Planning Ahead - San Diego Miramar Collegefaculty.sdmiramar.edu/faculty/sdccd/sokumoto/...Common...
Transcript of Planning Ahead - San Diego Miramar Collegefaculty.sdmiramar.edu/faculty/sdccd/sokumoto/...Common...
Planning Ahead• Pay attention to “Free-Fall.”
• Homework, see the problems on the course
webpage. (Whether you get the right answer or
not, you still get the same points, provided that
you’ve demonstrated that you made a good
faith attempt at solving the problem. Also
attach any additional problems that you have
been working on).
Lecture Outline
• I. Motion Terminology
• II. Physics of the Sprinter
• III. Visualizing Motion
• Level III: Motion
Goals
• 1.) Interpret Motion Graphs.
• 2.) Understand the difference
between velocity and acceleration.
White Card – Check List
• 1. Identify the type of motion.
• 2. Sketch the motion (coordinate system).
• 3. Reasoning:
• 4. Find the Forces acting on the object.
• 5. Determine the acceleration of the object.
• 6. Write the Kinematics equations and solve.
• 7. Assess the answer.
Problem Solving Overview• Type of motion – determines the equation.
• Reasoning – determines the theory used to
explain the phenomenon.
• Sketch – determines the values that will go into
the equation.
• Coordinate system – determines if the values
are positive or negative. It also determines how
the graphs look.
Be consistent!
Review Physics Solution
Recall: Rules on Dimensions
𝑥 = 𝑦 + 𝑧
1. If x has dimensions of length, then y and z
must also have dimensions of length.
2. Most arguments in a function are unitless.
For example sin(x), log(x), e(x), all of the x
have no units.
Dimensions Drill/Due Today
𝐹 = 𝑚[? ]
If F has units of (kg × m/s2) and m has units
of kg, then what are the dimensions of [?]
A. m2
B. m/s2
C. m2/s2
D. None
Dimensions Drill/Due Today
𝐸 = 9800𝑘𝑔𝑚2
𝑠2𝑚 = 80𝑘𝑔
𝑔 = 10𝑚
𝑠2
Find the distance
Recall: Theory of Motion
– Newton’s First Law: (Inertia) Objects at rest
remain at rest unless acted upon by a net external
force; objects in motion remain in motion and
move in a straight line unless acted upon by a net
external force.
– Newton’s Second Law: F= ma
– Newton’s Third Law: For ever action there is an
Equal and Opposite action.
Known Key Equations
run
riseslope
heightbaseArea
Graphs Goals
)s(t
)s/m(vx
Slope = acceleration
displacement = area
Velocity vs. time graph
Key Concept Motion Graphs
)s(t )s(t )s(t
)m(x )s/m(vx )s/m(a 2
x
Displacement Velocity Acceleration
Slope = acceleration
displacement = area
Motion
acceleration
constantzero
stationary
Constant
velocity
Slowing
down
Momentarily
stopped
Speeding
up
Key Motion Equations
𝑥𝑓 = 𝑣𝑖𝑥𝑡 + 𝑥𝑖
𝑣𝑓𝑥 = 𝑣𝑖𝑥
If a = 0, thenIf a = constant
then
𝑥𝑓 =1
2𝑎𝑥𝑡
2 + 𝑣𝑖𝑥𝑡 + 𝑥𝑖
𝑣𝑓𝑥 = 𝑎𝑥𝑡 + 𝑣𝑖𝑥
From Newton’s 2nd Law F = ma:
The numbers put into the equation
come from the sketch.
x
t
t
v
Kinematics Equation
𝑥𝑓 = 𝑣𝑖𝑡 + 𝑥𝑖
𝑣𝑓 = 𝑣𝑖
If a = 0
then
If a = constant
then
𝑥𝑓 =1
2𝑎𝑥𝑡
2 + 𝑣𝑖𝑡 + 𝑥𝑖
𝑣𝑓 = 𝑎𝑥𝑡 + 𝑣𝑖
From Newton’s 2nd Law F = ma:
The numbers put into the equation
come from the sketch.
Displacement
xi xfO
0t t
𝑥𝑓 =1
2𝑎𝑥𝑡
2 + 𝑣𝑖𝑥𝑡 + 𝑥𝑖
𝑎𝑥 𝑎𝑥
𝑣𝑖𝑥 𝑣𝑓𝑥
Recall: Particle Model of Motion
MCAT Graphs
Which position-versus-time graph represents the motion shown in the motion diagram?
I. Motion Terminology• 1. Displacement
• 2. Velocity
• 3. Acceleration
Motion Terminology• Position: location of the object at a given time.
• Displacement:
• Distance: total distance traveled.
Origin fxix
if xxx
Position and Velocity• 1. The value of the slope from
the Position vs. time data is the
velocity (at that time).
• 2. The value of the area under the
slope of the velocity vs time
graph is the displacement of the
object in that time interval.
Velocity
• Velocity measures the displacement during
a time interval.
www.winstonmotorsports.com
Unit:
s
m
hr
mi
Dimensions
time
distance
or
Velocity
• Velocity is the rate of change of position.
velocity
Change in position
Change in time
Arrow indicates vector
റ𝑣 = ∆ റ𝑥
∆𝑡
റ𝑣
Which velocity-versus-time graph goes with the position-versus-time graph on the left?
Drill: Draw the Visualization of
this motion.
Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m.
Drill: Draw the Visualization of this motion.
Motion Drill/Due Today
Draw the velocity vs time graph.
po
siti
on
(m
)
Region I
Region II
Drill: Draw the Visualization of this motion.
Velocity and Acceleration
• 1. The value of the slope from
the Velocity vs. time data is the
acceleration.
• 2. The value of the area under
the slope of the acceleration vs
time graph is the velocity at that
time.
Acceleration
• Acceleration measures how much velocity
changes during a time interval.
www.winstonmotorsports.com
Acceleration
• Acceleration is the rate of change of velocity.
t
va
acceleration
Change in velocity
Change in time
a
Arrow indicates vector
Do You Know the Facts
• Which of the following is fatal to you?
• 10,000 mph
• 9.8 m/s2
• 100 mph
• 100 m/s2
• 100,000,000 m/s
Common Mistakes
• 9.8 m/s2 is a faster acceleration than 4
m/s2.
• Acceleration is not a speed nor velocity, so
words like fast or slow cannot be used.
• 9.8 m/s2 is a larger acceleration than 4
m/s2.
www.winstonmotorsports.com
Which velocity-versus-time graph or graphs goes with this acceleration-versus-time graph? The particle is initially moving to the right and eventually to the left.
Motion• Dynamics – branch of Mechanics that
deals with the motion of objects.
– Kinematics – study of motion without
regard to the forces producing it.
– Kinetics – the study of the forces that
produce or change motion. Motion is
caused by an unbalanced force acting on
a body.
Motion Graphs
)s(t )s(t )s(t
)m(x )s/m(vx )s/m(a 2
x
Displacement Velocity Acceleration
Slope = acceleration
displacement = area
Acceleration Drill/Due Today
• A car starts from the origin and
accelerates 6.0 m/s2 in the positive x-
direction. Draw the pictorial
representation of this problem.
Acceleration Sketch
xi=0 xf =? Origin
ft
2f,xs
m0.6a
2i,xs
m0.6a
0v i,x ?v f,x
Acceleration Drill/Due Today
• A car starts from the origin and
accelerates 6.0 m/s2 in the positive x-
direction. Explain this motion from
the Fundamental Laws of Motion.
Acceleration Drill/Due Today
• A car starts from the origin and
accelerates 6.0 m/s2 in the positive x-
direction. Draw the velocity vs time
and position vs time graphs for this
motion.
Acceleration Drill/Due Today
• A car starts from the origin and
accelerates 6.0 m/s2 in the positive x-
direction. Derive the velocity and
position equations for this motion.
Acceleration Drill/Due Today
• A car starts from the origin and
accelerates 6.0 m/s2 in the positive x-
direction.
• Predict the position of the car 3 s
later?
• What is the car’s velocity at 3 s?
Life Science Example• The speed of blood during one heart beat is
shown below. Approximate how far the blood
moves in one heart beat?
Life Science Example• Problem 18, page 62: The speed of blood during one heart beat is shown below. Approximate how far the blood moves in one
heart beat?
Reasoning: The
distance the blood
moves in one heart beat
is the area under the
curve between 0.2 and
0.4 s.
s
m75.0)s20.0(
2
1x m075.0
Assessment Drill/Due Today• Determine the magnitude of the acceleration
for both phases, speeding up and slowing
down.
Reasoning is?
Assessment Drill/Due Today• How many beats of heart will it take the blood
to get from your heart to brain?
Acceleration Drill/Due Today• A car starts from rest at the origin and
accelerates at 2 m/s2 for 8 s.
• Draw the pictorial representation for the
motion
• Explain the motion from the fundamental laws
of motion.
• Draw the x vs t and v vs t graphs.
• Write the two equations for this motion.
Motion Graphs
)s(t )s(t )s(t
)m(x )s/m(vx )s/m(a 2
x
Displacement Velocity Acceleration
Slope = acceleration
displacement = area
Life Science Drill/Due Today• When striking, the pike, a predatory fish,
can accelerate from rest to a speed of 4.0
m/s in 0.11 s.
• Draw a detailed sketch of this problem.
8:30
Motion Drill/Due Today• When striking, the pike, a predatory fish, can accelerate from rest to a speed of 4.0 m/s in 0.11 s.
• Draw a detailed sketch of this problem.
0x i xf = ?
t = 0.11s
𝑣𝑖 = 0 𝑣𝑓 = 4.0𝑚
𝑠𝑎𝑥 =?
Motion Drill/Due Today• When striking, the pike, a predatory fish,
can accelerate from rest to a speed of 4.0
m/s in 0.11 s.
• Draw a the velocity vs. time graph.
Motion Drill/Due Today• When striking, the pike, a predatory fish, can accelerate from rest to a speed of 4.0 m/s in 0.11 s.
• Draw a the velocity vs. time graph.
v
t0.11 s
4 𝑚
𝑠
Motion Drill/Due Today• When striking, the pike, a predatory fish,
can accelerate from rest to a speed of 4.0
m/s in 0.11 s.
• Determine the slope of the graph.
Motion Drill/Due Today• When striking, the pike, a predatory fish,
can accelerate from rest to a speed of 4.0
m/s in 0.11 s.
• Determine the area of the graph from 0 to
0.11s.
Motion Drill/Due Today• When striking, the pike, a predatory fish,
can accelerate from rest to a speed of 4.0
m/s in 0.11 s.
• Check the units.
Group Drill• A car accelerates from rest to a speed of 30.0 m/s in
5 s. Draw the velocity vs. time graph.
• What part of the graph contains information about the
acceleration?
• Determine the acceleration.
• What part of the graph contains information about
displacement?
• Determine the displacement.
• Use the acceleration you determined above in the
following equation: 2at2
1x