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PHYS 218: General Physics
Summer 2013
Lecture 3:
Analyzing motion and
Newton’s Laws
Read: Ch 2
Quick Review of Motion
Position is the location of some object
relative to a fixed point.
Velocity is the slope of position vs. time. It
tells you how position is changing.
Acceleration is the slope of velocity vs.
time. It tells you how velocity is
changing.
Quick Review of Motion
Two Types of Motion
“constant acceleration”
=> Net force
x position (m)
x position (m)
“constant velocity”
=> No net force
Time (sec)
Time (sec)
Quiz 1
position (m)
Consider the following position vs. time graph:
Time (sec)
Which of these scenarios might this graph represent?
A.
B.
C.
D.
E.
A car starting from rest when a traffic light turns green.
A car coming slowly to a stop when a traffic light turns red.
A car moving at constant velocity.
A car moving at constant acceleration.
It cannot be a car.
Quiz 2
velocity (m/s)
Consider the following velocity vs. time graph:
Time (sec)
Which of these scenarios might this graph represent?
A.
B.
C.
D.
E.
A car starting from rest when a traffic light turns green.
A car coming slowly to a stop when a traffic light turns red.
A car moving at constant velocity.
A car moving at constant acceleration.
It cannot be a car.
50 miles
Imagine a flight from
the Great Smokey
Mountains to West
Lafayette.
50 miles
50 miles
The change in
position is called
displacement.
In this case 400
miles.
50 miles
Question 3
Which type of motion, discussed last lecture, does a flight from
the Great Smokey Mountains to Lafayette most resemble?
A. Constant acceleration
B. Constant velocity
C. At rest
Question 3
Which type of motion, discussed last lecture, does a flight from
the Great Smokey Mountains to Lafayette most resemble?
A. Constant acceleration
B. Constant velocity
C. At rest
Takes off and accelerate
briefly, fly for a few hours at
constant velocity, and then
decelerating briefly and
land.
Most of the time is spent
flying at constant velocity.
Question 3
Which type of motion, discussed last lecture, does a flight from
the Great Smokey Mountains to Lafayette most resemble?
B. Constant velocity
Takes off and accelerate
briefly, fly for a few hours at
constant velocity, and then
decelerating briefly and
land.
velocity (mph)
140
Time (hr)
3
Most of the time is spent
flying at constant velocity.
Question 4
Which graph could describe the position of the helicopter along
the direction of travel as a function of time?
B.
A.
400
position (miles)
position (miles)
400
Time (hr)
3
Time (hr)
3
Question 4
Which graph could describe the position of the helicopter along
the direction of travel as a function of time?
B.
A.
400
position (miles)
position (miles)
400
Time (hr)
3
Time (hr)
3
If you didn’t have a speedometer how could you estimate the
speed of the helicopter from its position?
position (miles)
400
Time (hr)
3.0
If you didn’t have a speedometer how could you estimate the
speed of the helicopter from its position?
displacement,
Dx = 400 miles
position (miles)
400
Time (hr)
3.0
total time, Dt = 3.0 hr
If you didn’t have a speedometer how could you estimate the
speed of the helicopter from its position?
Average speed,
|Vavg |= |Dx|/ Dt
= 400 miles/3 hr
= 130 mph
displacement,
Dx = 400 miles
position (miles)
400
Average velocity,
Time (hr)
3.0
total time, Dt = 3.0 hr
Vavg = Dx/ Dt
= 400 miles/3 hr
= +130 mph
direction
If you didn’t have a speedometer how could you estimate the
speed of the helicopter from its position?
400
position (miles)
displacement,
Dx = 400 miles
Average speed,
|Vavg |= |Dx|/ Dt
= 400 miles/3 hr
= 130 mph
Time (hr)
3.0
total time, Dt = 3.0 hr
Question 5
Is the speed you would read on the speedometer somewhere
in the middle of the flight
A. Bigger
B. Smaller
Than the average speed?
400
position (miles)
displacement,
Dx = 400 miles
Average speed,
|Vavg |= |Dx|/ Dt
= 400 miles/3 hr
= 130 mph
Time (hr)
3.0
total time, Dt = 3.0 hr
Question 5
Is the speed you would read on the speedometer somewhere
in the middle of the flight
A. Bigger
B. Smaller
Than the average speed?
400
position (miles)
displacement,
Dx = 400 miles
Average speed,
|Vavg |= |Dx|/ Dt
= 400 miles/3 hr
= 130 mph
Time (hr)
3.0
total time, Dt = 3.0 hr
Question 5
The speed read off the speedometer is the instantaneous
speed, corresponding to one point in time. In the middle of the
flight, this slope is bigger than the average speed.
400
position (miles)
displacement,
Dx = 400 miles
Average speed,
|Vavg |= |Dx|/ Dt
= 400 miles/3 hr
= 130 mph
Time (hr)
3.0
total time, Dt = 3.0 hr
Question
Here’s the position and velocity of the helicopter:
400
velocity (mph)
position (miles)
140
Time (hr)
Time (hr)
What would a graph of the acceleration look like?
3
Question
Here’s the position and velocity of the helicopter:
400
velocity (mph)
position (miles)
140
Time (hr)
Time (hr)
3
What is the average acceleration? Where is the instantaneous
acceleration large?
Newton’s First Law
If the total force acting on a
body is zero, it will maintain its
velocity* forever.
*The object at rest is just a special case of this
with velocity equal to zero.
Quiz
Consider a helicopter sitting at rest on the
ground. The total force on the helicopter is:
A. 0
B. downward
C. upward
Quiz
Consider a helicopter hovering. The total force
on the helicopter is:
A. 0
B. downward
C. upward
Quiz
Consider a helicopter gaining altitude at a
constant rate. The total force on the helicopter
is:
v
A. 0
B. downward
C. upward
Consider a helicopter cruising
along at a constant 140 m.p.h.
Using Newton’s First Law to
help, identify all of the forces
exerted on the helicopter.
Newton’s Second Law
The acceleration of an object is
given by:

 FTotal
a
m
with


FTotal   F
Newton’s Second Law
Let’s focus on

 FTotal
a
m
Cart Demo
For Next Time
Read Chapter 3.1-3.3
(CHIP, iClickers, Books, etc.)

 FTotal
a
m
Acceleration is proportional to force divided by mass:
More force -> Greater acceleration

 FTotal
a
m
Acceleration is proportional to force divided by mass:
More mass -> Less acceleration
Newton’s Second Law
The acceleration on an object
is given by:

 FTotal
a
m
with


FTotal   F
Newton’s Second Law


FTotal   F
If multiple forces are present,
calculate the total force as a
vector sum.

 FTotal
a
m
Forces add as vectors


FTotal   F

 FTotal
a
m
Forces add as vectors


FTotal   F


FTotal   F
y
Fx  F cos
Fy  F sin 
Fx
F
tan  
Fy
Fy
Fx
F  Fx2  Fy2

x
Home at
11:45 a.m.
Exit I-65 into
Lafayette
11:30 a.m.
What sort ofComplex
quantities
Motion
will we use to describe
position and distance?
Got gas and
breakfast
around
Lexington at
8:00 a.m.
What information
would you need to give
in order for someone to
retrace your steps?
Pickup
Interstate 75
5:45 a.am
Left Smokey
Mountains,
3:45 a.am
50 miles
Home at
11:45 a.m.
Exit I-65 into
Lafayette
11:30 a.m.
Complex Motion
Got gas and
breakfast
around
Lexington at
8:00 a.m.
Pickup
Interstate 75
5:45 a.am
Left Smokey
Mountains,
3:45 a.am
50 miles