In reference to Newton’s 3rd Law
"Professor Goddard does not know the relation between action and
reaction and the need to have something better than a vacuum
against which to react. He seems to lack the basic knowledge ladled
out daily in high schools."
New York Times editorial, 1921,
about Robert Goddard's revolutionary
rocket work.
"Correction: It is now definitely
established that a rocket can
function in a vacuum.
The 'Times' regrets the error."
New York Times editorial, July 1969.
Physics 207: Lecture 7, Pg 1
Lecture 7

Goals:
 Identify the types of forces
 Use a Free Body Diagram to solve 1D and 2D
problems with forces in equilibrium and non-equilibrium
(i.e., acceleration) using Newton’ 1st and 2nd laws.
 Distinguish static and kinetic coefficients of friction
 Differentiate between Newton’s 1st, 2nd and 3rd Laws
Assignment: HW4, (Chapters 6 & 7)
Read Chapter 7
1st Exam Thursday, Oct. 7 from 7:15-8:45 PM Chapters 1-7
Physics 207: Lecture 7, Pg 2
Example Non-contact Forces
All objects having mass exhibit a mutually attractive force
(i.e., gravity) that is distance dependent
At the Earth’s surface this variation is small so little “g” (the
associated acceleration) is typically set to 9.80 or 10. m/s2
FB,G
Physics 207: Lecture 7, Pg 3
Contact (i.e., 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
Physics 207: Lecture 7, Pg 4
No net force  No acceleration
 

 F  Fnet  ma  0
 Fx  0
 Fy  0
y
(Force vectors are not always
drawn at contact points)
FB,T Normal force is always  to a surface
 Fy  mg  N  0
FB,G
N  mg
Physics 207: Lecture 7, Pg 5
No net force  No acceleration
 

 F  Fnet  ma  0
If zero velocity then “static equilibrium”
 If non-zero velocity then “dynamic equilibrium”


Forces are vectors
 
   
 F  Fnet  ma  F1  F2  F3  
Physics 207: Lecture 7, Pg 6
High Tension
A crane is lowering a load of bricks on a pallet. A
plot of the position vs. time is
 There are no frictional forces
 Compare the tension in the
crane’s wire (T) at the point
it contacts the pallet to the
weight (W) of the load (bricks
+ pallet)
Time
Height

A: T > W B: T = W C: T< W D: don’t know
Physics 207: Lecture 7, Pg 7
Analyzing Forces: Free Body Diagram
A heavy sign is hung between two poles by a rope at
each corner extending to the poles.
Eat at Mickey’s
A hanging sign is an example of static equilibrium
(depends on observer)
What are the forces on the sign and how are they
related if the sign is stationary (or moving with
constant velocity) in an inertial reference frame ?
Physics 207: Lecture 7, Pg 8
Free Body Diagram
Step one: Define the system
T2
T1
q2
q1
Eat at Mickey’s
mg
T2
T1
q1
q2
mg
Step two: Sketch in force vectors
Step three: Apply Newton’s 2nd Law
(Resolve vectors into appropriate components)
Physics 207: Lecture 7, Pg 9
Free Body Diagram
T1
T2
q2
q1
Eat at Bucky’s
mg
Vertical :
y-direction
Horizontal :
x-direction
0 = -mg + T1 sinq1 + T2 sinq2
0 = -T1 cosq1 + T2 cosq2
Physics 207: Lecture 7, Pg 10
Scale Problem

You are given a 1.0 kg mass and you hang it
directly on a fish scale and it reads 10 N (g is
10 m/s2).
10 N
1.0 kg




Now you use this mass in a second
experiment in which the 1.0 kg mass hangs
from a massless string passing over a
massless, frictionless pulley and is anchored
to the floor. The pulley is attached to the fish
scale.
What does the string do?
What does the pulley do?
What does the scale now read?
?
1.0 kg
Physics 207: Lecture 7, Pg 11
Pushing and Pulling Forces


String or ropes are examples of
things that can pull
You arm is an example of an object
that can push or push
Physics 207: Lecture 7, Pg 12
Examples of Contact Forces:
A spring can push
Physics 207: Lecture 7, Pg 13
A spring can pull
Physics 207: Lecture 7, Pg 14
Ropes provide tension (a pull)
In physics we often use a “massless” rope with opposing
tensions of equal magnitude
Physics 207: Lecture 7, Pg 15
Moving forces around
Massless strings: Translate forces and reverse their
direction but do not change their magnitude
(we really need Newton’s 3rd of action/reaction to justify)

string
T1

-T1
Massless, frictionless pulleys: Reorient force direction
but do not change their magnitude
T2
T1
-T1
| T1 | = | -T1 | = | T2 | = | T2 |
-T2
Physics 207: Lecture 7, Pg 16
Scale Problem

You are given a 1.0 kg mass and you hang it
directly on a fish scale and it reads 10 N (g is
10 m/s2).
10 N
1.0 kg


Now you use this mass in a second
experiment in which the 1.0 kg mass hangs
from a massless string passing over a
massless, frictionless pulley and is anchored
to the floor. The pulley is attached to the fish
scale.
What force does the fish scale now read?
?
1.0 kg
Physics 207: Lecture 7, Pg 17
What will the scale read?
A 5N
B 10 N
C 15 N
D 20 N
E something else
Physics 207: Lecture 7, Pg 18
Scale Problem


Step 1: Identify the system(s).
In this case it is probably best to treat each
object as a distinct element and draw three
force body diagrams.
 One around the scale
 One around the massless pulley (even
though massless we can treat is as an
“object”)
 One around the hanging mass
Step 2: Draw the three FBGs. (Because this
is a now a one-dimensional problem we
need only consider forces in the y-direction.)
?
1.0 kg
Physics 207: Lecture 7, Pg 19
Scale Problem
3:
T”
T’
1:
2:
T
?
W

1.0 kg
-T ’
S Fy = 0 in all cases
-T
-T
?
-mg
1: 0 = -2T + T ’
2: 0 = T – mg  T = mg
3: 0 = T” – W – T ’ (not useful here)
 Substituting 2 into 1 yields T ’ = 2mg = 20 N
(We start with 10 N but end with 20 N)
1.0 kg
Physics 207: Lecture 7, Pg 20
A “special” contact force: Friction


What does it do?
 It opposes motion (velocity, actual or that which
would occur if friction were absent!)
How do we characterize this in terms we have learned?
 Friction results in a force in a direction opposite to
the direction of motion (actual or, if static, then
“inferred”)!
j
N
FAPPLIED
fFRICTION
ma
i
mg
Physics 207: Lecture 7, Pg 21
Friction...

Friction is caused by the “microscopic” interactions between
the two surfaces:
Physics 207: Lecture 7, Pg 22
Static and Kinetic Friction

Friction exists between objects and its behavior has been
modeled.
At Static Equilibrium: A block, mass m, with a horizontal force F
applied,
Direction: A force vector  to the normal force vector N and
the vector is opposite to the direction of acceleration if m were
0.
Magnitude: f is proportional to the applied forces such that
fs ≤ ms N
ms called the “coefficient of static friction”
Physics 207: Lecture 7, Pg 23
Friction...

Force of friction acts to oppose motion:
 Parallel to a surface
 Perpendicular to a Normal force.
j
N
F
ma
fF
i
mg
Physics 207: Lecture 7, Pg 24
Sliding Friction: Quantitatively

Direction: A force vector  to the normal force vector N and
the vector is opposite to the velocity.

Magnitude: fk is proportional to the magnitude of N
 fk = mk N
( = mK mg in the previous example)

The constant mk is called the “coefficient of kinetic friction”

Logic dictates that
mS > mK
for any system
Physics 207: Lecture 7, Pg 25
Static Friction with a bicycle wheel
You are pedaling hard
and the bicycle is
speeding up.
What is the direction of
the frictional force?

You are breaking and
the bicycle is slowing
down
What is the direction of
the frictional force?

Physics 207: Lecture 7, Pg 28
Recap
 Assignment:
Soon….HW4 (Chapters 6 & 7, due 10/5)
 Read through first half of Chapter 7
Physics 207: Lecture 7, Pg 30