Physics 121,Lecture 2,Pg 1
Physics 121,Sections 9,10,11,and 12
Lecture 2
Announcements
? Lectures available on the web (short version)
? For over-enrollment please go to the Physics office P107
? Laboratory sessions start next week
? Go to my web site www.phys.uconn.edu/~rcote
? Syllabus + homeworks + lectures,etc.
? WebAssign,ready Friday night …
? go to www.webassign.net and log in
? username,first letter of first name plus last name
? e.g,John Fernando Lachance,jlachance
? institution,uconn
? password,your PeopleSoft ID # (with the initial,0”)
Physics 121,Lecture 2,Pg 2
Physics 121,Sections 9,10,11,and 12
Lecture 2
Today’s Topics:
? Chapter 1:
? Units + significant digits
? Strategy to solve problems
? Chapter 2,Forces and vectors
? Types of forces
?Newton’s Laws of motion
? Net force and vector addition
? Contact force and tension
Physics 121,Lecture 2,Pg 3
Significant Figures
? The number of digits that matter in a measurement or
calculation,
? When writing a number,all non-zero digits are significant.
? Zeros may or may not be significant.
?those used to position the decimal point are not
significant.
?those used to position powers of ten ordinals may or
may not be significant.
? in scientific notation all digits are significant
? Examples:
?2 1 sig fig
?40 ambiguous,could be 1 or 2 sig figs
?4.0 x 101 2 sig figs
?0.0031 2 sig figs
?3.03 3 sig figs
Physics 121,Lecture 2,Pg 4
Significant Figures
? When multiplying or dividing,the answer should have the
same number of significant figures as the least accurate of
the quantities in the calculation.
? When adding or subtracting,the number of digits to the
right of the decimal point should equal that of the term in
the sum or difference that has the smallest number of digits
to the right of the decimal point.
? Examples:
?2 x 3.1 = 6
?3.1 + 0.004 = 3.1
?4.0 x 101 ? 2.04 x 102 = 1.6 X 10-1
Physics 121,Lecture 2,Pg 5
Adding or Subtracting
? When numbers are added or subtracted,the
number of decimal places in the result equal the
smallest number of decimal places of any term in
the sum.
x = 123; y = 5.35
123.xxx
+ 5.35x
128.xxx
Physics 121,Lecture 2,Pg 6
Order-of Magnitude Calculations
? Sometimes it is necessary to know a quantity
only within a factor of 10
? This is know as an order of magnitude
? For example that is the total mass of everyone in
this class?
mass of a person m ~ 75 kg
Number of people n ~ 75
mTotal ~ 75 ′ 75 kg = 5625 kg ~ 6 ′ 103 kg
Physics 121,Lecture 2,Pg 7
Problem Solution Method:
Five Steps:
1) Focus the Problem
- draw a picture – what are we asking for?
2) Describe the physics
- what physics ideas are applicable
- what are the relevant variables known and unknown
3) Plan the solution
- what are the relevant physics equations
4) Execute the plan
- solve in terms of variables
- solve in terms of numbers
5) Evaluate the answer
- are the dimensions and units correct?
- do the numbers make sense?
Physics 121,Lecture 2,Pg 8
Chap.2,Forces and vectors
? In classical mechanics
?Need to study interactions between objects
?Described by forces
? We have an idea of what a force is from everyday life.
? Physicist must be precise.
?A force is that which causes a body to accelerate.
(See Newton’s Second Law)
?A Force is a push or a pull.
?A Force has magnitude & direction (vector).
F
Physics 121,Lecture 2,Pg 9
Fundamental Forces
? Example of Forces
?Hooke’s law for ideal spring,F = -k x
?Units of a force are 1 N= 1 kg m/s2
? Fundamental Forces
?Gravity (more later)
?For motion of planets,etc.
?Strong and weak nuclear forces (not here !)
?Explains behavior of nucleus in atoms
?Electromagnetic force (next semester in PHY122)
?Relevant for electric systems,chemical properties,etc.
Physics 121,Lecture 2,Pg 10
The Laws of Motion
? Isaac Newton (1642 - 1727) published Principia Mathematica
in 1687,In this work,he proposed three,laws” of motion:
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 = ??F = ma
Law 3,Forces occur in pairs,FA,B = - FB,A
(For every action there is an equal and opposite reaction.)
More in following chapters
Physics 121,Lecture 2,Pg 11
Net Force,adding vectors
? A Force has magnitude & direction (vector).
?Adding forces is like adding vectors (more next chapter)
? The net force is obtained by adding all forces
? Adding collinear vectors
?2 vectors in the same direction
?Magnitude is the sum of both magnitudes
?Direction remains the same
?2 vectors in opposite direction
?Magnitude is the absolute value of the difference of
both magnitudes
?Direction is the same as the longest vector
?Sum of 2 vectors is zero if they have opposite directions
and same magnitude
500 N
200 N 300 N
100 N
200 N
300 N
500 N
500 N
Physics 121,Lecture 2,Pg 12
The Free Body Diagram
? Newton’s 2nd Law 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:
?We obtain the FBD
Physics 121,Lecture 2,Pg 13
FBD,an example
? A mass is suspended to
the ceiling with a rope
? The FBD of the mass is
simply given by all forces
on acting on it
mg
T
m
mg
T
m
Physics 121,Lecture 2,Pg 14
Internal and External Forces
? Consider a system
?E.g,a baseball
? All atoms/particles inside interact with each other
?Atom 1 acts on atom 2 with F21
?But atom 2 also acts on atom 1 with F12
?Newton’s 3rd law says that F12 = - F21
?So the net force is zero … same for all pairs of particles
?All interanl forces add up to zero
? Only external forces remains
?E.g.,gravity or the contact of a stick !
? We will deal with external forces mostly
Physics 121,Lecture 2,Pg 15
Force …
? We will consider two kinds of forces
? Field Forces (Non-Contact),(action through,empty” space)
?Moon and Earth
?Gravity
?Electricity
? Contact force,(physical contact between objects)
?This is the most familiar kind.
?Kicking a ball
?I push on the desk.
?The ground pushes on the chair...
? On a microscopic level,all forces are non-contact
Physics 121,Lecture 2,Pg 16
Action at a distance
? Gravity:
next
Physics 121,Lecture 2,Pg 17
Newton’s Law of Universal Gravitation
? Every particle in the Universe attracts every other
particle with a force that is directly proportional the
product of their masses and inversely proportional to
the square of the distance between them.
? Constant of Universal gravitation:
2
21
r
mmGF ?
221110673.6 kgmNG ??? ?
m1
m2
r12
F21 F12
Physics 121,Lecture 2,Pg 18
Weight W
? Near the surface of the Earth
?r ≈ RE (Earth radius)
?So the gravitation force between an object of
mass m and the Earth is simply
? With the numbers for Earth:
??
F ? W ? G M E mR
E
2 ? m G
M E
R E2
??
????
??
???? ? mg
??
g ? G
M E
R E2
?
6, 673 ? 10 ? 11 N ? m 2 / kg 2 ? ( 5, 98 ? 10 24 kg )
( 6, 37 ? 10 6 m ) 2
? 9, 8 N / kg
Physics 121,Lecture 2,Pg 19
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
next
Physics 121,Lecture 2,Pg 20
Examples of Contact Forces
? Normal forces
?Forces due to a surface pushing on an object
?perpendicular to the surface
? Box on a table
? Box on inclined slope
next
FX
N = mg
mg
FX
N = mg
mg
FBD
?
m a
mg
N
mg sin ?
mg cos ?
?
Physics 121,Lecture 2,Pg 21
Examples of Contact Forces
? Friction
? What does it do?
?It opposes motion!
? How do we characterize this in terms we have
learned?
?Friction results in a force in a direction
opposite to the direction of motion!
ma
FAPPLIED
fFRICTION mg
N
i
j
Physics 121,Lecture 2,Pg 22
Friction...
? Friction is caused by the,microscopic”
interactions between the two surfaces:
Physics 121,Lecture 2,Pg 23
Friction...
? Force of friction acts to oppose motion:
?Parallel to surface.
?Perpendicular to Normal force.
ma
F
fF mg
N
i
j
Physics 121,Lecture 2,Pg 24
Model for Sliding Friction
? The direction of the frictional force vector is perpendicular to the
normal force vector N.
? The magnitude of the frictional force vector |fF| is proportional to
the magnitude of the normal force |N |.
? |fF| = ?K | N | ( = ?K?|?mg | in the previous example)
?The,heavier” something is,the greater the friction will
be...makes sense!
? The constant ?K is called the,coefficient of kinetic friction”.
Physics 121,Lecture 2,Pg 25
Tools,Ropes & Strings
? Can be used to pull from a distance.
? Tension (T) at a certain position in a rope is the
magnitude of the force acting across a cross-
section of the rope at that position.
?The force you would feel if you cut the rope
and grabbed the ends.
?An action-reaction pair
(more later about 3rd law)
cut
T
T
T
Physics 121,Lecture 2,Pg 26
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
ideal peg
or pulley
F2
| F1 | = | F2 |
Physics 121,Lecture 2,Pg 27
Recap of today’s lecture
? Finished Chapter 1
? Started Chapter 2,Forces and vectors
?Types of forces
?Newton’s Laws of motion
?Net force and vector addition
?Contact force and tension
? Homework 1 on WebAssign
? Accounts ready Friday evening
Physics 121,Sections 9,10,11,and 12
Lecture 2
Announcements
? Lectures available on the web (short version)
? For over-enrollment please go to the Physics office P107
? Laboratory sessions start next week
? Go to my web site www.phys.uconn.edu/~rcote
? Syllabus + homeworks + lectures,etc.
? WebAssign,ready Friday night …
? go to www.webassign.net and log in
? username,first letter of first name plus last name
? e.g,John Fernando Lachance,jlachance
? institution,uconn
? password,your PeopleSoft ID # (with the initial,0”)
Physics 121,Lecture 2,Pg 2
Physics 121,Sections 9,10,11,and 12
Lecture 2
Today’s Topics:
? Chapter 1:
? Units + significant digits
? Strategy to solve problems
? Chapter 2,Forces and vectors
? Types of forces
?Newton’s Laws of motion
? Net force and vector addition
? Contact force and tension
Physics 121,Lecture 2,Pg 3
Significant Figures
? The number of digits that matter in a measurement or
calculation,
? When writing a number,all non-zero digits are significant.
? Zeros may or may not be significant.
?those used to position the decimal point are not
significant.
?those used to position powers of ten ordinals may or
may not be significant.
? in scientific notation all digits are significant
? Examples:
?2 1 sig fig
?40 ambiguous,could be 1 or 2 sig figs
?4.0 x 101 2 sig figs
?0.0031 2 sig figs
?3.03 3 sig figs
Physics 121,Lecture 2,Pg 4
Significant Figures
? When multiplying or dividing,the answer should have the
same number of significant figures as the least accurate of
the quantities in the calculation.
? When adding or subtracting,the number of digits to the
right of the decimal point should equal that of the term in
the sum or difference that has the smallest number of digits
to the right of the decimal point.
? Examples:
?2 x 3.1 = 6
?3.1 + 0.004 = 3.1
?4.0 x 101 ? 2.04 x 102 = 1.6 X 10-1
Physics 121,Lecture 2,Pg 5
Adding or Subtracting
? When numbers are added or subtracted,the
number of decimal places in the result equal the
smallest number of decimal places of any term in
the sum.
x = 123; y = 5.35
123.xxx
+ 5.35x
128.xxx
Physics 121,Lecture 2,Pg 6
Order-of Magnitude Calculations
? Sometimes it is necessary to know a quantity
only within a factor of 10
? This is know as an order of magnitude
? For example that is the total mass of everyone in
this class?
mass of a person m ~ 75 kg
Number of people n ~ 75
mTotal ~ 75 ′ 75 kg = 5625 kg ~ 6 ′ 103 kg
Physics 121,Lecture 2,Pg 7
Problem Solution Method:
Five Steps:
1) Focus the Problem
- draw a picture – what are we asking for?
2) Describe the physics
- what physics ideas are applicable
- what are the relevant variables known and unknown
3) Plan the solution
- what are the relevant physics equations
4) Execute the plan
- solve in terms of variables
- solve in terms of numbers
5) Evaluate the answer
- are the dimensions and units correct?
- do the numbers make sense?
Physics 121,Lecture 2,Pg 8
Chap.2,Forces and vectors
? In classical mechanics
?Need to study interactions between objects
?Described by forces
? We have an idea of what a force is from everyday life.
? Physicist must be precise.
?A force is that which causes a body to accelerate.
(See Newton’s Second Law)
?A Force is a push or a pull.
?A Force has magnitude & direction (vector).
F
Physics 121,Lecture 2,Pg 9
Fundamental Forces
? Example of Forces
?Hooke’s law for ideal spring,F = -k x
?Units of a force are 1 N= 1 kg m/s2
? Fundamental Forces
?Gravity (more later)
?For motion of planets,etc.
?Strong and weak nuclear forces (not here !)
?Explains behavior of nucleus in atoms
?Electromagnetic force (next semester in PHY122)
?Relevant for electric systems,chemical properties,etc.
Physics 121,Lecture 2,Pg 10
The Laws of Motion
? Isaac Newton (1642 - 1727) published Principia Mathematica
in 1687,In this work,he proposed three,laws” of motion:
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 = ??F = ma
Law 3,Forces occur in pairs,FA,B = - FB,A
(For every action there is an equal and opposite reaction.)
More in following chapters
Physics 121,Lecture 2,Pg 11
Net Force,adding vectors
? A Force has magnitude & direction (vector).
?Adding forces is like adding vectors (more next chapter)
? The net force is obtained by adding all forces
? Adding collinear vectors
?2 vectors in the same direction
?Magnitude is the sum of both magnitudes
?Direction remains the same
?2 vectors in opposite direction
?Magnitude is the absolute value of the difference of
both magnitudes
?Direction is the same as the longest vector
?Sum of 2 vectors is zero if they have opposite directions
and same magnitude
500 N
200 N 300 N
100 N
200 N
300 N
500 N
500 N
Physics 121,Lecture 2,Pg 12
The Free Body Diagram
? Newton’s 2nd Law 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:
?We obtain the FBD
Physics 121,Lecture 2,Pg 13
FBD,an example
? A mass is suspended to
the ceiling with a rope
? The FBD of the mass is
simply given by all forces
on acting on it
mg
T
m
mg
T
m
Physics 121,Lecture 2,Pg 14
Internal and External Forces
? Consider a system
?E.g,a baseball
? All atoms/particles inside interact with each other
?Atom 1 acts on atom 2 with F21
?But atom 2 also acts on atom 1 with F12
?Newton’s 3rd law says that F12 = - F21
?So the net force is zero … same for all pairs of particles
?All interanl forces add up to zero
? Only external forces remains
?E.g.,gravity or the contact of a stick !
? We will deal with external forces mostly
Physics 121,Lecture 2,Pg 15
Force …
? We will consider two kinds of forces
? Field Forces (Non-Contact),(action through,empty” space)
?Moon and Earth
?Gravity
?Electricity
? Contact force,(physical contact between objects)
?This is the most familiar kind.
?Kicking a ball
?I push on the desk.
?The ground pushes on the chair...
? On a microscopic level,all forces are non-contact
Physics 121,Lecture 2,Pg 16
Action at a distance
? Gravity:
next
Physics 121,Lecture 2,Pg 17
Newton’s Law of Universal Gravitation
? Every particle in the Universe attracts every other
particle with a force that is directly proportional the
product of their masses and inversely proportional to
the square of the distance between them.
? Constant of Universal gravitation:
2
21
r
mmGF ?
221110673.6 kgmNG ??? ?
m1
m2
r12
F21 F12
Physics 121,Lecture 2,Pg 18
Weight W
? Near the surface of the Earth
?r ≈ RE (Earth radius)
?So the gravitation force between an object of
mass m and the Earth is simply
? With the numbers for Earth:
??
F ? W ? G M E mR
E
2 ? m G
M E
R E2
??
????
??
???? ? mg
??
g ? G
M E
R E2
?
6, 673 ? 10 ? 11 N ? m 2 / kg 2 ? ( 5, 98 ? 10 24 kg )
( 6, 37 ? 10 6 m ) 2
? 9, 8 N / kg
Physics 121,Lecture 2,Pg 19
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
next
Physics 121,Lecture 2,Pg 20
Examples of Contact Forces
? Normal forces
?Forces due to a surface pushing on an object
?perpendicular to the surface
? Box on a table
? Box on inclined slope
next
FX
N = mg
mg
FX
N = mg
mg
FBD
?
m a
mg
N
mg sin ?
mg cos ?
?
Physics 121,Lecture 2,Pg 21
Examples of Contact Forces
? Friction
? What does it do?
?It opposes motion!
? How do we characterize this in terms we have
learned?
?Friction results in a force in a direction
opposite to the direction of motion!
ma
FAPPLIED
fFRICTION mg
N
i
j
Physics 121,Lecture 2,Pg 22
Friction...
? Friction is caused by the,microscopic”
interactions between the two surfaces:
Physics 121,Lecture 2,Pg 23
Friction...
? Force of friction acts to oppose motion:
?Parallel to surface.
?Perpendicular to Normal force.
ma
F
fF mg
N
i
j
Physics 121,Lecture 2,Pg 24
Model for Sliding Friction
? The direction of the frictional force vector is perpendicular to the
normal force vector N.
? The magnitude of the frictional force vector |fF| is proportional to
the magnitude of the normal force |N |.
? |fF| = ?K | N | ( = ?K?|?mg | in the previous example)
?The,heavier” something is,the greater the friction will
be...makes sense!
? The constant ?K is called the,coefficient of kinetic friction”.
Physics 121,Lecture 2,Pg 25
Tools,Ropes & Strings
? Can be used to pull from a distance.
? Tension (T) at a certain position in a rope is the
magnitude of the force acting across a cross-
section of the rope at that position.
?The force you would feel if you cut the rope
and grabbed the ends.
?An action-reaction pair
(more later about 3rd law)
cut
T
T
T
Physics 121,Lecture 2,Pg 26
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
ideal peg
or pulley
F2
| F1 | = | F2 |
Physics 121,Lecture 2,Pg 27
Recap of today’s lecture
? Finished Chapter 1
? Started Chapter 2,Forces and vectors
?Types of forces
?Newton’s Laws of motion
?Net force and vector addition
?Contact force and tension
? Homework 1 on WebAssign
? Accounts ready Friday evening
