
This is the definition of mass.
The mass of an object is a constant property of that
object, and is independent of external influences.

Force has units of [M]x[L/T2] = kg m/s2 = N (Newton)
Honors Physics , Pg 9
Newton’s Second Law...

Components of F = ma :
FX = maX
FY = maY
FZ = maZ

Suppose we know m and FX , we can solve for a
and apply the things we learned about kinematics over the
last few weeks:
v f  vi  at
d 
1
vi t 
a t2
2
Honors Physics , Pg 10
Example: Pushing a Box on Ice.

A skater is pushing a heavy box (mass m = 100 kg) across
a sheet of ice (horizontal & frictionless). He applies a force
of 50N in the x direction. If the box starts at rest, what is
it’s speed v after being pushed a distance d=10m ?
v=0
F
m
a
x
Honors Physics , Pg 11
Example: Pushing a Box on Ice.

A skater is pushing a heavy box (mass m = 100 kg) across
a sheet of ice (horizontal & frictionless). He applies a force
of 50N in the x direction. If the box starts at rest, what is
it’s speed v after being pushed a distance d=10m ?
v
F
m
a
x
d
Honors Physics , Pg 12
Example: Pushing a Box on Ice...

Start with F = ma.
a = F / m.
Recall that v22 - v12 = 2ad
So
v2
(lecture 1)
v
= 2Fd / m
2 Fd
m
v
F
m
a
x
d
Honors Physics , Pg 13
Example: Pushing a Box on Ice...
v

2 Fd
m
Plug in F = 50N, d = 10m, m = 100kg:
Find v = 3.2 m/s.
v
F
m
a
x
d
Honors Physics , Pg 14
Forces

Units of force (mks): [F] = [m][a] = kg m s-2 = N (Newton)

We will consider two kinds of forces:
Contact force:
» This is the most familiar kind.
I push on the desk.
 The ground pushes on the chair...

Action at a distance (a bit mysterious):
» Gravity
» Electromagnetic, strong & weak nuclear forces.
Honors Physics , Pg 15
Contact forces:

Objects in contact exert forces.

Convention: Fa,b means “the
force acting on a due to b”.

So Fhead,thumb means “the force on
the head due to the thumb”.
Fhead,thumb
Honors Physics , Pg 16
Gravity...

Near the earth’s surface... Fg  G
Me m
Re2
 Me 
 m  G 2   mg
 Re 

But we have just learned that: Fg = ma
This must mean that g is the “acceleration due to
gravity” that we already know!

So, the force on a mass m due to gravity near the earth’s
surface is Fg = mg where g is 9.8m/s2 “down”.
and
Me
g G 2
Re
Honors Physics , Pg 17
Example gravity problem:

What is the force of gravity exerted by the earth on a typical
physics student?
Typical student mass m = 55kg
g = 9.8 m/s2.
Fg = mg = (55 kg)x(9.8 m/s2 )
Fg = 539 N
Fg

The force that gravity exerts on any object is
called its Weight
See text example Mass and Weight.
Honors Physics , Pg 18
Newton’s Third Law:

Forces occur in pairs: FA ,B = - FB ,A.
For every “action” there is an equal and opposite “reaction”.

In the case of gravity:
m1
F12
F21
m2
F12  G
m1 m2
 F21
2
R12
R12
Honors Physics , Pg 19
Newton’s Third Law...

FA ,B = - FB ,A. is true for contact forces as well:
Fm,w
Fw,m
Ff,m
Fm,f
Honors Physics , Pg 20
Example of Bad Thinking

Since Fm,b = -Fb,m why isn’t Fnet = 0, and a = 0 ?
Fm,b
Fb,m
a ??
ice
Honors Physics , Pg 21
Example of Good Thinking

Consider only the box as the system!
Fon box = mabox = Fb,m
Free Body Diagram (next time).
Fm,b
Fb,m
abox
ice
Honors Physics , Pg 22
The Free Body Diagram

Newtons 2nd says that for an object F = ma.

Key phrase here is for an object.

So before we can apply F = ma to any given object we
isolate the forces acting on this object:
Honors Physics , Pg 23
Example

Example dynamics problem:
A box of mass m = 2kg slides on a horizontal frictionless
floor. A force Fx = 10N pushes on it in the x direction. What
is the acceleration of the box?
y
F = Fx i
a =?
m
x
Honors Physics , Pg 24
Example...

Draw a picture showing all of the forces
y
FBF
F
x
FFB
FBE
FEB
Honors Physics , Pg 25
Example...


Draw a picture showing all of the forces.
Isolate the forces acting on the block.
y
FBF
F
x
FFB = mg
Honors Physics , Pg 26
Example...



Draw a picture showing all of the forces.
Isolate the forces acting on the block.
Draw a free body diagram.
y
FBF
F
x
FFB = mg
Honors Physics , Pg 27
Example...


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Draw a picture showing all of the forces.
Isolate the forces acting on the block.
Draw a free body diagram.
Solve Newtons equations for each component.
 FX = maX
 FBF - mg = maY
FBF
y
x
F
mg
See strategy: Solving Newton’s Law Problems,
Honors Physics , Pg 28
Example...


FX = maX
 So aX = FX / m = (10 N)/(2 kg) = 5 m/s2.
FBF - mg = maY
 But aY = 0
 So FBF = mg.
N
y
FX
x
mg


The vertical component of the force
of the floor on the object (FBF ) is
often called the Normal Force (N).
Since aY = 0 , N = mg in this case.
Honors Physics , Pg 29
Example Recap
N = mg
y
FX
a X = FX / m
x
mg
Honors Physics , Pg 30
Problem: Elevator

A student of mass m stands in an elevator accelerating
upward with acceleration a. What is her apparent weight?
Apparent weight = the magnitude of the normal force of
the floor on her feet.
This is the weight a scale would read if she were
standing on one!
See example pge. 99: An Elevator
Honors Physics , Pg 31
See text: 6-1
Elevator...


First draw a Free Body Diagram
of the student:
y
Recall that FNet = ma.
ma
mg
N
See example p 99: An Elevator
Honors Physics , Pg 32
See text: 6-1
Elevator...

Add up the vectors accordingly!
FNet =
N
+
mg
y
=
ma
In this case FNet = N - mg.
(note that N and g are vectors)
 Considering the y (upward) component:
N - mg = ma

N = m (g + a)
See example p 99: An Elevator
Honors Physics , Pg 33
See text: 6-1
Elevator...
N = m (g + a)

Interesting limiting cases:
y


If a = 0, N = mg (ok).
 Like previous example.
ma
If a = -g, N = 0 (free fall).
 The vomit comet!
mg
N
See example : An Elevator
Honors Physics , Pg 34
Scales:

Springs can be calibrated to tell us the applied force.
 We can calibrate scales to read Newtons, or...
Fishing scales usually read
weight in kg or lbs.
0
2
4
6
8
Honors Physics , Pg 35
Tools: Pegs & Pulleys

Used to change the direction of forces.
An ideal massless pulley or ideal smooth peg will
change the direction of an applied force without altering
the magnitude:
F1
| F1 | = | F2 |
ideal peg
or pulley
F2
Honors Physics , Pg 36
Tools: Pegs & Pulleys

Used to change the direction of forces.
An ideal massless pulley or ideal smooth peg will
change the direction of an applied force without altering
the magnitude:
FW,S = mg
T
T = mg
m
mg
Honors Physics , Pg 37
Recap of Newton’s 3 laws of motion

Newtons 3 laws:
Law 1: An object subject to no external forces is at rest or
moves with a constant velocity if viewed from an inertial
reference frame.
Law 2: For any object, FNET = S F = ma
Law 3: Forces occur in pairs: FA ,B = - FB ,A. For every “action”
there is an equal and opposite “re-action”.

Textbook problems
Honors Physics , Pg 38