Transcript Linear Motion - RschoolToday

Linear Motion
Begins with a Frame of Reference!
Frame of Reference
•Distance, Directions and
Displacement are always
measured relative to a frame of
reference
SI Units
(International System of Units)
•
•
•
•
•
•
Length
Mass
Time
Electrical Current
Temperature
Amount of
Substance
-Meter
-Kilogram
-Second
-Ampere
-Kelvin
-Mole
Frame of Reference
• The Earth is rotation once every 24 hours
The
circumference
of
earths
orbit
At
The
the
earth
equator
a person
around
is the
traveling
milky
The
earth
is rotates
rotating
around
the
sunisat
• 940
Circumference
of earth is 24,000 miles at
million
Kilometers
approximately
way galaxy
900,000
mphkm/hr
107,306
km/hrat 1000
the equator
Distance vs. Displacement
Displacement
Distance
Distance vs. Displacement
• Distance - A scalar quantity
which refers to how much ground
an object has covered
• Displacement - A vector which
refers to the object’s overall change
in position
Scalars are quantities which are fully described by a
magnitude (or numerical value) alone.
Vectors are quantities which are fully described by both a
magnitude and a direction.
Activity
Measuring Displacement
Distance = 420 m
• What is the displacement and distance
traveled?
Displacement = 140 m right
Measuring Displacement
• Mr. Hamann is recruited for his ninja like
skills as a Formula 1 racecar driver. After
winning the Indy 500 he contemplates
what his Distance and Displacement were.
• Distance = 500 Miles
• Displacement = 0 miles
Speed
• Speed is the ratio of the distance an object
moves to the amount of time the object
moves.
Or….how fast an object moves
• Average Speed
- Over the entire trip
• Instantaneous Speed -At a moment in time
Speed
• Avg. Speed = Total Distance/Total Time
Avg. Speed = ∆d/∆t
∆ = change in
∆d = d2-d1
∆d = 4.0km- 0
Exp: A person jogs 4.0 km in 32 minutes what is his avg.
speed in m/s?
Avg. Speed = (4.0 km * 1000m/km) / (32 min * 60 s/min)
= 4000 m/1920 s
= 2.1 m/s
Distance / Time Graphs
• Constant speed vs. Varying speed
Time
Distance
Time
Distance
Distance
Distance
Distance / Time Graphs
Time
Avg. Speed = ∆d/∆t
Avg. Speed = Slope
Time
Instantaneous Velocity
v = 4 m/s
Distance
v = 20 m/s
v = -15 m/s
Time
• http://graphs.mathwarehouse.com/distanc
e-time-graph-activity.php
Rolling Marble of Doom!
1.
2.
3.
4.
5.
6.
7.
8.
9.
Form a ramp by placing 1 end of the ramp on a stack of 6 identical
books.
Release the marble at the top of the ramp and use a stopwatch to
measure the time it takes for the marble to reach the bottom
Record this time
Prediction: How many books tall would the stack have to be to double
the time required for the marble to reach the bottom of the ramp?
Record this prediction
Test your prediction. Remove one book at a time and repeat step 2
until there is only 1 book left.
Make a table and graph the resulting speed.
How much time does the marble need to get to the bottom of a
horizontal ramp?
If an infinite number of books were added to the stack would the
time required for the marble to reach the bottom continue to
decrease? Explain.
Velocity
• Why do cars have a speedometers and
not velocimeters?
• Velocity describes both speed and
direction
• Velocity is a vector!
Mr. Hamann’s Ninja
car is traveling
around the track at
120 km/hr
What is the velocity
at this point?
Is the velocity
constant?
Velocity
• Constant Velocity
• Constant speed and constant direction
• Combining Velocities
• Lesson in Vector Addition
• 5 m/s
• 10 m/s
Combining Velocities
• 5 m/s
• 10 m/s
• Boat was traveling at 10m/s with the current on a river moving at
5m/s
10 m/s
10 m/s
m/s
10 m/s – 5m/s == 515m/s
+
5 m/s
5 m/s
• Boat was traveling at 10m/s against the current on a river moving at
5m/s
• Relative to the river bank
Combining Velocities
• Ninja boat is traveling across a river at 10 m/s while the current
pushes it sideways at 3.0 m/s
10.0 m/s
3.0 m/s
3.0 m/s
a2 + b2 = c2
c2 = √ a2 + b2
= √ (10 m/s)2 + (3m/s)2
= √ (100m2/s2 + 9m2/s2)
= √ 109 m2/s2
= 10.4 m/s
Vector Direction
10.0 m/s
θ
10.4 m/s
3.0 m/s
Vector Direction
10.0 m/s
θ
10.4 m/s
• SOH CAH TOA
• Sin θ = 3.0 / 10.4
• Sin θ = 0.29
• Θ = 17°
3.0 m/s
Labs
•
•
•
•
•
•
Physics 500
Frisbee velocity
Velocity of sinking marble
Probeware cart on ramp
Cannon Balls launch velocity
Domino Effect
Acceleration
• Acceleration – the rate at which velocity
changes
• So it is technically a rate of a rate
• A change is speed, change in direction, or changes
in both
• Acceleration is a vector
Accelerationavg = Change of velocity/ Change in Time
= ∆v / ∆ t
= (vf – vi) / (tf - ti)
Acceleration
• Acceleration – the rate at which velocity
changes
• So it is technically a rate of a rate
• A change is speed, change in direction, or changes
in both
• Acceleration is a vector
• Acceleration = Object speeds up?
Acceleration
• We feel acceleration all the time
– Cars
• Gas pedal
• Brakes
• Steering wheel
– Planes
– Gravity
Vomit Comet
Question?
• Suppose a velociraptor moving in a straight line
steadily increases its speed each second, first
from 35 to 40 km/h, then from 40 to 50 km/h,
then from 50 to 70 km/h. What is this dinosaur’s
acceleration in each of these time intervals?
Answer
Acceleration = Change of velocity/Time
= ∆v / ∆ t
= (vf – vi) / (tf – ti)
Acceleration= (40km/h-35km/h) / 1 s
= 5 km/h /1s
= 5 km/h *s
= 1.39 m/s2
Acceleration= (50km/h-40km/h) / 1 s
= 10 km/h /1s
= 10 km/h *s
= 2.78 m/s2
Acceleration= (70km/h-50km/h) / 1 s
= 20 km/h /1s
= 20 km/h *s
= 5.55 m/s2
Measuring Acceleration Lab
•
•
Personal Acceleration and Top Speed
Objective: Determine your top speed and rate of acceleration from a motion graph
Equipment: Pasco DataStudio© motion detector or other timing device
Methods and Analysis
1. Line yourself up with the motion detector near the back of the room. Your partner
will hit the Start button and cue you to start running to top speed as fast as you can.
Be sure to run the designated line so that you remain in line with the motion detector.
2. Print your graph from the computer. This will be a distance-time graph. Indicate
on your graph where you are accelerating and where your velocity is constant.
3. Determine where your velocity is constant on the graph, draw a line to best fit this
region, then find the slope. Record this as your top speed in both m/s and km/hr.
4. Based on the time and distance to reach your top speed, calculate your rate of
acceleration in m/s2. Compare this value to the acceleration of gravity (9.8 m/s2).
5. Compare your top speed with the fastest ever recorded human speed of Donovan
Bailey, 11.91 m/s.
6. If Donovan Bailey reaches top speed in 3.00 seconds, what is his rate of
acceleration?
7. On your graph, sketch a runner with a rate of acceleration higher than yours and
label as a higher.
8. Accurately sketch a velocity vs time graph of your motion out to 10 seconds.
9. Summary.
Free -Fall
• Time(s)
•
•
•
•
•
•
•
•
•
0
1
2
3
4
5
…
…
t
Instantaneous velocity
0 m/s
10 m/s
20 m/s
30 m/s
40 m/s
50 m/s
….
….
10*t m/s
When Dealing with free fall 10m/s2 is the acceleration
do to gravity
Free -Fall
v= gt (How fast)
•
•
Where g= acceleration due to gravity on earth
» g= 9.8m/s2
If Acceleration due to gravity is constant
on earth why are we hesitant to catch a
baseball dropped off the empire state
building?
Speed vs time graph
v= 20m/s 1s
5s
speed
v= 0 m/s
3s
v= 10m/s
v= 10m/s
4s
2s
Slope = acceleration
v= 20m/s
v= 30m/s
0s
6s
v= 30m/s
Time
v= 40m/s
7s
Lab
• - Free fall exploration-find acceleration
(physical science easyplanner p.234
• TAP 206- 3: Measuring the acceleration
of free fall
Acceleration
v= at
(How fast)
Rocket Sled
• How
Whatfar
is the
does
acceleration
this Rocketofsled
a rocket
travelsled
in
2.1
thatseconds
goes from
when
0 tostarting
700mphatinrest?
2.1
seconds?
2
D =v½= at
at
D =m/s
½ (149)
313
= 4.4
a(2.1)
D = 2.2(149)
2
a
=
149
m/s
D = 328 m
Motion at constant Acceleration
• Why does v=at?
• Avg. Velocity = ∆d/∆t
• vavg = (xf – xi) / (tf - ti)
(direction)
– Since ti =0 then… vavg = (xf – xi) / t
• a = (vf - vi) / t
• v = vi + at
Free –Fall
How Far?
• Time(s)
•
•
•
•
•
•
•
•
•
0
1
2
3
4
5
…
…
t
Distance Fallen (m)
0
5
20
45
80
125
….
….
½ gt2
When Dealing with free fall 10m/s2 is the acceleration
do to gravity
Free -Fall
• How Far?
•d = ½
40
Distance (m)
Speed (m/s)
50
30
20
10
0
0
1
2
3
Time (s)
4
5
130
120
110
100
90
80
70
60
50
40
30
20
10
0
2
at
0
1
2
3
4
Time (s)
5
Distance (m)
40
30
20
10
0
0
1
2
3
Time (s)
Acceleration m/s2
Speed (m/s)
50
4
0
0
5
1
2
130
120
110
100
90
80
70
60
50
40
30
20
10
0
3
0
4
1
2
3
4
Time (s)
5
Time (s)
5
Reaction Time
• How fast is your reaction time?
Reaction Time
2
at
d = ½
t= √(2d/g)