Transcript Physics 131: Lecture 6 Notes

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Physics 151: Lecture 7
Today’s Agenda
Announcements:
Homework #2 : due Fri. (Sept. 15) by 5.00 PM
Homework #3 : due Fri. (Sept. 22) by 5.00 PM
Physics learning Center (P207-C) Mon.-Fri 9 am - 5pm
Review sessions:
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Today’s topics
Newton’s Laws 1 and 2 (Chapter 5.1-4)
Physics 151: Lecture 7, Pg 1
KYNEMATICS (previous chapters):
description of motion: r(t), v(t), a(t)
DYNAMICS (next chapter):
what makes the objects move the way they
do, learn about forces and how to calculate
just what acceleration is.
Physics 151: Lecture 7, Pg 2
EXAMPLE from EVERYDAY LIFE :
A passenger sitting in the rear of a bus claims that he was
injured when the driver slammed on the brakes, causing
a suitcase to come flying toward the passenger from the
front of the bus.
•
Do you agree with this statement ?
Physics 151: Lecture 7, Pg 3
Isaac Newton (1643 - 1727)
published Principia Mathematica in 1687.
Physics 151: Lecture 7, Pg 4
See text: Chapter 5
Dynamics
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Isaac Newton (1643 - 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.)
Physics 151: Lecture 7, Pg 5
See text: 5-1
Force
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We have an idea of what a force is from everyday life.
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Physicist must be precise.
A force is that which causes a body to accelerate.
(See Newton’s Second Law)
Examples
Contact
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Non-Contact
On a microscopic level, all forces are non-contact
Question: What force causes an automobile to move ?
Physics 151: Lecture 7, Pg 6
See text: 5-3
Mass
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We have an idea of what mass is from everyday life.
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Physicist must be precise.
mass (for this class) is a quantity that specifies how much
inertia an object has.
(See Newton’s First Law)
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Mass is an inherent property of an object.
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Mass and weight are different quantities.
weight is a force.
Animation
Physics 151: Lecture 7, Pg 7
See text: 5-2
Newton’s First Law
An object subject to no external forces moves with a constant
velocity if viewed from an inertial reference frame.
If no forces act, there is no acceleration.
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The above 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!
Physics 151: Lecture 7, Pg 8
Is Storrs a good IRF?
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Is Storrs accelerating?
YES!
Storrs is on the Earth.
The Earth is rotating.
What is the centripetal acceleration of Storrs?
2
v2
 2 
aS 
  2R  
 R
R
T 
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T = 1 day = 8.64 x 104 sec,
R ~ RE = 6.4 x 106 meters .
Plug this in: aS = .034 m/s2 ( ~ 1/300 g)
Close enough to 0 that we will ignore it.
Storrs is a pretty good IRF.
Physics 151: Lecture 7, Pg 9
See text: 5-2
Question / Newton’s First Law
What is wrong with this statement, "Because the car is at
rest, there are no forces acting on it” ?
Mistake one: The car might be momentarily at rest, in the process of
(suddenly) reversing forward into the backward motion. In this case,
the forces on it add to a (large) backward resultant.
Mistake two: There are no cars in interstellar space. If the car is remaining
at rest, there are some large forces on it, including its weight and some
force or forces of support.
Mistake three: The statement reverses cause and effect.
Physics 151: Lecture 7, Pg 10
See text: 5-4
Newton’s Second Law
The acceleration of an object is directly proportional to the
net force acting upon it. The constant of proportionality is
the mass.
 
F  F
NET
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
 ma
Units
The units of force are kg m/s2 = Newtons (N)
The English unit of force is Pounds (lbs)
Physics 151: Lecture 7, Pg 11
Lecture 7, ACT 1
Newton’s Second Law
I push with a force of 2 Newtons on a cart that is initially at
rest on an air table with no air. I push for a second. Because
there is no air, the cart stops after I finish pushing. It has
traveled a certain distance (before removing the force).
F= 2N
Cart
Air Track
For a second shot, I push just as hard but keep pushing for
2 seconds. The distance the cart moves the second time
versus the first is (before removing the force) :
A) 8 x as long
B) 4 x as long
C) Same
D) 2 as long
E) can’t determine
Physics 151: Lecture 7, Pg 12
Lecture 7, ACT 1
F= 2N
t1 =1s, v1
to , vo =
0
Cart
Dx1
t2 =2s, v2
Cart
Cart
Air Track
Dx2
A) 8 x as long
B) 4 x as long
C) Same
D) 2 as long
E) can’t determine
B) 4 x as long
Physics 151: Lecture 7, Pg 13
Lecture 7, ACT 1a
What is the distances traveled after Fapp
removed in the two cases:
(i) after applying Fapp for 1 s
vs.
(ii) after aplying Fapp for 2 s ?
Fapp
Cart
Air Track
Cart
Cart
at rest
A) 8 x as long
B) 4 x as long
D) 2 as long
E) can’t determine
C) Same
Physics 151: Lecture 7, Pg 14
Lecture 7, ACT 1a
What is the distances traveled after Fapp removed ?
Fapp= 2N
Cart
Air Track
Fapp = 0
to , vo1
Ftot = 0 ?otherwise v1=v01, cart keeps moving !
t1 , v1 =
0
Cart
Cart
at rest
Dx1
Fapp= 2N
Fapp = 0
to , vo2
Ftot = 0 ?
Cart
Cart
Air Track
t2 , v2 =
0
Cart
Dx2
at rest
B) 4 x as long
Physics 151: Lecture 7, Pg 15
Lecture 7, ACT 2
Newton’s Second Law
A constant force is applied to a body that is
F
already moving. The force is directed at an
60o
angle of 60 degrees to the direction of the
vo
body’s velocity. What is most likely to happen is
that:
A) the body will stop moving.
B) the body will move in the direction of the force.
C) the body’s velocity will increase in magnitude but
not change direction.
D) the body will gradually change direction more
and more toward that of the force while speeding up.
E) the body will first stop moving and then move in
the direction of the force.
Physics 151: Lecture 7, Pg 16
See text: 5-6
Newton’s Third Law:
If object 1 exerts a force on object 2 (F1,2 ) then object 2 exerts an
equal and opposite force on object 1 (F2,1)
F1,2 = -F2,1
For every “action” there is an equal and opposite “reaction”
This is among the most abused and misunderstood
concepts in physics, along with Einstein’s ideas of
relative motion (inertial reference frames) and
Heisenberg’s uncertainty principle.
Physics 151: Lecture 7, Pg 17
See text: 5-6
Newton's Third Law...
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"When the locomotive in
Figure on the right broke
through the wall of the train
station, the force exerted by
the locomotive on the wall was
greater than the force the wall
could exert on the locomotive.”
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Is this statement true or in
need of correction?
Physics 151: Lecture 7, Pg 18
An Example
Consider the forces on an object undergoing
projectile motion
FB,E = - mB g
FE,B = mB g
Physics 151: Lecture 7, Pg 19
Lecture 7, ACT 3a
Newton’s Third Law
A fly gets smushed onto the windshield of a speeding bus.
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The force exerted by the bus on the fly is,
A) greater than
B) the same as
C) less than
that exerted by the fly on the bus.
Physics 151: Lecture 7, Pg 20
Lecture 7, ACT 3b
Newton’s Third Law
A fly gets smushed onto the windshield of a speeding bus.
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The acceleration due to this collision of the bus is,
A) greater than
B) the same as
C) less than
that of the fly.
Physics 151: Lecture 7, Pg 21
See text: 5-6
Newton's Third Law...
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FA ,B = - FB ,A an example,
Fm,w
Fw,m
Ff,m
Fm,f
Physics 151: Lecture 7, Pg 22
Example of Bad Thinking
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Since Fm,b = -Fb,m why isn’t Fnet = 0, and a = 0 ?
Fm,b
Fb,m
a ??
ice
Physics 151: Lecture 7, Pg 23
Example of Good Thinking
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Consider only the box as the system!
Free Body Diagram
Fm,b
Fb,m
ice
Physics 151: Lecture 7, Pg 24
Example of Good Thinking
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Consider only the box as the system!
Free Body Diagram
abox = Fb,m/mbox
Fb,m
abox
FN
Fg
Physics 151: Lecture 7, Pg 25
Normal Forces
Certain forces act to keep an object in place.
These have what ever force needed to balance all others
(until a breaking point).
FB,T
FT,B
Physics 151: Lecture 7, Pg 26
Force Pairs
Newton’s 3rd law concerns force pairs. Two members of
a force pair cannot act on the same object.
Don’t confuse gravity (the force of the earth on an object)
and normal forces. It’s an extra part of the problem.
FB,T
FB,E = -mg
FT,B
FE,B = mg
Physics 151: Lecture 7, Pg 27
An Example
Consider the following two cases
Physics 151: Lecture 7, Pg 28
An Example
The Free Body Diagrams
mg
FB,T= N
mg
Ball Falls
For Static Situation
N = mg
Physics 151: Lecture 7, Pg 29
An Example
The action/reaction pair forces
FB,E = -mg
FB,T= N
FT,B= -N
FE,B = mg
FB,E = -mg
FE,B = mg
Physics 151: Lecture 7, Pg 30
Recap for today:
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Definition of force and mass (Ch. 5.1 and 5.3)
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Newton’s Laws
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Reading assignment for Monday
Newton’s Laws 2 and 3
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Homework #2 : due Fri. (Sept. 15) by 5.00 PM
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Homework #3 : due Fri. (Sept. 22) by 5.00 PM
Physics 151: Lecture 7, Pg 31