Rossana Viola e Maria Bortoluzzi Scientific secondary school Course: technological First class Place: classroom and physics laboratory. MOTION UNDER A.

Rossana Viola e Maria Bortoluzzi

Scientific secondary school

Course: technological

First class

Place: classroom and physics laboratory.

Title: MOTION UNDER A CONSTANT FORCEMOTION UNDER A CONSTANT FORCE


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.


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.


Module planningModule planningTeacher activities

Students activities

interaction Cognitive process

Language demands

Language/

learning support

Introduces topic listen Whole class Describing process

Listening vocabulary

slides

Presents experiment, gives instructions for data processing

Listen, copy chart Whole class

individual

Describing process, apparatus instruction

“ + talk connectors, relevant functions of language

Slides black(white-) board, apparatus

Monitors, talks to groups and 1:1

Talk in group

Fill in diagrams and plots

Groupwork pairwork

individual

Understanding instructions

“+ writing

layout

Key terms, individual charts, diagrams

Elicits reports and conclusions

report, draw conclusions

Whole class Give and support opinions

“ Blackboard key terms diagrams

Presents topics Listen Whole class Describing process

Listen, vocabulary, relevant functions of language

“ + slides

Outlines written report

respond Whole class groupwork

Describing objectives, apparatus,hypotheses, process,result

“ “+ report writing frame

Gives homework

Whole class


MOTION UNDER A CONSTANT FORCE

MOTION WITH A CONSTANT ACCELERATION


VOCABULARY:

• VelocityVelocity: : vettore velocità.

• SpeedSpeed: : modulo del vettore velocità.

• GradeGrade: : pendenza di una retta in un sistema di riferimento (piano cartesiano)

• Air-bearing rail: Air-bearing rail: rotaia a cuscinetto d’aria.


m otion o f an esca la to r m otion o f a con veyor b e lt m otion o f w a te r in a can a l

n ear l y un if o r m mo t io n


Butthey are difficult motions to describe because of their

irregular speed variations !

a car is aboutto leave

or brakes

a sphere slidesaccross an

inclined plane

a m an lengthensone's stride to take

a bus

the m otionof a player

during afootball m atch

mo t io n wit h speed var iat io ns


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!


• 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.


Activity: • AIM: represent in a speed - time plot the values of average speeds of the sphere in considered intervals t calculated through the relation :

sv

t

Δt (s) t (s) Δs (cm) v (cm/s)

0.00 0 0 0

0.05 0.05 1.5 30

0.05 0.1 3.5

0.05 0.15

0.05

0.05

0.05

0.05

0.05

0.05


t

(s)

Δs (cm)

v (cm/s)

0.00 0 0

0.05 1.5 30

0.1 3.5 70

0.15 6.0 120

0.2 8.5 170

0.25 11.0 220

0.3 13.5 270

0.35 16.2 324

0.4 18.3 366

0.45 21.0 420

Speed and time are directly proportional quantities !!

velocity-time plot

0

500

0 0,1 0,2 0,3 0,4 0,5

t (s)v (

cm/s)


We know that

Thus we obtain the speed-time relation:

with a = constant.

If and

that relation becomes

or, in general,

v=aּt with a = constant.

2 1

2 1m

v va

t t

2 1 2 1( )v v a t t

1 0t 1 0v

2 2v at


v = aּt is the equation of the line in previous graph.

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

02468

10121416

0 2 4 6

t (s)

v (m

/s)

a = 2 m/s^2

0

5

10

15

0 2 4 6

t (s)

v (m/

s)


acceleration-time plot

The graph is a time axis parallel segment.

At time variation, acceleration takes the same value.

0

1

2

3

4

0 2 4 6

t (s)

a (m

/s^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

but v=at, thus

therefore

time law

1

2s vt

1( )

2s at t

21

2s at

0

0,5

1

1,5

0 0,2 0,4 0,6 0,8 1 1,2

t (s)

v (m

/s)

A


Activity

Represent the space-time plot t (s) s (cm)

0.00 0

0.05 1.5

0.1 5

0.15

0.2

0.25

0.3

0.35

0.4

0.45


Activity

Represent the space-time plot

It’s a parabolic curve.

There’s a quadratic relation between space and time

21

2s at

t (s) s (cm)

0.00 0

0.05 1.5

0.1 4

0.15 11

0.2 19.5

0.25 30.5

0.3 44

0.35 60.2

0.4 78.5

0.45 99.5

space-time plot

050

100150

0 0,1 0,2 0,3 0,4 0,5

t (s)

s (c

m/s

^2)


exerciseComplete following text with some 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


exerciseComplete following text with some 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

Newton

force

straight line

time intervals


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.


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.

2 2 22 2

1 2 2*1008

2 5

(8*5) 40

ss at a m s m s

t

v at m s m s


Laboratory experimentAim: 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

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:

Theory:

Equipment:

Evaluation statements:

Knowledge statements:

Data processing:

Gathered data:

Event:


What to do:1) make a REPORT.

2) fill in a GOWIN CONCEPT MAP like this:Theoretical-conceptual side Methodological side

Focal request:

How to study a straight line

motion with a constant

acceleration?

Concepts:

s, t, v, a

Theory:

v=at

s=1/2 at^2

Error theory

Equipment:

Air-bearing rail

Evaluation statements:

At the start it’s better push the truck with an electromagnetic

device than manually.

Knowledge statements:

a(m)=……

Data processing:

Calculation of v, a, a(m).

s-t v-t a-t plots

Gathered data:

s,tEvent:

The truck slides on the rail.

Rossana Viola e Maria Bortoluzzi Scientific secondary school Course: technological First class Place: classroom and physics laboratory. MOTION UNDER A.

Documents

class slide

constant acceleration

speed time

constant force slide

constant speed

time t ss

speedtime relation

time law