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Lecture 7
 Goals:
 Analyze motion in different frames of reference (nonaccelerated)
 Identify the types of forces
 Distinguish Newton’s Three Laws of Motion
 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.
1st Exam Monday, Feb. 20 7:15-8:45 PM Chapters 1-4
2103 Chamberlin Hall (M. Tobin, A. Chehade, T. Sinensky)
Sections: 604, 605, 606, 609, 610, 611
Room Change B102 Van Vleck (E. Poppenheimer, Z. Dong, D. Crow)
Sections: 602, 603, 607, 608, 612
Physics 201: Lecture 7, Pg 1
Relative Motion and reference frames?
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
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If you are moving relative to another person do you see the
same physics?
Two observers moving relative to each other generally do not
agree on the outcome of an experiment (path)
For example, observers A and B below see different paths for
the ball
Physics 201: Lecture 7, Pg 2
Relative motion and frames of reference




Reference frame S is stationary (with origin O)
Reference frame S’ is moving at vo (with origin O ’)
This also means that S moves at – vo relative to S’
Define time t = 0 as that time when the origins coincide
Physics 201: Lecture 7, Pg 3
Relative motion and frames of reference


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Reference frame S is stationary, A is stationary
Reference frame S’ is moving at vo
A moves at – vo relative to an observer in S’
Define time t = 0 as that time (O & O’ origins coincide)
t later
t=0
-v0
-v0 t
A
A
r’= r-v0t
r
O,O’
r
O’
Physics 201: Lecture 7, Pg 4
Relative Velocity




The positions, r and r’, as seen from the two reference frames
are related through the velocity, vo, where vo is velocity of the
r’ reference frame relative to r

r’ = r – vo t
The derivative of the position equation will give the velocity
equation

v’ = v – vo
These are called the Galilean transformation equations
Reference frames that move with “constant velocity” (i.e., at
constant speed in a straight line) are defined to be inertial
reference frames (IRF); anyone in an IRF sees the same
acceleration of a particle moving along a trajectory.

a’ = a
(dvo / dt = 0)
Physics 201: Lecture 7, Pg 5
x and y motions are independent


Example: Man on cart tosses a ball straight up in the air.
You can view the trajectory from two reference frames:
Reference frame
on the moving cart.
Reference frame
on the ground.
y(t) motion governed by
1) a = -g y
2) vy = v0y – g t
3) y = y0 + v0y – g t2/2
x motion: x’= 0
x = vxt
Physics 201: Lecture 7, Pg 6
Exercise Relative Trajectories: Monkey and Hunter
All free objects, if acted on by gravity, accelerate similarly.
A hunter sees a monkey in a tree, aims his gun at the
monkey and fires. At the same instant the monkey lets
go.
Does the bullet …
A.
B.
C.
go over the
monkey.
hit the monkey.
go under the
monkey.
Physics 201: Lecture 7, Pg 7
Schematic of the problem




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xB(t) = d = v0 cos q t
yB(t) = hf = v0 sin q t – ½ g t2
xM(t) = d
yM(t) = h – ½ g t2
Does yM(t) = yB(t) = hf?
(x,y) = (d,h)
Monkey
Does anyone want to change their answer ?
What happens if g=0 ?
How does introducing g change things?
g
v0
q
Bullet
(x0,y0) = (0 ,0)
(vx,vy) = (v0 cos q, v0 sin q)
Physics 201: Lecture 7, Pg 8
hf
Exercise, Relative Motion

You are swimming across a 50. m wide river in which the
current moves at 1.0 m/s with respect to the shore. Your
swimming speed is 2.0 m/s with respect to the water.
You swim perfectly perpendicular to the current,
how fast do you appear to be moving to an observer on shore?

v  1 m/s î  2 m/s ĵ
2 m/s
50m
1 m/s

2
2
| v |  1.0  2.0 m/s  2.2 m/s
Physics 201: Lecture 7, Pg 9
Chap 5
What causes motion?
(actually changes in motion)
What kinds of forces are there ?
How are forces & changes in motion related?
Physics 201: Lecture 7, Pg 12
What are forces and how to they relate to motion?

Aristotle: Continuation of motion depends on
continued action of a force.

Newton: An object in motion will remain in motion
(i.e. with constant velocity) unless acted upon a
force.
Was Aristotle wrong?
Physics 201: Lecture 7, Pg 13
Newton’s First Law and IRFs
An object subject to no external forces moves with constant
velocity if viewed from an inertial reference frame (IRF).
If no net external force acting on an object, there is
no acceleration.

The above statement can be used to define inertial
reference frames.
Physics 201: Lecture 7, Pg 14
IRFs
 An IRF is a reference frame that is not
accelerating (or rotating) with respect to the “fixed
stars”.
 In many cases the surface of the Earth is
considered to approximate an IRF
Physics 201: Lecture 7, Pg 15
Forces are vectors

Forces have magnitudes and direction

SI unit of force is the kg meter /second2 or Newton
F
Physics 201: Lecture 7, Pg 16
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 201: Lecture 7, Pg 17
Contact (e.g., “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).
Here: A contact force from the table opposes gravity,
Normal forces are always perpendicular to a surface.
FB,T
Physics 201: Lecture 7, Pg 18
Force is a vector quantity
No net force  No acceleration
 

 F  Fnet  0  a  0
If zero velocity then “static equilibrium”
 If non-zero velocity then “dynamic equilibrium”


If more that one external force acts, vector addition
 
  
 F  Fnet  F1  F2  F3  
Physics 201: Lecture 7, Pg 19
Newton’s Second Law
The acceleration of an object is directly proportional to the
net external force acting upon it.
The constant of proportionality is the mass.

This is a vector expression

F  Fx î  Fy ĵ  Fz k̂
FNETx  ma x
FNETy  ma y
FNETz  ma z
Physics 201: Lecture 7, Pg 20
No net force  No acceleration (expt. observation)
 

 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
Normal force is conditional
 Fy  mg  N  0
FB,G
N  mg
Physics 201: Lecture 7, Pg 21
Newton’s 3rd Law

For every action there is an equal and opposite
reaction.

The 3rd Law requires two objects. If a force from
one object acts on a second object then a second
force (equal in magnitude and opposite in
direction) acts on the second object.

Newton’s 1st and 2nd Laws pertain to just a single
object or system.
Physics 201: Lecture 7, Pg 22
Example
Consider the forces on an object undergoing projectile motion
These are force pairs (3rd Law)
FB,E = - mB g
FB,E = - mB g
FE,B = mB g
FE,B = mB g
EARTH
This is NOT a force pair
FB,T
FB,G
Physics 201: Lecture 7, Pg 23
Measuring Forces
 Hanging
scales
T =50 N
m=0
T =50 N
 Floor
scales
5.0 kg
Physics 201: Lecture 7, Pg 24
Moving forces around

Massless strings: Translate forces and reverse their
direction but do not change their magnitude
string
T1

-T1
Massless, frictionless pulleys: Reorient force direction but
do not change their magnitude
T2
T1
-T1
| T1 | = | -T1 | = | T2 | = | T2 |
-T2
Physics 201: Lecture 7, Pg 25
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 201: Lecture 7, Pg 26
Newton’s 2nd Law, Forces are conditional
A woman is straining to lift a large crate, without success. It
is too heavy. We denote the forces on the crate as follows:
P is the upward force being exerted on the crate by the person
C is the contact or normal force on the crate by the floor, and
W is the weight (force of the earth on the crate).
Which of following relationships between these forces is
true, while the person is trying unsuccessfully to lift the
crate? (Note: force up is positive & down is negative)
A.
B.
C.
D.
P+C<W
P+C>W
P=C
P+C=W
Physics 201: Lecture 7, Pg 27
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 Bucky’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 201: Lecture 7, Pg 28
Free Body Diagram
Step one: Define the system
T2
T1
q2
q1
Eat at Bucky’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 201: Lecture 7, Pg 29
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 201: Lecture 7, Pg 30
Scale Problem

You are given a 5.0 kg mass and you hang it
directly on a fish scale and it reads 50 N (g is
10 m/s2).
50 N
5.0 kg


Now you use this mass in a second
experiment in which the 5.0 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?
?
5.0 kg
Physics 201: Lecture 7, Pg 31
What will the scale read?
A 25 N
B 50 N
C 75 N
D 100 N
E something else
Physics 201: Lecture 7, Pg 32
Fini

Next Tuesday….all of Chapter 5
Physics 201: Lecture 7, Pg 33