The Mystery Bottle II

This Time Is Personal

Objectives

Physics 2 The student will investigate and understand how to analyze and interpret data. Key concepts include

a description of a physical problem is translated into a mathematical statement in order to find a solution;

relationships between physical quantities are determined using the shape of a curve passing through experimentally obtained data;

the slope of a linear relationship is calculated and includes appropriate units

interpolated, extrapolated, and analyzed trends are used to make predictions;

The Basic Idea

Add a certain volume of water to a container measure how much the height increases.

I’ve collected data for 3 bottles

Task 1

Graph Total Volume vs. Height for each of the bottles

Figure out what the slope of a Total Volume vs. Height graph means

What would be the graph for a beaker?

What would be the graph for a flask?

What would be the graph for a funnel?

What is the shape of this container?

How about this one?

And this guy?

Is this container possible?

What Does The Slope Mean

The slope is the reciprocal of the area of the bottle€

Slope =Δy

Δx

Slope =h

V=

cm

cm3=

1

cm2=

1

A

What would the slope of a graph that had Force and acceleration on the axis (remember Newton’s Second Law)?

What is the cross sectional area of this container?

€

A =1

Slope=

Δx

Δy=

ΔV

Δh=

100

5= 20cm3

What is the cross sectional area of this container?

What is the cross sectional area of this container?

Assessment

See if you can estimate the shape of the mystery bottle

Task 2: See if you can sketch the shape of the bottle

Task 2: Graph the shape of the mystery bottle

Given the data and the formula for area come up with a way to calculate the radius for each data point.

Come up with a graph of the Bottle Radius vs. Height

Given To Us

Some Collected Data We can assume that the bottle has a circular

circumference. Areacircle = r2

Possible Solutions

€

A =1

Slope=

Δx

Δy=

ΔV

Δh

A = πr2

πr2 =ΔV

Δh

r =ΔV

π ⋅Δh

Task 2: See if you can sketch the shape of the bottle

Which volume to use?

Volume Added Total Added

Which height to use?

Volume Added Total Added

Which height to use?

Volume Added Total Added

Just how do you get h?

height fluid previous -height fluidcurrent =height

height

Activity Development

Objectives

Assessment

DevelopInstructionalsequence

Development SequenceGet your

operationalparameters

Decide on the type of Lesson

Inquiry

Inductive

Jigsaw

Direct Instruction

Group Work

Choose your weapons

Spreadsheets

Simulations

Modeling Software

Digital Imaging

Electronic Data Collection

Presentation Software

Information Systems

Communication Tools

Then You…

Tinker Tinker Tinker