Transcript MOTION UNDER A COSTANT FORCE
Scientific secondary school Course: technological First class Place:
classroom and physics laboratory.
Title
:
MOTION UNDER A CONSTANT FORCE
Rossana Viola e Maria Bortoluzzi
Skills:
to make sense of phenomena students observe and interpret information from a variety of sources. To use appropriate scientific terminology to communicate their conceptual understanding.
Present scientific information in written, oral, diagrammatic and graphic forms.
Carry out investigative work. Present analyses and evaluations of scientific data in appropriate form.
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Prerequisites: contents
lenght, time, mass, vectors and vector algebra, equations, s-t v-t a-t plots, particle, reference frames and coordinate systems, trajectory and time-law, velocity, acceleration, Straight line motion with a constant speed, covered space as area in a v-t graph. Rossana Viola e Maria Bortoluzzi
Teacher activities
Introduces topic
Students
Module planning
interaction Cognitive process Language activities
listen Presents experiment, gives instructions for data processing Listen, copy chart Monitors, talks to groups and 1:1 Talk in group Fill in diagrams and plots Elicits reports and conclusions report, draw conclusions Whole class Whole class individual Groupwork pairwork individual Whole class Describing process
demands
Listening vocabulary
Language/ learning support
slides Describing process, apparatus instruction “ + talk connectors, relevant functions of language Understanding instructions “+ writing layout Slides black(white-) board, apparatus Key terms, individual charts, diagrams Give and support opinions “ Blackboard key terms diagrams Presents topics Outlines written report Listen respond Whole class Whole class groupwork Describing process Describing objectives, apparatus,hypothe ses, process,result Listen, vocabulary, relevant functions of language “ “ + slides “+ report writing frame Gives homework Rossana Viola e Maria Bortoluzzi Whole class
MOTION UNDER A CONSTANT FORCE
MOTION WITH A CONSTANT ACCELERATION
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VOCABULARY:
• Velocity : vettore velocità.
• Speed : modulo del vettore velocità.
• Grade : pendenza di una retta in un sistema di riferimento (piano cartesiano) • Air-bearing rail: rotaia a cuscinetto d’aria.
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near l y unif or m mot ion
motion of an escalator motion of a conveyor belt motion of water in a canal Rossana Viola e Maria Bortoluzzi
a car is about to leave or brakes mot ion wit h speed var iat ions a sphere slides accross an inclined plane a man lengthens one's stride to take a bus the motion of a player during a football match But
they are difficult motions to describe because of their
irregular
speed variations !
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There is a
natural
motion in which speed variation in time is almost
regular
:
it’s the motion of drop of a body close to the earth’s surface
It may be described in a simple enough way!
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• In figure a sphere drop is represented.
• It has been photographed at equal intervals t= 0.05 s.
• In following intervals t the distance covered by the sphere
is not
constant but it
progressively increases .
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Δt (s) 0.00
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
Activity:
t (s) 0 0.05
0.1
0.15
Δs (cm) 0 1.5
3.5
v (cm/s) 0 30 Rossana Viola e Maria Bortoluzzi • AIM: represent in a speed - time plot the values of average speeds of the sphere in considered intervals t calculated through the relation :
v
s
t
t (s) 0.00
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Δs (cm) 0 1.5
3.5
6.0
8.5
11.0
13.5
16.2
18.3
21.0
v (cm/s) 0 30 70 120 170 220 270 324 366 420 500 0 0 0,1
velocity-time plot Speed and time are directly proportional quantities !!
Rossana Viola e Maria Bortoluzzi 0,2
t (s)
0,3 0,4 0,5
We know that
a m
v
2
t
2
v
1
t
1 Thus we obtain the
speed-time relation
:
v
2 1 ( 2
t
1 ) with a = constant.
If and 1
v
1 0 that relation becomes
v
2
at
2 or, in general,
v=aּt
with a = constant . Rossana Viola e Maria Bortoluzzi
v = aּt
is the equation of the line in previous graph.
15 10 5 0 0
a
is the grade of that line: the greater the acceleration is, the greater the grade will be.
For example:
a= 3 m/s^2 a = 2 m/s^2
2
t (s)
4 16 14 12 10 8 6 4 2 0 6 0 Rossana Viola e Maria Bortoluzzi 2
t (s)
4 6
acceleration-time plot
4 3 2 1 0 0 2
t (s)
4 The graph is a time axis parallel segment.
6 At time variation, acceleration takes the same value.
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1,5 0,5 1 0 0 0,2 0,4
A
0,6
t (s)
0,8 1 1,2 We know that in a speed-time plot the area A under the line represents the distance covered by the point in motion in considered time interval.
Let’s deduce the
space-time relation
: area A is
s
1 2 but v=at, thus
s
1 2 therefore 1
s
at
2 2
time law
vt
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Activity
Represent the space-time plot
Rossana Viola e Maria Bortoluzzi t (s) 0.00
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
s (cm) 0 1.5
5
Activity
Represent the space-time plot space-time plot
150 100 50 0 0 0,1 0,2
t (s)
0,3 0,4 0,5 It’s a parabolic curve.
There’s a quadratic
s
1
at
2 relation between space and time 2 Rossana Viola e Maria Bortoluzzi t (s) 0.00
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
s (cm) 0 1.5
4 11 19.5
30.5
44 60.2
78.5
99.5
exercise
Complete following text with some of the words at the bottom of this slide.
According to ………’s second law, F=ma, if the …… acting on a particle remains constant in magnitude and direction, the point will move in a ………… with a constant acceleration. This means that the point will acquire equal increments of velocity in equal …………… .
Galileo force Newton space time intervals parabolic curve Giuseppe straight line Rossana Viola e Maria Bortoluzzi
exercise
Complete following text with some of the words at the bottom of this slide.
particle remains constant in magnitude and direction, the point will move in a ………… with a constant acceleration. This means that the point will acquire equal increments of velocity in equal …………… .
Galileo force Newton space time intervals parabolic curve Giuseppe straight line Rossana Viola e Maria Bortoluzzi
exercise
A car moves and in
5 seconds
covers a distance
s=100m
.
Assuming that the car has a constant acceleration, calculate the value of
acceleration
and than the
speed
at the end of these 5 seconds.
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exercise
A car moves and in
5 seconds
covers a distance
s=100m
.
Assuming that the car has a constant acceleration, calculate the value of
acceleration
and than the
speed
at the end of these 5 seconds.
s v
1 2
at
2
at
2
t
2 (8*5)
m s s
2 *100 5 2 40
m s m s
2 8
m s
2 Rossana Viola e Maria Bortoluzzi
Laboratory experiment
Aim:
to study a straight line motion with a costant acceleration.
Equipment:
air-bearing rail.
Gathered data:
space (s) and time (t).
Data processing:
calculation of speed (v), acceleration (a) and mean value of acceleration.
Make a table with all these values.
Required plots:
1) space-time 2) speed-time Rossana Viola e Maria Bortoluzzi 3) acceleration-time.
What to do: 1) make a REPORT.
2) fill in a GOWIN CONCEPT MAP like this: Theoretical-conceptual side Methodological side Focal request: Concepts: Evaluation statements : Knowledge statements: Theory: Data processing: Equipment: Gathered data: Event:
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What to do: 1) make a REPORT .
2) fill in a GOWIN CONCEPT MAP Theoretical-conceptual side Focal request: like this: Methodological side Evaluation statements: Concepts:
How to study a s, t, v, a
Theory:
straight line motion with a constant acceleration?
At the start it’s better push the truck with an electromagnetic device than manually.
Knowledge statements:
v=at a(m)=…… s=1/2 at^2
Data processing:
Error theory Calculation of v, a, a(m).
s-t v-t a-t plots
Equipment:
Air-bearing rail
Gathered data:
s,t
Event:
The truck slides on the rail.
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